Quantum Field Theory

This paper updates earlier thoughts by the author on a putative propulsion system. The concept was based around static electromagnetic momentum, as expounded in the "Feynman Disk" and experimentally verified by Graham and Lahoz. That said, naïve static electromagnetic momentum schemes to achieve linear translation are defeated by "hidden momentum" mechanisms, so too are simple arrangements just cycling the fields; we shall survey the flaws in their arguments. It may however be possible to achieve linear translation by means of arrangements of torques with a novel mechanism to break the symmetry of forces (or torques) on the second half of the cycle as the field is switched off. At the time of earlier presentation no mechanism could be found to explain the momentum balance for the process but it was believed that momentum was being given to the zero-point of the field. We show that it is possible to dump angular momentum and thence linear momentum to the ground state by standard quantum analysis of the EM field. None of this violates the conservation of momenergy.

The Society for the Phenomenology of Religious Experience invites submissions of high quality abstracts of 150-300 words for its group meeting at the Central APA. The APA is currently planning the Central Division meeting at the Palmer House Hilton in Chicago, IL, on February 23-26, 2022, with virtual backup plans. Abstracts should be anonymized and sent by email to apacentral@sophere.org before August 15 with the subject line “Central APA Submission”. Notifications of acceptance will be emailed by Aug 25. Paper presentation time should be no more than 20-30 minutes.

Religious/Spiritual Experience and Metaphysics
Sessions Co-Chairs: Olga Louchakova-Schwartz (UC Davis) and Andrew Oberg (University of Kochi)

In these two panels, we seek to address relationships between religious or spiritual experience (RSE) and metaphysics.
RSE are associated with interruptions in ordinary language/common sense experience of the everyday (cf. Dahl; Barber; Heidegger). RSE interruptions create specific changes in perception, but it is not clear if and how RSE phenomena as described by i.e. mystics (such as internal perception of light, sound, altered perception of the body (re: spatiality, density, depth, other parameters), internal stillness, motion, presence or disconnect, etc.) impact one’s beliefs and/or attendant metaphysical (pre)suppositions. Do RSE change empirical realism of the natural attitude, religious attitude, or one’s metaphysics of the self? In the first panel, we invite concrete empirical and textual investigations of relationships between the perceptual and conceptual aspects of RSE across different traditions. The papers can include both first person and second person descriptive phenomenological researches or an intertwining of different phenomenological analyses.
The second panel seeks revisionist metaphysical proposals that include a reference to formal phenomenological analyses of consciousness in RSE. By contrast with the ordinary experience of objects, originary self-giving in RSE can be non-associative, open-ended, undetermined; in other words, excluding mental or "real" (empirically so) objects. Therefore, a descriptive metaphysics of such consciousness needs to be non-object related (cf. Ladyman, French). What is the nature of reality “displayed” by RSE? Besides covering the metaphysics of consciousness, the panel welcomes speculative extensions of such phenomenologically grounded metaphysics into realist contexts, such as e.g., metaphysics of the quantum world or Minkowski space-time.
Contact: olouchakova@gmail.com

For most of the last century, condensed matter physics has been dominated by band theory and Landau's symmetry breaking theory. In the last twenty years, however, there has been an emergence of a new paradigm associated with fractionalization, emergent gauge bosons and fermions, topological order, string-net condensation, and long range entanglements. These new physical concepts are so fundamental that they may even influence our understanding of the origin of light and electrons in the universe.

The charged quantum geometry of mass-ENERGY-Matter - developed from the foundational postulate that quantised angular momenta of Planck's constant is in fact reflective of an equilateral mass-energy geometry from which all 2d immaterial EM fields and 3D material particles are created.

