ON AN AMBIGUOUS INTEGRAL IN QUANTUM ELECTRODYNAMICS

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.

PHASE STRUCTURE OF QED3 AT FINITE CHEMICAL POTENTIAL AND TEMPERATURE

2007 ◽  
Vol 22 (06) ◽  
pp. 449-456 ◽  
Author(s):  
MIN HE ◽  
HONG-TAO FENG ◽  
WEI-MIN SUN ◽  
HONG-SHI ZONG
Keyword(s):  
Phase Diagram ◽  
Wave Function ◽  
Symmetry Breaking ◽  
Quantum Electrodynamics ◽  
Phase Structure ◽  
Chemical Potential ◽  
Chiral Symmetry Breaking ◽  
Three Dimensional ◽  
Mass Function ◽  
Wave Function Renormalization

We study the dynamical chiral symmetry breaking (DCSB) of three-dimensional quantum electrodynamics (QED3) at finite chemical potential and temperature in the framework of Dyson–Schwinger approach. Based on the rainbow approximation and assumption that the wave-function renormalization factor equals to one, the dynamically generated mass function is derived and then the corresponding phase diagram in the (T, μ) plane is obtained.

scholarly journals AXIAL ANOMALY THROUGH ANALYTIC REGULARIZATION

1999 ◽  
Vol 14 (03) ◽  
pp. 177-183 ◽  
Author(s):  
L. A. MANZONI ◽  
B. M. PIMENTEL ◽  
J. L. TOMAZELLI
Keyword(s):  
Quantum Electrodynamics ◽  
Vacuum Polarization ◽  
Green's Functions ◽  
Green’S Functions ◽  
Gauge Invariant ◽  
Axial Anomaly ◽  
Analytic Regularization ◽  
Correct Implementation

In this work we consider the two-point Green's functions in (1+1)-dimensional quantum electrodynamics and show that the correct implementation of analytic regularization gives a gauge invariant result for the vacuum polarization amplitude and the correct coefficient for the axial anomaly.

scholarly journals A General Treatment of Oblique Parameters

1997 ◽  
Vol 12 (08) ◽  
pp. 1511-1529 ◽  
Author(s):  
Anirban Kundu ◽  
Probir Roy
Keyword(s):  
Wave Function ◽  
Linear Approximation ◽  
Gauge Boson ◽  
Vacuum Polarization ◽  
Wave Function Renormalization ◽  
Weak Boson ◽  
The Third ◽  
The Difference ◽  
First Time ◽  
Expansion Scheme

A re-examination is made of one-loop oblique electroweak corrections. General definitions are given of the oblique parameters without reference to any q2 expansion scheme. The old oblique parameters S, T and U are defined as differences of gauge boson vacuum polarization Π functions and suffice for describing certain observable ratios on the Z peak and the ρ parameter at q2 = 0. Regarding the new oblique parameters V, W and X, the first two are defined in terms of differences of Π functions as well as the wave function renormalization of the corresponding weak boson, and the third in terms of the difference of differences of two Π functions for γ - Z mixing. Explicit expressions for measurable quantities involving all six oblique parameters are given and experimental bounds are obtained on the latter, some for the first time. A review of these constraints suggests that the linear approximation of Peskin and Takeuchi is robust.

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.

scholarly journals Photon splitting in strongly magnetized medium with taking into account positronium influence

2018 ◽  
Vol 191 ◽  
pp. 08011
Author(s):  
R.A. Anikin ◽  
M.V. Chistyakov ◽  
D.A. Rumyantsev ◽  
D.M. Shlenev
Keyword(s):  
Wave Function ◽  
Absorption Rate ◽  
Wave Function Renormalization ◽  
Selection Rules ◽  
Dispersion Properties ◽  
Photon Splitting

The process of the photon splitting, γ → γγ, is investigated in strongly magnetized vacuum with taking into account positronium influence. The dispersion properties of photons and the new polarization selection rules are obtained. The absorption rate of the leading photon splitting channels are calculated with taking account of the photon dispersion and wave function renormalization.

scholarly journals If the propagator of QED were reversed, the mathematics of Nature would be much simpler

2020 ◽  
Vol 18 ◽  
pp. 129-153
Author(s):  
Jeffrey Boyd
Keyword(s):  
Wave Function ◽  
Path Integral ◽  
Quantum Electrodynamics ◽  
Probability Amplitude ◽  
Integral Approach ◽  
Everyday Experience ◽  
Wave Function Collapse ◽  
Path Integral Approach ◽  
Classical World ◽  
The Many

In Quantum ElectroDynamics (QED) the propagator is a function that describes the probability amplitude of a particle going from point A to B. It summarizes the many paths of Feynman’s path integral approach. We propose a reverse propagator (R-propagator) that, prior to the particle’s emission, summarizes every possible path from B to A. Wave function collapse occurs at point A when the particle randomly chooses one and only one of many incident paths to follow backwards with a probability of one, so it inevitably strikes detector B. The propagator and R-propagator both calculate the same probability amplitude. The R-propagator has an advantage over the propagator because it solves a contradiction inside QED, namely QED says a particle must take EVERY path from A to B. With our model the particle only takes one path. The R-propagator had already taken every path into account. We propose that this tiny, infinitesimal change from propagator to R-propagator would vastly simplify the mathematics of Nature. Many experiments that currently describe the quantum world as weird, change their meaning and no longer say that. The quantum world looks and acts like the classical world of everyday experience.

scholarly journals Semi-classical approximations based on Bohmian mechanics

2020 ◽  
Vol 35 (14) ◽  
pp. 2050070 ◽  
Author(s):  
Ward Struyve
Keyword(s):  
Wave Function ◽  
Quantum Theory ◽  
Quantum Gravity ◽  
Quantum Electrodynamics ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Bohmian Mechanics ◽  
Expectation Values ◽  
Usual Approach ◽  
Classical Approximation

Semi-classical theories are approximations to quantum theory that treat some degrees of freedom classically and others quantum mechanically. In the usual approach, the quantum degrees of freedom are described by a wave function which evolves according to some Schrödinger equation with a Hamiltonian that depends on the classical degrees of freedom. The classical degrees of freedom satisfy classical equations that depend on the expectation values of quantum operators. In this paper, we study an alternative approach based on Bohmian mechanics. In Bohmian mechanics the quantum system is not only described by the wave function, but also with additional variables such as particle positions or fields. By letting the classical equations of motion depend on these variables, rather than the quantum expectation values, a semi-classical approximation is obtained that is closer to the exact quantum results than the usual approach. We discuss the Bohmian semi-classical approximation in various contexts, such as nonrelativistic quantum mechanics, quantum electrodynamics and quantum gravity. The main motivation comes from quantum gravity. The quest for a quantum theory for gravity is still going on. Therefore a semi-classical approach where gravity is treated classically may be an approximation that already captures some quantum gravitational aspects. The Bohmian semi-classical theories will be derived from the full Bohmian theories. In the case there are gauge symmetries, like in quantum electrodynamics or quantum gravity, special care is required. In order to derive a consistent semi-classical theory it will be necessary to isolate gauge-independent dependent degrees of freedom from gauge degrees of freedom and consider the approximation where some of the former are considered classical.

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