A gauge-invariant model of quantum electrodynamics without spinor fields

E. Prugovečki

doi:10.1007/bf02856389

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

Journal of High Energy Physics ◽

10.1007/jhep02(2021)127 ◽

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.

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

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1970.0192 ◽

1970 ◽

Vol 319 (1539) ◽

pp. 549-563 ◽

Cited By ~ 44

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.

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Infrared asymptotic behavior of gauge-invariant propagator in quantum electrodynamics

Theoretical and Mathematical Physics ◽

10.1007/bf01029098 ◽

1987 ◽

Vol 71 (1) ◽

pp. 376-385 ◽

Cited By ~ 3

Author(s):

N. B. Skachkov ◽

I. L. Solovtsov ◽

O. Yu. Shevchenko

Keyword(s):

Asymptotic Behavior ◽

Quantum Electrodynamics ◽

Gauge Invariant

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a0(980) AND f0(980) MESONS AS HADRONIC MOLECULES

International Journal of Modern Physics A ◽

10.1142/s0217751x09044097 ◽

2009 ◽

Vol 24 (02n03) ◽

pp. 568-571 ◽

Cited By ~ 2

Author(s):

T. BRANZ ◽

T. GUTSCHE ◽

V. E. LYUBOVUTSKIJ

Keyword(s):

Size Effects ◽

Bound States ◽

Finite Size ◽

Finite Size Effects ◽

Gauge Invariant ◽

Electromagnetic Decay ◽

Invariant Model ◽

Scalar Mesons ◽

Decay Properties ◽

Good Agreement

We discuss a possible interpretation of the scalar mesons f0(980) and a0(980) as hadronic molecules - bound states of K and [Formula: see text] mesons. Using a phenomenological Lagrangian approach we calculate strong as well as the electromagnetic decay properties of both scalars. The covariant and gauge invariant model, which also allows for finite size effects of the hadronic molecule, delivers results in good agreement with experimental data.

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ON AN AMBIGUOUS INTEGRAL IN QUANTUM ELECTRODYNAMICS

Canadian Journal of Physics ◽

10.1139/p67-001 ◽

1967 ◽

Vol 45 (1) ◽

pp. 1-5

Author(s):

Robert E. Pugh

Keyword(s):

Wave Function ◽

Quantum Electrodynamics ◽

Vacuum Polarization ◽

Wave Function Renormalization ◽

Gauge Invariant ◽

Photon Field

An integral that appears in several contexts in quantum electrodynamics is evaluated without the usual ambiguity. The result is applied to (1) the contribution of vacuum polarization to the interpolating photon field, (2) wave-function renormalization, and (3) a gauge-independent formulation of quantum electrodynamics. In the first two cases the expected results are obtained, while in the last case the particular formulation is shown to be, in fact, not gauge invariant.

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