Contextuality and entanglement are valuable resources for quantum computing and quantum information. Bell inequalities are used to certify entanglement; thus, it is important to understand why and how they are violated. Quantum mechanics and behavioral sciences teach us that random variables measuring the same content (the answer to the same Yes or No question) may vary, if measured jointly with other random variables. Alice and Bob raw data confirm Einsteinian non-signaling, but setting dependent experimental protocols are used to create samples of coupled pairs of distant outcomes and to estimate correlations. Marginal expectations, estimated using these final samples, depend on distant settings. Therefore, a system of random variables measured in Bell tests is inconsistently connected and it should be analyzed using a Contextuality-by-Default approach, what is done for the first time in this paper. The violation of Bell inequalities and inconsistent connectedness may be explained...

We give a quantum field theoretical derivation of the scalar Abraham-Lorentz-Dirac (ALD) equation and the self-force for a scalar charged particle interacting with a quantum scalar field in curved spacetime. We regularize the causal Green's function using a quasi-local expansion in the spirit of effective field theory and obtain a regular expression for the self-force. The scalar ALD equation obtained in this way for the classical motion of the particle checks with the equation obtained by Quinn earlier [1]. We further derive a scalar ALD-Langevin equation with a classical stochastic force accounting for the effect of quantum fluctuations in the field, which causes small fluctuations on the particle trajectory. This equation will be useful for the study of stochastic motion of charges under the influence of both quantum and classical noise sources, derived either self-consistently (as done here) or put in by hand (with warnings). We show the possibility of secular effects from such stochastic influences on the trajectory that may impact on the present calculations of gravitational waveform templates.

This paper has few different, but interrelated, goals. At first, we will propose a version of discretization of quantum field theory (Chapter 3). We will write down Lagrangians for sample bosonic fields (Section 3.1) and also attempt to generalize them to fermionic QFT (Section 3.2). At the same time, we will insist that the elements of our discrete space are embedded into a continuum. This will allow us to embed several different "lattices" into the same continuum and view them as separate "quantum" field configurations. Classical parameters will be used in order to specify "which lattice" each given element "belongs to". Furthermore, another set of "classical" parameters will be proposed in order to define so-called "probability amplitude" of each "field configuration", embodied by a corresponding lattice, "taking place" (Chapter 2). Apart from that, we will propose a set of "classical" signals that propagate throughout continuum, and define their dynamics in such a way that they produce the mathematical information consistent with the desired "quantum" effects within the lattices we are concerned about (Chapter 4). Finally, we will take advantage of the lack of "true" quantum mechanics, and "add" gravity in such a way that avoids the issue of its quantization altogether (Chapter 5). In the process of doing so, we will propose a gravity-based collapse model of a wave function. In particular, we will claim that the collapse of a wave function is merely a result of states that violate Einstein's equation being "thrown away". The mathematical structure of this model (in particular, the appeal to gambler's ruin) will be similar to GRW collapse models.

Neutrino oscillation is a quantum mechanical phenomenon in which neutrino flavor changes spontaneously to another flavor. In the simple two flavor (ν µ , ν e) case, the probability that ν µ changes to ν e is expressed by P νµ→νe = sin 2 2θ sin 2 m 2 2 − m 2 1 4E ν L where E ν is the neutrino energy, L is the distance between the neutrino source and detector, m 1 and m 2 are the neutrino masses of the mass eigenstates and θ is the mixing angle between flavor eigenstates and mass eigenstates.

We propose a microphysical theory of the triboelectric effect by which mechanical rubbing separates charges across the interface between two surfaces. Surface electrons are treated as an open system, weakly coupled to two baths, corresponding to the bulk materials. We show that work can be extracted from the motion-induced population inversion of fermions, thus extending and generalizing Zel'dovich's theory of bosonic superradiance. We argue that this is consistent with the basic phenomenology of triboelectrification and triboluminescence as off-equilibrium processes.

Sakharov's 1967 notion of "induced gravity" is currently enjoying a significant resurgence. The basic idea, originally presented in a very brief 3-page paper with a total of four formulas, is that gravity is not "fundamental" in the sense of particle physics. Instead it was argued that gravity (general relativity) emerges from quantum field theory in roughly the same sense that hydrodynamics or continuum elasticity theory emerges from molecular physics. In this article we will translate the key ideas into modern language, and explain the various versions of Sakharov's idea currently on the market.

