M.E. Hogan is a holistic, trans-disciplinary researcher specializing in a number of fields, primarily: quantum gravity, quantum information theory, and quantum cosmology; deep ecology, queer ecofeminism, emergent/complex systems, and post-colonial and integral/process theory; and global electronic/hip-hop music, performing as 'TWISTOR'. Supervisors: Dr. Jonathan Steven Engle Phone: 508-264-0231 Address: Department of Mathematical and Physical Sciences,
Wells College,
170 Main Street,
In this paper we work out in detail a new proposal to define rigorously a sector of loop quantum ... more In this paper we work out in detail a new proposal to define rigorously a sector of loop quantum gravity at the diffeomorphism invariant level corresponding to homogeneous and isotropic cosmologies, and propose how to compare in detail the physics of this sector with that of loop quantum cosmology. The key technical steps we have completed are (a) to formulate conditions for homogeneity and isotropy in a diffeomorphism covariant way on the classical phase space of general relativity, and (b) to translate these conditions consistently using well-understood techniques to loop quantum gravity. To impose the symmetry at the quantum level, on both the connection and its conjugate momentum, the method used necessarily has similiarities to the Gupta-Bleuler method of quantizing the electromagnetic field. Lastly, a strategy for embedding states of loop quantum cosmology into this new homogeneous isotropic sector, and using this embedding to compare the physics, is presented.
International Journal of Modern Physics D, Jul 2016
This paper summarizes a new proposal to define rigorously a sector of loop quantum gravity at the... more This paper summarizes a new proposal to define rigorously a sector of loop quantum gravity at the diffeomorphism invariant level corresponding to homogeneous and isotropic cosmologies, thereby enabling a detailed comparison of results in loop quantum gravity and loop quantum cosmology. The key technical steps we have completed are (a) to formulate conditions for homogeneity and isotropy in a diffeomorphism covariant way on the classical phase-space of general relativity, and (b) to translate these conditions consistently using well-understood techniques to loop quantum gravity. Some additional steps, such as constructing a specific embedding of the Hilbert space of loop quantum cosmology into a space of (distributional) states in the full theory, remain incomplete. However, we also describe, as a proof of concept, a complete analysis of an analogous embedding of homogeneous and isotropic loop quantum cosmology into the quantum Bianchi I model of Ashtekar and Wilson-Ewing. Details will appear in a pair of forthcoming papers.
The gauge-invariant wave function of the photon and
its probability density are usually not dis... more The gauge-invariant wave function of the photon and its probability density are usually not discussed in quantum mechanics, because such a photon wave function with Born's position probability has not been established. We discuss a gauge-invariant photon wave function ${{a}}_\mu= A_\mu - \p_{\mu}\p^{\a} \p^{-2}A_{\a}(x)$ and demonstrate that the observable probabilistic nature of the photon can be understood through the photon wave function ${a}_\mu$ and the Green's function associated with the photon wave equation. Physical implications of the gauge-invariant wave function and the lack of a photon probability density satisfying the continuity equation are also discussed.
This paper presents comparisons between recent models of parton distribution functions (viz. CTEQ... more This paper presents comparisons between recent models of parton distribution functions (viz. CTEQ6) and experimental data from NuTeV deep inelastic neutrino scattering experiments. First, the basics of parton distribution functions will be described. These may be calculated using the Durham University program LHAPDF. Next we move on to an explication of the NuTeV neutrino deep inelastic scattering (DIS) experiment at Fermilab. We then present some of the leading-order (LO) cross-section calculations from QCD and their associated corrections. Finally, we compare error analysis for the previous CTEQ6 parton standard with the new ‘FIT4’ curves, and draw our conclusions. Our goal is to conduct both a graphical and a statistical analysis of the effect of these new PDFs in regards to the experimental data.
