A product picture for quantum electrodynamics

TY - JOUR

T1 - A product picture for quantum electrodynamics

AU - Kay, Bernard S.

N1 - © Author(s) 2022 to appear in the special collection "Celebrating Sir Roger Penrose's Nobel Prize" [AVS Quantum Science, Guest Editors: Ivette Fuentes and Hendrik Ulbricht]

PY - 2022/7/11

Y1 - 2022/7/11

N2 - We present a short account of our work to provide quantum electrodynamics with a 'product picture'. It aims to complement the longer exposition in a recent paper in 'Foundations of Physics' and to help to make that work more accessible. The product picture is a formulation of QED, equivalent to standard Coulomb gauge QED, but in which the Hilbert space arises as (a certain physical subspace of) a product of a Hilbert space for the electromagnetic field and a Hilbert space for charged matter (i.e. the Dirac field) and in which the Hamiltonian arises as the sum of an electromagnetic Hamiltonian and a charged matter Hamiltonian and an interaction term. (The Coulomb gauge formulation of QED is not a product picture because, in it, the longitudinal part of the electromagnetic field is made out of charged matter operators.) We also recall a 'Contradictory Commutator Theorem' for QED which exposes flaws in previous attempts at temporal gauge quantization of QED and we explain how our product picture appears to offer a way to overcome those flaws. Additionally, we discuss the extent to which that theorem generalizes to Yang-Mills fields. We also develop a product picture for nonrelativistic charged particles in interaction with the electromagnetic field and point out how this leads to a novel way of thinking about the theory of many nonrelativistic electrically charged particles with Coulomb interactions. We explain how the provision of a product picture for QED gives hope that one will be able likewise to have a product picture for (Yang Mills and) quantum gravity -- the latter being needed to make sense of the author's 'matter-gravity entanglement hypothesis'. In an afterword, we briefly discuss similarities and differences between that hypothesis and its predictions and ideas of Roger Penrose related to a possible role of gravity in quantum state reduction and to cosmological entropy.

AB - We present a short account of our work to provide quantum electrodynamics with a 'product picture'. It aims to complement the longer exposition in a recent paper in 'Foundations of Physics' and to help to make that work more accessible. The product picture is a formulation of QED, equivalent to standard Coulomb gauge QED, but in which the Hilbert space arises as (a certain physical subspace of) a product of a Hilbert space for the electromagnetic field and a Hilbert space for charged matter (i.e. the Dirac field) and in which the Hamiltonian arises as the sum of an electromagnetic Hamiltonian and a charged matter Hamiltonian and an interaction term. (The Coulomb gauge formulation of QED is not a product picture because, in it, the longitudinal part of the electromagnetic field is made out of charged matter operators.) We also recall a 'Contradictory Commutator Theorem' for QED which exposes flaws in previous attempts at temporal gauge quantization of QED and we explain how our product picture appears to offer a way to overcome those flaws. Additionally, we discuss the extent to which that theorem generalizes to Yang-Mills fields. We also develop a product picture for nonrelativistic charged particles in interaction with the electromagnetic field and point out how this leads to a novel way of thinking about the theory of many nonrelativistic electrically charged particles with Coulomb interactions. We explain how the provision of a product picture for QED gives hope that one will be able likewise to have a product picture for (Yang Mills and) quantum gravity -- the latter being needed to make sense of the author's 'matter-gravity entanglement hypothesis'. In an afterword, we briefly discuss similarities and differences between that hypothesis and its predictions and ideas of Roger Penrose related to a possible role of gravity in quantum state reduction and to cosmological entropy.

UR - https://arxiv.org/abs/2204.01177

U2 - 10.1116/5.0085813

DO - 10.1116/5.0085813

M3 - Article

SN - 2639-0213

VL - 4

JO - AVS Quantum Science

JF - AVS Quantum Science

M1 - 031401

ER -