Conformal invariance takes a new meaning in two dimensions and requires special attention. Indeed, there exists in two dimensions an infinite variety of coordinate transformations which although not everywhere well-defined are locally conformal: they are the holomorphic mappings from the complex plane (or a part it) onto itself. Amongst this infinite set of mappings one must distinguish the 6-parameter global conformal group made of one-to-one mappings of the complex plane into itself. A local field theory should be sensitive to local symmetries and it is the local invariance that enables exact solutions of two-dimensional conformal field theories.

A unified Mathematical framework which describes particles interactions both in classical field theory of gravity and quantum field theory is presented, by introducing a velocity gauge field. The velocity gauge field Lagrangian is developed and shown to be equivalent to the Dirac field and related to the Electromagnetic field. The velocity fields interactions are shown to produce the Einstein-Hilbert action Lagrangian. Similar extension of the Mathematical framework to the Electromagnetic field produces the Quantum electrodynamics and Yang-Mills fields Lagrangians. Finally, a unified Lagrangian describing both velocity field and Electromagnetic field types is presented and alternative formulation suggested.

We present an exact solution of Einstein's field equations in toroidal coordinates. The solution has three regions: an interior with a string equation of state; an Israel boundary layer; and an exterior with constant isotropic pressure and constant density, locally isometric to anti-de Sitter space-time. The exterior can be a cosmological vacuum with negative cosmological constant. The size and mass of the toroidal loop depend on the size of Lambda.

Amplitudes for fermion-fermion, boson-boson and fermion-boson interactions are calculated in the second order of perturbation theory in the Lobachevsky space. An essential ingredient of the model is the Weinberg's 2(2j + 1)− component formalism for describing a particle of spin j. The boson-boson amplitude is then compared with the two-fermion amplitude obtained long ago by Skachkov on the basis of the Hamiltonian formulation of quantum field theory on the mass hyperboloid, p 2 0 − p 2 = M 2 , proposed by Kadyshevsky. The parametrization of the amplitudes by means of the momentum transfer in the Lobachevsky space leads to same spin structures in the expressions of T − matrices for the fermion case and the boson case. However, certain differences are found. Possible physical applications are discussed.

The experimental conditions by which electromagnetic signals (EMS) of low frequency can be emitted by diluted aqueous solutions of some bacterial and viral DNAs are described. That the recorded EMS and nanostructures induced in water carry the DNA information (sequence) is shown by retrieval of that same DNA by classical PCR amplification using the TAQ polymerase, including both primers and nucleotides. Moreover, such a transduction process has also been observed in living human cells exposed to EMS irradiation. These experiments suggest that coherent long range molecular interaction must be at work in water so to allow the observed features. The quantum field theory analysis of the phenomenon is presented.

Graphene quantum dots (GQDs) hold great promise for applications in electronics, optoelectronics and bioelectronics, but the fabrication of widely tunable GQDs has remained elusive. Here, we report the fabrication of atomically precise GQDs consisting of low-bandgap N = 14 armchair graphene nanoribbon (AGNR) segments that are achieved through edge fusion of N = 7 AGNRs. The so-formed intraribbon GQDs reveal deterministically defined, atomically sharp interfaces between wide and narrow AGNR segments and host a pair of low-lying interface states. Scanning tunneling microscopy/spectroscopy measurements complemented by extensive simulations reveal that their energy splitting depends exponentially on the length of the central narrow bandgap segment. This allows tuning of the fundamental gap of the GQDs over one order of magnitude within a few nanometers length range. These results are expected to pave the way for the development of widely tunable intraribbon GQD-based devices.

