The Stability of Matter and Quantum Electrodynamics

Stability of relativistic quantum electrodynamics in the Coulomb gauge

We show that relativistic quantum electrodynamics in the Coulomb gauge satisfies the following bound, which establishes stability: let $H(Λ,V)$ denote the Hamiltonian of $QED_{1+3}$ on the three-dimensional torus of volume $V$ and with ultraviolet cutoff $Λ$. Then there exists a constant $0<μ(Λ,V)<\infty$ (the vacuum energy renormalization) such that the renormalized Hamiltonian is positive: $H_{ren}(Λ,V) \equiv H_{Λ,V}+μ_{Λ, V}\cdot \mathbb{1} \ge 0 $.

Stability and consistent interactions in Podolsky's generalized electrodynamics

We confirm the stability of Podolsky's generalized electrodynamics by constructing a series of two-parametric bounded conserved quantities which includes the canonical energy-momentum tensors. In addition, we evaluate the transition-amplitude of this higher derivative system in BV antifield formalism and obtain the desirable generalized radiation gauge condition by choosing appropriate gauge-fixing fermion. Within the framework of Lagrangian BRST cohomology, we present the constructions of consistent interactions in Podolsky's model and when concentrating on the antighost number zero part of t…

Stability of a Model of Relativistic Quantum Electrodynamics

The relativistic ``no pair'' model of quantum electrodynamics uses the Dirac operator, D(A), for the electron dynamics together with the usual self-energy of the quantized ultraviolet cutoff electromagnetic field A -- in the Coulomb gauge. There are no positrons because the electron wave functions are constrained to lie in the positive spectral subspace of some Dirac operator, D, but the model is defined for any number, N, of electrons, and hence describes a true many-body system. In addition to the electrons there are a number, K, of fixed nuclei with charges \leq Z. If the fields are not qua…

Quantum Mechanics, The Stability of Matter and Quantum Electrodynamics

Much progress has been made in the last few decades in developing the necessary mathematics for understanding the full implications of the quantum-mechanical many-body problem and why the material world appears to be as stable as it is despite the serious -1/|x|singularity of the Coulomb potential that attracts negative electrons to positive atomic nuclei. Many problems remain, however, especially the understanding of the interaction of matter and the quantized radiation field discovered by Planck in 1900. A short review of some of the main topics is given.

Axion electrodynamics and dark matter fingerprints in the terrestrial magnetic and electric fields

We consider mathematical aspects of the axion electrodynamics in application to the problem of evolution of geomagnetic and terrestrial electric fields, which are coupled by relic axions born in the early Universe and (hypothetically) forming now the cold dark matter. We find axionic analogs of the Debye potentials, well-known in the standard Faraday - Maxwell electrodynamics, and discuss exact solutions to the equations of the axion electrodynamics describing the state of axionically coupled electric and magnetic fields in a spherical resonator Earth-Ionosphere. We focus on the properties of …

经典场电动力学中渐近场的长程效应与角动量

Long-range effects in asymptotic fields and angular momentum of classical field electrodynamics

本文研究经典场电动力学中渐近场的长程结构，证明守恒庞加莱量可由渐近场表示，并揭示长程变量导致角动量中库仑场与红外自由场特征的混合。