Dirac equation

Quaternion Dirac equation has been analyzed and its supersymmetrization has been discussed consistently. It has been shown that the quaternion Dirac equation automatically describes the spin structure with its spin up and spin down components of two component quaternion Dirac spinors associated with positive and negative energies. It has also been shown that the supersymmetrization of quaternion Dirac equation works well for different cases associated with zero mass, nonzero mass, scalar potential and generalized electromagnetic potentials. Accordingly we have discussed the splitting of supersymmetrized Dirac equation in terms of electric and magnetic fields.

In this chapter we present Excess Entropy Production for human aging system as the sum of their respective subsystems and electrophysiological status. Additionally, we support the hypothesis of human brain and central neural system quantumness and we strongly suggest the theoretical and philosophical status of human brain as one of the unknown natural Dirac magnetic monopoles placed in the center of a Riemann sphere.

In this study, the analytical solutions of the Dirac equation have been presented for the Hulthén and Eckart potentials by applying an approximation to centrifugal-like term in the case of spin symmetry, Delta(r) = C = constant, and pseudospin symmetry, Sigma(r) = C = constant, for any spin-orbit quantum number kappa. The energy eigenvalues and corresponding spinor wave functions are

I know about the universe because it influences me.  Light excites the photoreceptors in my eyes, surfaces apply pressure to my touch receptors and my eardrums are buffeted by relentless waves of air molecules.  My entire sensorium is excited by all that surrounds me.  These experiences are all I have ever known, and for this reason, they comprise my reality.
This essay considers a simple model of observers that are influenced by the world around them.  Consistent quantification of information about such influences results in a great deal of familiar physics.  The end result is a new perspective on relativistic quantum mechanics, which includes both a way of conceiving of spacetime as well as particle “properties” that may be amenable to a unification of quantum mechanics and gravity.  Rather than thinking about the universe as a computer, perhaps it is more accurate to think about it as a network of influences where the laws of physics derive from both consistent descriptions and optimal information-based inferences made by embedded observers.

Schrödinger's equation and the heat equation are connected to one another by analytic continuation, as are the Feynman integral and the Wiener integral. We extend this form of correspondence to the relativistic domain by identifying Poisson processes whose real version gives rise ...

Leía por allí en el océano del Internet lo siguiente: "Ella dijo: " Escríbeme algo bonito " y él le escribió: " (∂ + m) ψ = 0 ". Esa es la ecuación de Paul Dirac. Gracias a esto, se describe el fenómeno de entrelazamiento cuántico que en la práctica dice que: " Si dos sistemas interactúan uno con el otro durante un cierto período de tiempo y luego se separan, lo podemos describir como dos sistemas separados, pero, de alguna manera sutil, están convertidos en un solo sistema. Uno de ellos sigue influyendo en el otro, a pesar de kilómetros de distancia o años luz ". Esto es el entrelazamiento cuántico o conexión cuántica. Dos partículas que, en algún momento estuvieron unidas, siguen estando de algún modo relacionadas. No importa la distancia entre ambas, aunque se hallen en extremos opuestos del universo. La conexión entre ellas es instantánea." Claro, él era un Físico teórico y esta anécdota ha quedado como una poesía físico – matemática, romántica para unos, inentendible para otros.

The foundations of Modern Physics are derived from the basic Mechanics of waves that propagate at c in a physical medium.  The foundation theories are unified  and all the usual relativistic and quantum paradoxes are removed.  Spacelike causal correlations are identified within the model, without invoking any form of nonlocality or superluminality.

“The Schrödinger equation and the Dirac equation are wrong because length can not be smaller than Planck length and time can not be smaller than Planck time.”
Adrian Ferent

“To quantize the energy operator, the wave function must be multiplied by ħ:”
Adrian Ferent

“The Schrödinger equation is wrong because time can not be smaller than Planck time”
Adrian Ferent

“The Schrödinger equation is wrong because length can not be smaller than Planck length”
Adrian Ferent

“The Dirac equation is wrong because length can not be smaller than Planck length and time can not be smaller than Planck time.”
Adrian Ferent

In this notes the background independent formulation of the gauge theories on D-branes in flat space-time is considered, some examples of the solutions of their equations of motion are presented, the solutions of Dirac equation in these backgrounds are analyzed, and the generalizations to the orbifolded spaces are looked upon.

In this notes the background independent formulation of the gauge theories on D-branes in flat space-time is considered, some examples of the solutions of their equations of motion are presented, the solutions of Dirac equation in these backgrounds are analyzed, and the generalizations to the orbifolded spaces are looked upon.

Dirac equation was written in form
of real derivatives for first order for electron and
positron , from paper Energy equation in complex
plane[4] it was clear that energy of any matter or
antimatter is complex, so there was a need of
getting differential equation in complex derivatives.
This paper gets a generic differential equation of
electron and positron in complex differentials of
single order.

The Dirac equation may be thought as originating from a theory of five-dimensional (5D) space-time. We define a special 5D Clifford algebra and introduce a spin-1/2 constraint equation to describe null propagation in a 5D space-time manifold. We explain how the 5D null formalism breaks down to four dimensions to recover two single-particle theories. Namely, we obtain Dirac's relativistic quantum mechanics and a formulation of statistical mechanics. Exploring the non-relativistic limit in five and four dimensions, we identify a new spin-electric interaction with possible applications to magnetic resonance spectroscopy (within quantum mechanics) and superconductivity (within statistical mechanics).

