scholarly journals Normalizability analysis of the generalized quantum electrodynamics from the causal point of view

2017 ◽  
Vol 32 (27) ◽  
pp. 1750165 ◽  
Author(s):  
R. Bufalo ◽  
B. M. Pimentel ◽  
D. E. Soto
Keyword(s):  
Perturbation Theory ◽  
Physical Model ◽  
Gauge Invariance ◽  
Quantum Electrodynamics ◽  
Lorentz Invariance ◽  
Point Of View ◽  
Inductive Method ◽  
S Matrix ◽  
Causal Approach

The causal perturbation theory is an axiomatic perturbative theory of the S-matrix. This formalism has as its essence the following axioms: causality, Lorentz invariance and asymptotic conditions. Any other property must be showed via the inductive method order-by-order and, of course, it depends on the particular physical model. In this work we shall study the normalizability of the generalized quantum electrodynamics in the framework of the causal approach. Furthermore, we analyze the implication of the gauge invariance onto the model and obtain the respective Ward–Takahashi–Fradkin identities.

scholarly journals Slavnov–Taylor Identities from the Causal Point of View

1997 ◽  
Vol 12 (18) ◽  
pp. 3205-3248 ◽  
Author(s):  
Michael Dütsch
Keyword(s):  
Perturbation Theory ◽  
Gauge Invariance ◽  
Point Of View ◽  
Green Functions ◽  
Gauge Transformations ◽  
Yang Mills ◽  
S Matrix ◽  
Free Fields ◽  
Matter Fields ◽  
Slavnov Taylor Identities

We continue the investigation of quantized Yang–Mills theories coupled to matter fields in the framework of causal perturbation theory which goes back to Epstein and Glaser. In this approach gauge invariance is expressed by a simple commutator relation for the S matrix and the corresponding gauge transformations are simple transformations of the free fields only. In spite of this simplicity, gauge invariance implies the usual Slavnov–Taylor identities. The main purpose of this paper is to prove the latter statement. Since the Slavnov–Taylor identities are formulated in terms of Green functions, we investigate the agreement of two perturbative definitions of Green functions, namely Epstein and Glaser's definition with the Gell-Mann–Low series.

scholarly journals A New Family of Interactions between Clothed Particles in QED

2021 ◽  
Vol 66 (10) ◽  
pp. 833
Author(s):  
A. Arslanaliev ◽  
Y. Kostylenko ◽  
O. Shebeko
Keyword(s):  
Perturbation Theory ◽  
Compton Scattering ◽  
Quantum Electrodynamics ◽  
Matrix Elements ◽  
Energy Shell ◽  
New Family ◽  
Shell Matrix ◽  
Electron Positron ◽  
S Matrix ◽  
Novel Interactions

The method of unitary clothing transformations (UCTs) has been applied to the quantum electrodynamics (QED) by using the clothed particle representation (CPR). Within CPR, the Hamiltonian for interacting electromagnetic and electron-positron fields takes the form in which the interaction operators responsible for such two-particle processes as e−e− → e−e−, e+e+ → e+e+, e−e+ → e−e+, e−e+ → yy, yy → e−e+, ye− → ye−, and ye+ → ye+ are obtained on the same physical footing. These novel interactions include the off-energy-shell and recoil effects (the latter without any expansion in (v/c)2-series) and their on-energy shell matrix elements reproduce the well-known results derived within the perturbation theory based on the Dyson expansion for the S-matrix (in particular, the Møller formula for the e−e−-scattering, the Bhabha formula for e−e+-scattering, and the Klein–Nishina one for the Compton scattering).

On the mass-independent renormalization scheme

1981 ◽  
Vol 59 (10) ◽  
pp. 1327-1333 ◽  
Author(s):  
Gerry McKeon
Keyword(s):  
Perturbation Theory ◽  
Quantum Electrodynamics ◽  
Renormalization Scheme ◽  
Second Order ◽  
Point Of View ◽  
Dimension Function ◽  
Order Coefficient ◽  
Mass Dimension ◽  
Made In

A calculation of the second order coefficient of the anomalous mass dimension function γm of Weinberg is made in quantum electrodynamics using the techniques of Sen and Sundaresan. The role of this quantity in perturbation theory is discussed from the point of view of the "Principle of Minimal Sensitivity" criterion of Stevenson.