The quantum deformation of the Hopf algebra describes the skeleton of quantum field theory, namely its characterizing feature consisting in the existence of infinitely many unitarily inequivalent representations of the canonical commutation relations. From this we derive the thermal properties of quantum field theory, with the entropy playing the role of the generator of the non-unitary time evolution. The entanglement of the quantum vacuum appears to be robust against interaction with the environment: on cannot "unknot the knots" in the infinite volume limit.

Quantum entanglement, a term coined by Erwin Schrodinger in 1935, is a mechanical phenomenon at the quantum level wherein the quantum states of two (or more) particles have to be described with reference to each other though these particles may be spatially separated. This phenomenon leads to paradox and has puzzled us for a long time. The behaviour of entangled particles is apparently inexplicable, incomprehensible and like magic at work. Locality has been a reliable and fruitful principle which has guided us to the triumphs of twentieth century physics. But the consequences of the local laws in quantum theory could seem "spooky" and nonlocal, with some theorists questioning locality itself. Could two subatomic particles on opposite sides of the universe be really instantaneously connected? Is any theory which predicts such a connection essentially flawed or incomplete? Are the results of experiments which demonstrate such a connection being misinterpreted? These question...

It will be argued here that the cosmological constant problem exists because of the way the vacuum is defined in quantum field theory. It has been known for some time that for QFT to be gauge invariant certain terms--such as part of the vacuum polarization tensor--must be eliminated either explicitly or by some form of regularization followed by renormalization. It has recently been shown that lack of gauge invariance is a result of the way the vacuum is defined, and redefining the vacuum so that the theory is gauge invariant may also offer a solution to the cosmological constant problem.

This survey treats the Hilbert Book Model Project. The project concerns a well-founded, purely mathematical model of physical reality. The project relies on the conviction that physical reality owns its own kind of mathematics and that this mathematics guides and restricts the extension of the foundation to more complicated levels of the structure and the behavior of physical reality. This results in a model that more and more resembles the physical reality that humans can observe.

This thesis contains a theoretical treatment of the time-dependent quantum transport of electrons through molecular junctions. In particular, the nonequilibrium Green's function (NEGF) method is used to obtain the time-dependent current and current fluctuations in response to an arbitrarily time-dependent spatially homogeneous bias in the leads and molecular region. All subsystems in the nanojunction are assumed to be noninteracting throughout, and in addition the wide-band limit approximation (WBLA) is made in order to simplify the treatment of the lead-molecule coupling.

The theoretical work involves a complete analytical solution in the two-time plane of the Kadanoff-Baym equations for all components of the molecular region Green's function defined on the imaginary time Konstantinov-Perel' contour. This enables the derivation of expressions for time-dependent quantities such as the particle number in the molecular region and a generalized time-dependent Landauer-Büttiker (LB) formula for the current through an arbitrarily large conducting molecule. The partition-free approach is assumed for the switch-on of a bias in the leads, which enables us to study the effects on the transient transport of the initial coupling between the subsystems of the nanojunction.

The analytical expression for the full two-time Green's function is then used to study the quantum correlations between currents in the different leads. Using many-body methods, the two-time current correlation function is expressed in terms of a matrix product of Green's functions which are all known exactly. Therefore, in similar fashion to the generalized LB current, the current correlations generalize the LB theory of shot and thermal noise so that it is (i) partition-free and (ii) valid for an arbitrary time-dependent bias. To check its generality, this formula is shown to reproduce results for the zero- and finite-frequency current noise that are known from the literature on this topic.

The formulas for the current and current fluctuations are originally obtained in terms of integrals over the frequency and time planes. To render these formulas useful for calculations on large molecules they are then re-expressed with all frequency integrals replaced with special functions, which may be computed via the Padé expansion of the Fermi function. This results in a formalism which is ideally multiscale in time, i.e. which does not get more expensive with increasing number of time steps, and which can therefore be used to study the short-time transient and steady-state transport quantities with identical computational expense. Some numerical calculations of the current and noise response to the switch-on of a time-dependent bias are then performed.

