Asymptotic Behavior of the Vertex Function in Quantum Electrodynamics

1971 ◽  
Vol 4 (2) ◽  
pp. 458-475 ◽  
Author(s):  
Paul M. Fishbane ◽  
J. D. Sullivan
Keyword(s):  
Asymptotic Behavior ◽  
Vertex Function ◽  
Quantum Electrodynamics

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

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.

ON THE ASYMPTOTIC BEHAVIOR OF THE PHOTON PROPAGATOR IN QUANTUM ELECTRODYNAMICS

2002 ◽  
Vol 17 (02) ◽  
pp. 279-296
Author(s):  
ANDRZEJ R. ALTENBERGER ◽  
JOHN S. DAHLER
Keyword(s):  
Functional Equation ◽  
Asymptotic Behavior ◽  
Quantum Electrodynamics ◽  
Anomalous Dimension ◽  
Group Method ◽  
Photon Propagator ◽  
Renormalization Group Method ◽  
Effective Coupling ◽  
Transverse Photon ◽  
Self Similar

A new renormalization group method is used to calculate the photon propagator in the high four-momentum regime. The assumption that this propagator is a self-similar object leads directly to a functional equation of evolution involving an invariant charge (effective coupling function) which, in turn, is a functional of the propagator. Numerical results produced by this theory depend on a single unknown, namely, the scale in which the four-momentum k is measured. Calculations are presented for several values of this scale. From these it is concluded that the transverse photon propagator behaves asymptotically as D⊥(k)~k2(λ-1) with the value of λ (the anomalous dimension) falling in the range (0.12, 1).

scholarly journals Quantum Electrodynamics in Strong Magnetic Fields. I. Electron States

1983 ◽  
Vol 36 (6) ◽  
pp. 755 ◽  
Author(s):  
DB Melrose ◽  
AJ Parle
Keyword(s):  
Vertex Function ◽  
Quantum Electrodynamics ◽  
Laguerre Polynomials ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Coordinate Space ◽  
Positron States ◽  
Symmetry Properties ◽  
Moment Operator ◽  
Independent Quantity

Dirac's equation in the presence of a static magnetic field is solved in terms of both cartesian and cylindrical coordinates, and solutions are found for three different spin operators. Choosing the spin to correspond to the parallel component Ilz of the magnetic moment operator leads to wavefunctions (a) which are symmetric between electron and positron states and (b) which are eigenfunctions of the Hamiltonian including radiative corrections. A vertex function [y:',~(k)l~ is defined and shown to be proportional to a gauge independent quantity [T::~(k)l". Symmetry properties of [T~:~(k)l~ are derived in the case where the spin corresponds to Ilz. The use of the vertex function is illustrated by deriving the electron propagator in coordinate space from the vacuum expectation value. Properties of functions J~, _n(x) which appear extensively and are related to generalized Laguerre polynomials are derived and summarized in the Appendix.

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