scholarly journals A PEDAGOGICAL INTRODUCTION TO THE SLAVNOV FORMULATION OF QUANTUM YANG–MILLS THEORY

2011 ◽  
Vol 08 (04) ◽  
pp. 821-834
Author(s):  
HOSSEIN GHORBANI ◽  
GIAMPIERO ESPOSITO
Keyword(s):  
Quantum Gravity ◽  
Gauge Invariance ◽  
Lorentz Invariance ◽  
Functional Integral ◽  
Coulomb Gauge ◽  
Gauge Transformations ◽  
Yang Mills ◽  
S Matrix ◽  
Ghost Field

Over the last few years, Slavnov has proposed a formulation of quantum Yang–Mills theory in the Coulomb gauge which preserves simultaneously manifest Lorentz invariance and gauge invariance of the ghost field Lagrangian. This paper presents in detail some of the necessary calculations, i.e. those dealing with the functional integral for the S-matrix and its invariance under shifted gauge transformations. The extension of this formalism to quantum gravity in the Prentki gauge deserves consideration.

scholarly journals The causal approach proof for the equivalence of SDKP4 and SQED4 at tree-level

2020 ◽  
Vol 35 (09) ◽  
pp. 2050042
Author(s):  
J. Beltrán ◽  
B. M. Pimentel ◽  
D. E. Soto
Keyword(s):  
Perturbation Theory ◽  
Gauge Theory ◽  
Cross Section ◽  
Quantum Electrodynamics ◽  
Electromagnetic Interaction ◽  
Tree Level ◽  
Alternative Formulation ◽  
Complete Proof ◽  
Scalar Quantum ◽  
Causal Approach

The description of the electromagnetic interaction of charged spinless particles is usually formulated by the Scalar Quantum Electrodynamics. However, there is an alternative formulation given by the Duffin–Kemmer–Petiau theory: the Scalar DKP gauge theory. The proof of the equivalence between these two formulations has been discussed in many researches, but there is not yet a conclusive proof. In this paper, we initiate a complete proof in the framework of the Causal Perturbation theory, showing that both scalar formulations provide the same results for the differential cross-section at tree level.

Energy, Information, and Superluminal Speed in Quantum Electrodynamics

2020 ◽  
pp. 27-33
Author(s):  
Boris A. Veklenko
Keyword(s):  
Electromagnetic Field ◽  
Perturbation Theory ◽  
Quantum Electrodynamics ◽  
Excited Atom ◽  
Standard Quantum ◽  
Energy Information

Without using the perturbation theory, the article demonstrates a possibility of superluminal information-carrying signals in standard quantum electrodynamics using the example of scattering of quantum electromagnetic field by an excited atom.

Note on Interference Effects in Two-Step Reaction Processes

1975 ◽  
Vol 53 (23) ◽  
pp. 2590-2592
Author(s):  
J. Cejpek ◽  
J. Dobeš
Keyword(s):  
Perturbation Theory ◽  
Point Of View ◽  
Order Perturbation ◽  
Interference Effects ◽  
Qualitative Explanation ◽  
First Order ◽  
One Step ◽  
Step Transition ◽  
Reaction Processes ◽  
First Order Perturbation

The reaction processes in which a one-step transition is forbidden are analyzed from the point of view of the first order perturbation theory. The interference between two competing two-step reaction paths is found to be always constructive. A qualitative explanation of the experimentally observed reaction intensities is presented.

Planar generalized electrodynamics for one-loop amplitude in the Heisenberg picture

2021 ◽  
pp. 2150142
Author(s):  
David Montenegro ◽  
B. M. Pimentel
Keyword(s):  
Gauge Invariance ◽  
Quantum Electrodynamics ◽  
Mass Shell ◽  
Natural Extension ◽  
Quantum Model ◽  
Covariant Quantization ◽  
Heisenberg Picture ◽  
Maxwell Electrodynamics ◽  
Loop Amplitude ◽  
The One

We examine the generalized quantum electrodynamics as a natural extension of the Maxwell electrodynamics to cure the one-loop divergence. We establish a precise scenario to discuss the underlying features between photon and fermion where the perturbative Maxwell electrodynamics fails. Our quantum model combines stability, unitarity, and gauge invariance as the central properties. To interpret the quantum fluctuations without suffering from the physical conflicts proved by Haag’s theorem, we construct the covariant quantization in the Heisenberg picture instead of the Interaction one. Furthermore, we discuss the absence of anomalous magnetic moment and mass-shell singularity.

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