The first kind of time-dependent driving considered in this thesis is periodic. Some preliminary calculations are performed on periodically-driven quantum dots, and the effect on the current of varying the driving frequency, temperature, lead-molecule coupling and driving amplitude is studied. Next, the problem of quantum pumping is considered, and sufficient conditions are found for a periodically driven system with zero time-average bias to generate a net time-averaged current through the system. The effects of finite size on the current response to static and periodic biases are investigated, again using the molecular wire as an illustrative model. Next, calculations of the quantum pump current are presented for a particular biharmonic bias model, and in particular the effect on this current of breaking the sinusoidal shape of the driving field. Finally, the discussion turns to calculations of the cross-lead current correlations in extended systems in response to static and periodic biases. By investigating molecular wires of different lengths and internal hopping parameters, a signature of the traversal time for electrons crossing the sample is found in both the transient and steady-state cross-lead current correlations.

As there are no restrictions on the nature of the time-dependent bias driving the system out of equilibrium, one can use this formalism to study the electronic response to a classically fluctuating bias in the leads. The second kind of time-dependent driving studied in this thesis is therefore non-deterministic, and exact formulas for the bias-averaged current response to a stochastic bias are derived for the first time. This problem is formally analogous to the use of the Langevin equation approach to obtain a relation between the conductance in a classical circuit and the strength of fluctuations in an external driving bias: the so-called Nyquist theorem. An exact quantum version of the Nyquist theorem is derived for a driving bias with colour noise which relates the strength of fluctuations, the correlation time of fluctuations, the temperature and conductance in a molecular junction. Due to the nonlinear relation between current and driving bias in these junctions, it is not always true that the conductance will decrease with increasing fluctuation strength. Instead, there can be particular intermediate values of the fluctuation strength at which peaks in the conductance are observed, in a stochastic resonance effect.

The operator construction of the interacting string field theory presented by Witten is completed. The ghost sector of the theory is discussed in detail, using the fermionic formulation of the ghosts. The Fock space representation of the functionals that represent integration, multiplication, and the interaction vertex are constructed explicitly. We prove that the formalism is invariant under reparametefizations and under BRST gauge transformation.

Warp drives are very interesting configurations in general relativity: At least theoretically, they provide a way to travel at superluminal speeds, albeit at the cost of requiring exotic matter to exist as solutions of Einstein's equations. However, even if one succeeded in providing the necessary exotic matter to build them, it would still be necessary to check whether they would survive to the switching on of quantum effects. Semiclassical corrections to warp-drive geometries have been analyzed only for eternal warp-drive bubbles traveling at fixed superluminal speeds. Here, we investigate the more realistic case in which a superluminal warp drive is created out of an initially flat spacetime. First of all we analyze the causal structure of eternal and dynamical warp-drive spacetimes. Then we pass to the analysis of the renormalized stress-energy tensor (RSET) of a quantum field in these geometries. While the behavior of the RSET in these geometries has close similarities to that in the geometries associated with gravitational collapse, it shows dramatic differences too. On one side, an observer located at the center of a superluminal warp-drive bubble would generically experience a thermal flux of Hawking particles. On the other side, such Hawking flux will be generically extremely high if the exotic matter supporting the warp drive has its origin in a quantum field satisfying some form of quantum inequalities. Most of all, we find that the RSET will exponentially grow in time close to, and on, the front wall of the superluminal bubble. Consequently, one is led to conclude that the warp-drive geometries are unstable against semiclassical backreaction.

Skew constacyclic codes are displaying vital role in the field of coding theory. This paper is mainly focused on skew-α constacyclic codes over R = Fq + uFq + vFq + uvFq, with u 2 = v 2 = 1, uv = vu, q = 3 m , and α is an unit of R fixed by the authomorphism θ. It is briey derived as well that the Gray map of skew cyclic code of length n over R is skew quasicyclic code of length 4n over Fq of index 4. Furthermore, the decomposition of a skew α constacyclic codes over R are also determined. A complete analysis about the relationship between skew α constacyclic code and its dual is also carried out.