For some 100 years physics has modelled space and time via the spacetime concept, with space being merely an observer dependent perspective effect of that spacetime - space itself had no observer independent existence - it had no ontological status, and it certainly had no dynamical description. In recent years this has all changed. In 2002 it was discovered that a dynamical 3-space had been detected many times, including the Michelson-Morley 1887 light-speed anisotropy experiment. Here we review the dynamics of this 3-space, tracing its evolution from that of an emergent phenomena in the information-theoretic Process Physics to the phenomenological description in terms of a velocity field describing the relative internal motion of the structured 3-space. The new physics of the dynamical 3-space is extensively tested against experimental and astronomical observations, including the necessary generalisation of the Maxwell, Schrodinger and Dirac equations, leading to a derivation and explanation of gravity as a refraction effect of quantum matter waves. The flat and curved spacetime formalisms are derived from the new physics, so explaining their apparent many successes.

“Maxwell’s equations are wrong because length can not be smaller than Planck length and time can not be smaller than Planck time”
Adrian Ferent

“Maxwell’s equations are wrong, because the Electric field E and the Magnetic field B are not continuous functions”
Adrian Ferent

“The Electric field E and the Magnetic field B are discrete functions”
Adrian Ferent

The main objective of this doctoral thesis is the derivation of an integral spectral representation of the massive Dirac propagator in the nonextreme Kerr geometry in horizon-penetrating advanced Eddington-Finkelstein-type coordinates. To this end, we divide the doctoral thesis into the following three parts. In the first part, we describe the nonextreme Kerr geometry in the Newman-Penrose formalism by means of a Carter tetrad in advanced Eddington-Finkelstein-type coordinates, which are regular across the event and the Cauchy horizon, respectively, and feature a temporal function for which the level sets are partial Cauchy surfaces. On this background geometry, we define the massive Dirac equation in the Weyl representation in 2-spinor form with a Newman-Penrose dyad basis for the spinor space. We perform Chandrasekhar’s mode analysis and thus show the separability of the massive Dirac equation expressed in such horizon-penetrating coordinates into systems of radial and angular ordinary differential equations. We compute asymptotic radial solutions at infinity, the event horizon, and the Cauchy horizon, and demonstrate that the corresponding errors have suitable decay. Furthermore, we study specific aspects of the set of eigenfunctions and the eigenvalue spectrum of the angular system. In the second part, we introduce a new method of proof for the essential self-adjointness of the Dirac Hamiltonian for a particular class of nonuniformly elliptic mixed initial-boundary value problems on smooth asymptotically flat Lorentzian manifolds, combining results from the theory of symmetric hyperbolic systems with near-boundary elliptic methods. Finally, in the third part, we present the Hamiltonian formulation of the massive Dirac equation in the nonextreme Kerr geometry in advanced Eddington-Finkelstein-type coordinates and, within this framework, derive an explicit integral spectral representation of the massive Dirac propagator, which yields the full time-dependent dynamics of massive spin-1/2 fermions outside, across, and inside the event horizon, up to the Cauchy horizon. For the construction of this propagator, we first prove that the Dirac Hamiltonian in the extended Kerr geometry is essentially self-adjoint by employing the method introduced in the second part, and then use the spectral theorem for unbounded self-adjoint operators as well as Stone’s formula, which links the spectral measure of the Dirac Hamiltonian to the associated resolvent. We determine the resolvent in a separated form in terms of the projector onto a finite-dimensional invariant spectral eigenspace of the angular operator and the radial Green’s matrix both obtained within the mode analysis of the Dirac equation presented in the first part. This propagator may be applied to study the long-time dynamics and the decay rates of massive Dirac fields in a rotating Kerr black hole spacetime. It can furthermore be used in the formulation of an algebraic quantum field theory.

Seminário de Física Nuclear. Tópicos: 1. De Broglie e as Ondas de Matéria; Equação de Schrödinger; Interpretação Estatística de Max Born;  2. Equação de Klein-Gordon; Construção da Equação de Dirac; Soluções da Eq. Dirac; Interpretação das Energias Negativas; 3. Lagrangeana de Dirac; Interação Fóton-Férmion.

Nota (16.12.2022): o segundo termo da equação (21) é linear em p_k, ou seja,
-mc( beta^k - gamma^k ) p_k .

Mostramos el campo de Dirac para una partícula masiva libre que describe el movimiento de un fermión relativístico, usando el formalismo de la teoría cuántica de campos. Introducimos una sustitución no-mínima en el operador de momentum, el cual nos produce el oscilador de Dirac, entonces procedemos a cuantizarlo canónicamente y expresamos el operador del campo del oscilador de Dirac en función de los operadores de creación y aniquilación. Palabras claves: Teoría cuántica de campos, fermiones, campo de Dirac. Dynamic of the Dirac Oscillator We show the Dirac field for a free massive particle describing the motion of a relativistic fermion, using the quantum field theory formalism. We introduce a non-minimal substitution on the momentum operator, which gives us the Dirac oscillator so we proceed to quantize canonically and to express the field operator of the Dirac oscillator in terms of creation and annihilation operators.