Construction of the Pauli–Villars-Regulated Dirac Vacuum in Electromagnetic Fields

@article{Gravejat2013ConstructionOT,
  title={Construction of the Pauli–Villars-Regulated Dirac Vacuum in Electromagnetic Fields},
  author={Philippe Gravejat and Christian Hainzl and Mathieu Lewin and {\'E}ric S{\'e}r{\'e}},
  journal={Archive for Rational Mechanics and Analysis},
  year={2013},
  volume={208},
  pages={603-665}
}
Using the Pauli–Villars regularization and arguments from convex analysis, we construct solutions to the classical time-independent Maxwell equations in Dirac’s vacuum, in the presence of small external electromagnetic sources. The vacuum is not an empty space, but rather a quantum fluctuating medium which behaves as a nonlinear polarizable material. Its behavior is described by a Dirac equation involving infinitely many particles. The quantum corrections to the usual Maxwell equations are… 
The Dirac-Klein-Gordon system in the strong coupling limit
We study the Dirac equation coupled to scalar and vector Klein-Gordon fields in the limit of strong coupling and large masses of the fields. We prove convergence of the solutions to those of a cubic
Derivation of the magnetic Euler–Heisenberg energy
Semi-Classical Dirac Vacuum Polarisation in a Scalar Field
We study vacuum polarisation effects of a Dirac field coupled to an external scalar field and derive a semi-classical expansion of the regularised vacuum energy. The leading order of this expansion
Stability, dispersion, and pair production for some infinite quantum systems
This thesis is devoted to the mathematical study of stability properties of infinite quantum systems described by nonlinear models. In chapters 1 and 2, we study the instability of the relativistic
Charge Renormalization and Static Electron/Positron Pair Production for a Nonlinear Dirac Model with Weak Interactions
TLDR
This paper constructs solutions to the Hartree-Fock approximation of Quantum Electrodynamics in the regime of weak interactions, and strong external fields, and proves that the critical strength of the external potential needed to produce an additional particle in the vacuum is $\alpha=0$ or $\alpha>0$.
External Field QED on Cauchy Surfaces
The Shale-Stinespring Theorem (1965) together with Ruijsenaar’s criterion (1977) provide a necessary and sufficient condition for the implementability of the evolution of external field quantum
Vacuum polarization in heavy atoms
We formulate the Hartree–Fock method using a functional integral approach. Then we consider a nonperturbative component of the vacuum polarization. For the Dirac– Coulomb operator the renormalization
Quantum fields with classical perturbations
The main purpose of these notes is a review of various models of Quantum Field Theory (QFT) involving quadratic Lagrangians. We discuss scalar and vector bosons, spin 12 fermions, both neutral and
A Perspective on External Field QED
In light of the conference Quantum Mathematical Physics held in Regensburg in 2014, we give our perspective on the external field problem in quantum electrodynamics (QED), i.e., QED without photons
Ju l 2 02 0 Lamb shift in heavy atoms
We formulate the Hartree–Fock method in large-N approximation using a functional integral approach and derive an exact renormalization group equation for the effective action. We consider only a
...
1
2
3
...

References

SHOWING 1-10 OF 49 REFERENCES
From quantum electrodynamics to mean-field theory. I. The Bogoliubov-Dirac-Fock formalism
A relativistic mean-field theory for interacting Dirac particles in an external field is derived from quantum-field theory using a minimisation principle, and discussed in the context of atomic
The mean‐field approximation in quantum electrodynamics: The no‐photon case
We study the mean‐field approximation of quantum electrodynamics (QED) by means of a thermodynamic limit. The QED Hamiltonian is written in Coulomb gauge and does not contain any normal ordering or
Minimization method for relativistic electrons in a mean-field approximation of quantum electrodynamics
We study a mean-field relativistic model which is able to describe both the behavior of finitely many spin-1/2 particles like electrons and of the Dirac sea which is self-consistently polarized in
A Formulation of Quantum Field Theory Realizing a Sea of Interacting Dirac Particles
In this survey article, we explain a few ideas behind the fermionic projector approach and summarize recent results which clarify the connection to quantum field theory. The fermionic projector is
Existence of a Stable Polarized Vacuum in the Bogoliubov-Dirac-Fock Approximation
According to Dirac’s ideas, the vacuum consists of infinitely many virtual electrons which completely fill up the negative part of the spectrum of the free Dirac operator D0. In the presence of an
Quantum Electrodynamics of Spinless Bosons
All considerations in this book so far have dealt with electrons (or muons) and their antiparticles, i.e. particles with spin 1/2, which are described by the Dirac equation. The theory of quantum
Renormalization and Asymptotic Expansion of Dirac’s Polarized Vacuum
We perform rigorously the charge renormalization of the so-called reduced Bogoliubov-Dirac-Fock (rBDF) model. This nonlinear theory, based on the Dirac operator, describes atoms and molecules while
Ground State and Charge Renormalization in a Nonlinear Model of Relativistic Atoms
We study the reduced Bogoliubov-Dirac-Fock (BDF) energy which allows to describe relativistic electrons interacting with the Dirac sea, in an external electrostatic potential. The model can be seen
On gauge invariance and vacuum polarization
This paper is based on the elementary remark that the extraction of gauge invariant results from a formally gauge invariant theory is ensured if one employs methods of solution that involve only
The Dirac Equation
Ever since its invention in 1929 the Dirac equation has played a fundamental role in various areas of modern physics and mathematics. Its applications are so widespread that a description of all
...
1
2
3
4
5
...