Recent work has conjectured that, under general boundary conditions, non-equilibrium Renormalization Group flows are likely to end up on strange attractors. If this conjecture is true, effective field theories must necessarily reflect the properties of these attractors. We start from the observation that, seemingly disparate concepts such as the Berry phase, gauge potentials and the curvature tensor of General Relativity (GR), share a common geometric foundation. Developing further, we posit that the dynamics of gauge and gravitational fields may be derived from the global attributes of strange attractors. The motivation behind this ansatz is that the Navier-Stokes equations bridge the gap between fluid turbulence, on the one hand, and the mathematics of GR and gauge theory, on the other.

We develop the recent proposal to use dimensional reduction from the four-dimensional spacetime D = (1 + 3) to the variant with a smaller number of space dimensions D = (1 + d), d < 3 at sufficiently small distances to construct a renormalizable quantum field theory. We study the Klein-Gordon equation on a few toy examples ("educational toys") of a space-time with variable special geometry, including a transition to a dimensional reduction. The examples considered contain a combination of two regions with a simple geometry (two-dimensional cylindrical surfaces with different radii) connected by a transition region. The new technique of transforming the study of solutions of the Klein-Gordon problem on a space with variable geometry into solution of a one-dimensional stationary Schrödinger-type equation with potential generated by this variation is useful. We draw the following conclusions: (1) The signal related to the degree of freedom specific to the higher-dimensional part does not penetrate into the smaller-dimensional part because of an inertial force inevitably arising in the transition region (this is the centrifugal force in our models).

Tables I-III. 1U Fart III: Real Space Methods for the XY Model Part IV: Transfer Matrix Methods for the Ising Chain in a Transverse Magnetic Field and members of the SLAC theory &roup for useful discussions •-especially Marvin Welnstein, who sugger.te-d the idea for the second part of the thesis. Many thanks to Jacqueline A. llahn, who typed the first manuscript. Finally, special thanks art-due to my family, and In particular to my father, mother and sister for their loving support Erum the very earliest stages of my unusual education to the present day. DISCLAIMER This report was prepared as an account of work sponsored by an agency of the United Stalin Govemncnt. Neither trie United States Government nor any agency thcrwf, nor iiny of their employees, makes any warranty, express or implied, or assumes any legal liability or responsi bility for the accuracy, complctene&s, or usefuln«*«v of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Refer ence hcreir. to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recom mendation, or favoring by the United Sta.-S Government or any agency thereof The view* and opinions of authors expressed herein do not neccssjr'k Male 'jr reflect those of the United States Government or any agency thereof.

In this paper we present a formulation of the nonlinear stochastic differential equation which allows for systematic approximations. The method is not restricted to the asymptotic, i.e., stationary, regime but can be applied to derive effective equations describing the relaxation of the system from arbitrary initial conditions. The basic idea is to reduce the nonlinear Langevin equation to an equivalent equilibrium problem, which can then be studied with the methods of conventional equilibrium statistical field theory. A particular well suited perturbative scheme is that developed in quantum field theory by Cornwall, Jackiw and Tomboulis. We apply this method to the study of N component Ginzburg-Landau equation in zero spatial dimension. In the limit of N → ∞ we can solve the effective equations and obtain closed forms for the time evolutions of the average field and of the two-time connected correlation

A model for measurement in collapse-free nonrelativistic fermionic quantum field theory is presented. In addition to local propagation and effectively-local interactions, the model incorporates explicit representations of localized observers, thus extending an earlier model of entanglement generation in Everett quantum field theory [M. A. Rubin, Found. Phys. 32, 1495-1523 (2002)]. Transformations of the field operators from the Heisenberg picture to the Deutsch-Hayden picture, involving fictitious auxiliary fields, establish the locality of the model. The model is applied to manifestly-local calculations of the results of measurements, using a type of sudden approximation and in the limit of massive systems in narrow-wavepacket states. Detection of the presence of a spin-1/2 system in a given spin state by a freely-moving two-state observer illustrates the features of the model and the nonperturbative computational methodology. With the help of perturbation theory the model is appli...

