A gauge invariant formulation of quantum electrodynamics using local currents

1977 ◽  
Vol 18 (3) ◽  
pp. 471-482 ◽  
Author(s):  
R. Menikoff ◽  
D. H. Sharp
Keyword(s):  
Quantum Electrodynamics ◽  
Gauge Invariant ◽  
Invariant Formulation

GAUGE-INVARIANT FORMULATION OF QUANTUM ELECTRODYNAMICS

1955 ◽  
Vol 33 (11) ◽  
pp. 650-660 ◽  
Author(s):  
P. A. M. Dirac
Keyword(s):  
Gauge Invariance ◽  
Quantum Electrodynamics ◽  
Coulomb Field ◽  
Gauge Invariant ◽  
Gauge Transformations ◽  
Invariant Formulation ◽  
Invariant Operation ◽  
General Gauge

Electrodynamics is formulated so as to be manifestly invariant under general gauge transformations, through being built up entirely in terms of gauge-invariant dynamical variables. The quantization of the theory can be carried out by the usual rules and meets with the usual difficulties.It is found that the gauge-invariant operation of creation of an electron involves the simultaneous creation of an electron and of the Coulomb field around it. The requirement of manifest gauge invariance prevents one from using the concept of an electron separated from its Coulomb field.

scholarly journals Gauge invariant canonical symplectic algorithms for real-time lattice strong-field quantum electrodynamics

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Qiang Chen ◽  
Jianyuan Xiao ◽  
Peifeng Fan
Keyword(s):  
Field Theory ◽  
Real Time ◽  
Quantum Electrodynamics ◽  
Symplectic Form ◽  
Strong Field ◽  
Relativistic Quantum ◽  
High Order ◽  
High Quality ◽  
Geometric Structures ◽  
Gauge Invariant

Abstract A class of high-order canonical symplectic structure-preserving geometric algorithms are developed for high-quality simulations of the quantized Dirac-Maxwell theory based strong-field quantum electrodynamics (SFQED) and relativistic quantum plasmas (RQP) phenomena. With minimal coupling, the Lagrangian density of an interacting bispinor-gauge fields theory is constructed in a conjugate real fields form. The canonical symplectic form and canonical equations of this field theory are obtained by the general Hamilton’s principle on cotangent bundle. Based on discrete exterior calculus, the gauge field components are discreted to form a cochain complex, and the bispinor components are naturally discreted on a staggered dual lattice as combinations of differential forms. With pull-back and push-forward gauge covariant derivatives, the discrete action is gauge invariant. A well-defined discrete canonical Poisson bracket generates a semi-discrete lattice canonical field theory (LCFT), which admits the canonical symplectic form, unitary property, gauge symmetry and discrete Poincaré subgroup, which are good approximations of the original continuous geometric structures. The Hamiltonian splitting method, Cayley transformation and symmetric composition technique are introduced to construct a class of high-order numerical schemes for the semi-discrete LCFT. These schemes involve two degenerate fermion flavors and are locally unconditional stable, which also preserve the geometric structures. Admitting Nielsen-Ninomiya theorem, the continuous chiral symmetry is partially broken on the lattice. As an extension, a pair of discrete chiral operators are introduced to reconstruct the lattice chirality. Equipped with statistically quantization-equivalent ensemble models of the Dirac vacuum and non-trivial plasma backgrounds, the schemes are expected to have excellent performance in secular simulations of relativistic quantum effects, where the numerical errors of conserved quantities are well bounded by very small values without coherent accumulation. The algorithms are verified in detail by numerical energy spectra. Real-time LCFT simulations are successfully implemented for the nonlinear Schwinger mechanism induced e-e+ pairs creation and vacuum Kerr effect, where the nonlinear and non-perturbative features captured by the solutions provide a complete strong-field physical picture in a very wide range, which open a new door toward high-quality simulations in SFQED and RQP fields.

Gauge-invariant formulation of axion-electrodynamics

2021 ◽  
Author(s):  
Stanley A. Bruce
Keyword(s):  
Dirac Fermion ◽  
Dirac Field ◽  
Gauge Invariant ◽  
Fermion Fields ◽  
Simple Generalization ◽  
Invariant Formulation ◽  
Em Field

In this paper, we propose a simple generalization of axion-electrodynamics (AED) for the general case in which Dirac fermion fields and scalar/pseudoscalar axion-like fields are present in the local [Formula: see text]([Formula: see text])[Formula: see text] gauge-invariant Lagrangian of the system. Our primary goal (which is not explored here) is to understand and predict novel phenomena that have no counterpart in standard (pseudoscalar) AED. With this end in view, we discuss on very general grounds, possible processes in which a Dirac field is coupled to axionic fields via the electromagnetic (EM) field.

The interaction of molecular multipoles with the electromagnetic field in the canonical formulation of non-covariant quantum electrodynamics

1970 ◽  
Vol 319 (1539) ◽  
pp. 549-563 ◽  
Keyword(s):  
Electromagnetic Field ◽  
Physical Interpretation ◽  
Quantum Electrodynamics ◽  
Unitary Transformation ◽  
Canonical Quantization ◽  
Multipole Moments ◽  
Gauge Invariant ◽  
Covariant Quantum ◽  
Canonical Formulation ◽  
Gauge Conditions

The procedure devised by Dirac for the canonical quantization of systems described by degenerate lagrangians is used to construct the hamiltonian for molecules interacting with the electromagnetic field. The hamiltonian obtained is expressed in terms of the gauge invariant field strengths and the electric and magnetic multipole moments of the molecules. The Coulomb gauge is introduced but other gauge conditions could be used. Finally, a physical interpretation of the unitary transformation that may be used to generate the multipole hamiltonian is given.

scholarly journals Gauge-Invariant Formulation of Time-Dependent Configuration Interaction Singles Method

2018 ◽  
Vol 8 (3) ◽  
pp. 433 ◽  
Author(s):  
Takeshi Sato ◽  
Takuma Teramura ◽  
Kenichi Ishikawa
Keyword(s):  
Configuration Interaction ◽  
Time Dependent ◽  
Gauge Invariant ◽  
Invariant Formulation

Infrared asymptotic behavior of gauge-invariant propagator in quantum electrodynamics

1987 ◽  
Vol 71 (1) ◽  
pp. 376-385 ◽  
Author(s):  
N. B. Skachkov ◽  
I. L. Solovtsov ◽  
O. Yu. Shevchenko
Keyword(s):  
Asymptotic Behavior ◽  
Quantum Electrodynamics ◽  
Gauge Invariant
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