In this paper we work out in detail a new proposal to define rigorously a sector of loop quantum ... more In this paper we work out in detail a new proposal to define rigorously a sector of loop quantum gravity at the diffeomorphism invariant level corresponding to homogeneous and isotropic cosmologies, and propose how to compare in detail the physics of this sector with that of loop quantum cosmology. The key technical steps we have completed are (a) to formulate conditions for homogeneity and isotropy in a diffeomorphism covariant way on the classical phase space of general relativity, and (b) to translate these conditions consistently using well-understood techniques to loop quantum gravity. To impose the symmetry at the quantum level, on both the connection and its conjugate momentum, the method used necessarily has similiarities to the Gupta-Bleuler method of quantizing the electromagnetic field. Lastly, a strategy for embedding states of loop quantum cosmology into this new homogeneous isotropic sector, and using this embedding to compare the physics, is presented.
International Journal of Modern Physics D, Jul 2016
This paper summarizes a new proposal to define rigorously a sector of loop quantum gravity at the... more This paper summarizes a new proposal to define rigorously a sector of loop quantum gravity at the diffeomorphism invariant level corresponding to homogeneous and isotropic cosmologies, thereby enabling a detailed comparison of results in loop quantum gravity and loop quantum cosmology. The key technical steps we have completed are (a) to formulate conditions for homogeneity and isotropy in a diffeomorphism covariant way on the classical phase-space of general relativity, and (b) to translate these conditions consistently using well-understood techniques to loop quantum gravity. Some additional steps, such as constructing a specific embedding of the Hilbert space of loop quantum cosmology into a space of (distributional) states in the full theory, remain incomplete. However, we also describe, as a proof of concept, a complete analysis of an analogous embedding of homogeneous and isotropic loop quantum cosmology into the quantum Bianchi I model of Ashtekar and Wilson-Ewing. Details will appear in a pair of forthcoming papers.
The gauge-invariant wave function of the photon and
its probability density are usually not dis... more The gauge-invariant wave function of the photon and its probability density are usually not discussed in quantum mechanics, because such a photon wave function with Born's position probability has not been established. We discuss a gauge-invariant photon wave function ${{a}}_\mu= A_\mu - \p_{\mu}\p^{\a} \p^{-2}A_{\a}(x)$ and demonstrate that the observable probabilistic nature of the photon can be understood through the photon wave function ${a}_\mu$ and the Green's function associated with the photon wave equation. Physical implications of the gauge-invariant wave function and the lack of a photon probability density satisfying the continuity equation are also discussed.
This paper presents comparisons between recent models of parton distribution functions (viz. CTEQ... more This paper presents comparisons between recent models of parton distribution functions (viz. CTEQ6) and experimental data from NuTeV deep inelastic neutrino scattering experiments. First, the basics of parton distribution functions will be described. These may be calculated using the Durham University program LHAPDF. Next we move on to an explication of the NuTeV neutrino deep inelastic scattering (DIS) experiment at Fermilab. We then present some of the leading-order (LO) cross-section calculations from QCD and their associated corrections. Finally, we compare error analysis for the previous CTEQ6 parton standard with the new ‘FIT4’ curves, and draw our conclusions. Our goal is to conduct both a graphical and a statistical analysis of the effect of these new PDFs in regards to the experimental data.
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its probability density are usually not discussed in quantum
mechanics, because such a photon wave function with Born's position probability has not been established. We discuss a gauge-invariant photon wave function ${{a}}_\mu= A_\mu - \p_{\mu}\p^{\a} \p^{-2}A_{\a}(x)$ and demonstrate that the observable probabilistic nature of the photon can be understood through the photon wave function ${a}_\mu$ and the Green's function associated with the photon wave equation. Physical implications of the gauge-invariant wave function and the lack of a photon probability density satisfying the continuity equation are also discussed.
its probability density are usually not discussed in quantum
mechanics, because such a photon wave function with Born's position probability has not been established. We discuss a gauge-invariant photon wave function ${{a}}_\mu= A_\mu - \p_{\mu}\p^{\a} \p^{-2}A_{\a}(x)$ and demonstrate that the observable probabilistic nature of the photon can be understood through the photon wave function ${a}_\mu$ and the Green's function associated with the photon wave equation. Physical implications of the gauge-invariant wave function and the lack of a photon probability density satisfying the continuity equation are also discussed.