Quantum Field Theory (QFT) posits that there are several fields (electro-magnetic, gravitational, Higgs) that permeate space throughout the universe.  A disturbance in one of those fields causes a wave of energy to be generated.  In the QFT view, everything we see and experience is a wave that is spread out like a cloud – there are no particles with a fixed location in space and a distinct boundary.  The author of this paper aims at unifying particles and waves, matter and energy.  This unification is suggested in Einstein’s famous formula, E=MC2 and deBroglie’s matter-wave theory. A particle of matter is defined as compressed energy that has a definite locality and involves inherently high potential energy but lower kinetic energy.  A wave of energy is defined as a rhythmic high speed, fine particles which are spread out like a cloud without a distinct location and firm boundaries.  Such a unification shows how quantum energy can make the transformation from waves to particles, energy to matter, from micro to macro matter and from quantum to classical.  The transition from energy to matter can be seen in the various states of matter from quanta to plasma to gas to liquid to solid.  If E=MC2 is correct, then the basic unit of mattergy (matter-energy) is the quantum.  Perhaps this is what Democritus had in mind when he envisioned the indivisible unit of matter.

We propose simple Felgln-Fuchs contour integral representations for the characters of a large class of rational conformal field theories These include the A, D and E series SU(2) WZW theories, the A and D series c < 1 mlmmal theories, and the k = 1 SU(N) WZW theories All these theories are characterized by the absence of the zeroes m the wronskaan determinant of the characters m the interior of moduh space Tins proposal is verified by several calculations

A superluminal quantum-vortex model of the electron and the positron is produced from a superluminal double-helix model of the photon during electron-positron pair production. The two oppositely-charged (with Q = ±e sqrt (2/α) = 16.6e) open-helix spin-½ half-photons compose the double-helix photon. These half-photons separate and curl up their separated superluminal single-helical trajectories to form an electrically-charged superluminal closed-helix spin-½ quantum-vortex electron model and a corresponding positron model. The helical radius and the Dirac equation's zitterbewegung angular frequency of the quantum vortex electron and positron models equal the helical radius and zitterbewegung angular frequency of the two spin-½ half-photons, each of energy E = mc^2 , that composed the double-helix photon model of energy E = 2mc^2 from which the electron and positron models were produced. The photon and electron models are also compatible when a photon of energy E > 2mc^2 produces a relativistic electron-positron pair. Implications of the quantum vortex electron model for electron stability are discussed.

Movement/propagation through the “Dark Matter”:
Effects the surrounding by propagation through “Dark matter” particles creating “waves” in a manner similar to a Ship/boat moving in water creating waves

When two ships/boats (in our case two objects) move in parallel (in 4th dimension) to each other in the same direction, they experience a lateral pressure due to which the ships/boats tend to come closer to each other. This is explained by Bernoulli's theorem. This greater lateral pressure forces the ships/boats to come closer to each other and they may even collide
In our case the ships/boats are any aggregate of “Atoms” – any kind of an object
The “Sea” is the “Dark Matter”
Bernoulli's theorem is named after Daniel Bernoulli

The formalism based on the equal-time Wigner function of the two-point correlation function for a quantized Klein-Gordon field is presented. The notion of the gauge-invariant Wigner transform is introduced and equations for the corresponding phase-space calculus are formulated. The equations of motion governing the Wigner function of the Klein-Gordon field are derived. It is shown that they lead to a relativistic transport equation with electric and magnetic forces and quantum corrections. The governing equations are much simpler than in the fermionic case which has been treated earlier. In addition the newly developed formalism is applied towards the description of spontaneous symmetry breakdown.