Landau-Khalatnikov-Fradkin transformation of the fermion propagator in massless reduced QED

A. James; A. V. Kotikov; S. Teber

doi:10.1103/physrevd.101.045011

The pole of the fermion propagator in a general class of gauges

Physics Letters B ◽

10.1016/j.physletb.2013.08.053 ◽

2013 ◽

Vol 726 (1-3) ◽

pp. 493-496 ◽

Cited By ~ 1

Author(s):

Ashok K. Das ◽

J. Frenkel

Keyword(s):

General Class ◽

Fermion Propagator

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Worldline master formulas for the dressed electron propagator. Part 2. On-shell amplitudes

Journal of High Energy Physics ◽

10.1007/jhep01(2022)050 ◽

2022 ◽

Vol 2022 (1) ◽

Author(s):

N. Ahmadiniaz ◽

V. M. Banda Guzmán ◽

F. Bastianelli ◽

O. Corradini ◽

J. P. Edwards ◽

...

Keyword(s):

Cross Sections ◽

Drop Out ◽

Matrix Elements ◽

Fermion Propagator ◽

Particle Path ◽

Path Integral Representation ◽

Fermion Line ◽

Electron Propagator ◽

The Matrix ◽

Standard Linear

Abstract In the first part of this series, we employed the second-order formalism and the “symbol” map to construct a particle path-integral representation of the electron propagator in a background electromagnetic field, suitable for open fermion-line calculations. Its main advantages are the avoidance of long products of Dirac matrices, and its ability to unify whole sets of Feynman diagrams related by permutation of photon legs along the fermion lines. We obtained a Bern-Kosower type master formula for the fermion propagator, dressed with N photons, in terms of the “N-photon kernel,” where this kernel appears also in “subleading” terms involving only N − 1 of the N photons.In this sequel, we focus on the application of the formalism to the calculation of on-shell amplitudes and cross sections. Universal formulas are obtained for the fully polarised matrix elements of the fermion propagator dressed with an arbitrary number of photons, as well as for the corresponding spin-averaged cross sections. A major simplification of the on-shell case is that the subleading terms drop out, but we also pinpoint other, less obvious simplifications.We use integration by parts to achieve manifest transversality of these amplitudes at the integrand level and exploit this property using the spinor helicity technique. We give a simple proof of the vanishing of the matrix element for “all +” photon helicities in the massless case, and find a novel relation between the scalar and spinor spin-averaged cross sections in the massive case. Testing the formalism on the standard linear Compton scattering process, we find that it reproduces the known results with remarkable efficiency. Further applications and generalisations are pointed out.

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O(\aplha_L^2) perturbative Green's functions of the fermion propagator, and of local and extended fermion bilinear operators, with Symanzik improved gluons and SLiNC fermions.

10.22323/1.105.0240 ◽

2011 ◽

Author(s):

Apostolos Skouroupathis ◽

Haralambos Panagopoulos

Keyword(s):

Green's Functions ◽

Green’S Functions ◽

Fermion Propagator ◽

Bilinear Operators

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Feynman rules for Weyl spinors with mixed Dirac and Majorana mass terms

Lithuanian Journal of Physics ◽

10.3952/physics.v56i3.3364 ◽

2016 ◽

Vol 56 (3) ◽

pp. 149-163

Author(s):

Vytautas Dūdėnas ◽

Thomas Gajdosik

Keyword(s):

Path Integral ◽

Tree Level ◽

Fermion Propagator ◽

Weyl Spinor ◽

Majorana Mass ◽

Basic Formalism ◽

Feynman Rules ◽

Mass Terms ◽

Level Analysis

We present a basic formalism for using the Weyl spinor notation in Feynman rules. We focus on Weyl spinors with mixed Dirac and Majorana mass terms. To clarify the definitions we derive the Feynman rules from the path integral and present two examples: loop corrections for a fermion propagator and a tree level analysis of a seesaw toy model.

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General Properties of Higher-Spin Fermion Interaction Currents and Their Test in πN-Scattering

Ukrainian Journal of Physics ◽

10.15407/ujpe57.11.1179 ◽

2021 ◽

Vol 57 (11) ◽

pp. 1179

Author(s):

Yu.V. Kulish ◽

E.V. Rybachuk

Keyword(s):

Angular Momentum ◽

Partial Wave ◽

Total Angular Momentum ◽

Mass Shell ◽

Present Approach ◽

Partial Wave Analysis ◽

Wave Analysis ◽

Fermion Propagator ◽

Higher Spin ◽

Spin Tensors

The currents of higher-spin fermion interactions with zero- and half-spin particles are derived. They can be used for the N*(J) ↔ Nπ-transitions (N*(J) is thenucleon resonance with the J spin). In accordance with the theorem on currents and fields, the spin-tensors of these currents are traceless, and their products with the γ-matrices and the higher-spin fermion momentum vanish, similarly to the field spin-tensors. Such currents are derived explicitly for J=3/2and 5/2. It is shown that, in the present approach, the scale dimension of a higher spin fermion propagator equals to –1 for any J ≥ 1/2. The calculations indicate that the off-mass-shell N* contributions to the s-channel amplitudes correspond to J = JπN only ( JπN is the total angular momentum of the πN-system). As contrast, in the usually exploited approaches, such non-zero amplitudes correspond to 1/2 ≤ JπN ≤ J. In particular, the usually exploited approaches give non-zero off-mass-shell contributions of the ∆(1232)-resonance to the amplitudes S31, P31( JπN = 1/2) and P33, D33(JπN = 3/2), but our approach – to P33 and D33 only. The comparison of these results with the data of the partial wave analysis on the S31-amplitude in the ∆(1232)-region shows the better agreement for the present approach.

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