Gauge invariance, the vertex function, and the magnitude of the renormalization constants of quantum electrodynamics

1963 ◽  
Vol 29 (5) ◽  
pp. 1098-1119 ◽  
Author(s):  
O. Fleischman
Keyword(s):  
Gauge Invariance ◽  
Vertex Function ◽  
Quantum Electrodynamics ◽  
Renormalization Constants

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.

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.

The full vertex functions constrained by the longitudinal and transverse Ward–Takahashi identities in massless QED3 theory

2021 ◽  
pp. 2150039
Author(s):  
Yang Yu ◽  
Jian-Feng Li
Keyword(s):  
Vertex Function ◽  
Quantum Electrodynamics ◽  
Gauge Theories ◽  
Chiral Limit ◽  
Wilson Line ◽  
Axial Vector ◽  
Fermion Masses ◽  
Low Dimensional ◽  
Full Vector

In this paper, we find apart from the Ward–Takahashi (WT) identity, the identity between gamma matrices can also constrain the vertex functions in low-dimensional gauge theories. In (1 + 1) dimensions, the identity between gamma matrices gives the identity between vector and axial-vector vertex functions while in (2 + 1) dimensions it leads to the identity between vector and tensor vertex functions. Then, we derive the expressions of the full scalar, vector and tensor vertex functions in (2 + 1) dimensions Quantum Electrodynamics (QED3) by using the longitudinal and transverse WT identities for vector and tensor currents. Furthermore, we find that in the chiral limit with zero fermion masses, the contribution of Wilson line in full vector vertex function is eliminated and the full vector vertex function is strictly expressed in terms of the fermion propagators when using the identity between vector and tensor vertex functions to further constraint the vertex functions.

The form of the divergencies in quantum electrodynamics

1956 ◽  
Vol 234 (1197) ◽  
pp. 296-300 ◽  
Keyword(s):  
Quantum Electrodynamics ◽  
Functional Equations ◽  
Asymptotic Form ◽  
Particle Charge ◽  
High Energies ◽  
Renormalization Constants

The results of Landau and his collaborators on the asymptotic form of the propagators for high energies and the dependence of the renormalization constants on the cut-off are re­-derived, starting from the functional equations of Gell-Mann & Low. It is proved further that, in electrodynamics, the cut-off cannot be made arbitrarily large, without the ‘bare-particle’ charge becoming imaginary.

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