Worldline Path-Integral Representations for Standard Model Propagators and Effective Actions

Bhattacharya, S.

doi:10.1155/2017/2165731

Cited by 10 publications

(7 citation statements)

References 49 publications

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“…The most specific feature of the method presented here, is the use of "Weyl symbols", defined in (3.6) below, to represent fermionic operators [91][92][93]. See [94][95][96]98] for the alternative "holomorphic representation. "…”

Section: Path Integral Representation Of the Electron Propagator In An Abelian Background Fieldmentioning

confidence: 99%

Worldline master formulas for the dressed electron propagator. Part I. Off-shell amplitudes

Ahmadiniaz

Guzman

Bastianelli

et al. 2020

J. High Energ. Phys.

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In the first-quantised worldline approach to quantum field theory, a longstanding problem has been to extend this formalism to amplitudes involving open fermion lines while maintaining the efficiency of the well-tested closed-loop case. In the present series of papers, we develop a suitable formalism for the case of quantum electrodynamics in vacuum (part one and two) and in a constant external electromagnetic field (part three), based on second-order fermions and the symbol map. We derive this formalism from standard field theory, but also give an alternative derivation intrinsic to the worldline theory. In this first part, we use it to obtain a Bern-Kosower type master formula for the fermion propagator, dressed with N photons, in terms of the "N -photon kernel," where offshell this kernel appears also in "subleading" terms involving only N − 1 of the N photons. Although the parameter integrals generated by the master formula are equivalent to the usual Feynman diagrams, they are quite different since the use of the inverse symbol map avoids the appearance of long products of Dirac matrices. As a test we use the N = 2 case for a recalculation of the one-loop fermion self energy, in D dimensions and arbitrary covariant gauge, reproducing the known result. We find that significant simplification can be achieved in this calculation by choosing an unusual momentum-dependent gauge parameter.

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Section: Path Integral Representation Of the Electron Propagator In An Abelian Background Fieldmentioning

confidence: 99%

Worldline master formulas for the dressed electron propagator. Part I. Off-shell amplitudes

Ahmadiniaz

Guzman

Bastianelli

et al. 2020

J. High Energ. Phys.

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“…theories presumably capture some of the properties of higher dimensional objects. Finally we discuss worldline fermions, which would be required to produce space-time fermions but can also be considered independently [4,[25][26][27][28].…”

Section: Jhep12(2020)069mentioning

confidence: 99%

Worldline theories with towers of internal states

Abel

Lewis

2020

J. High Energ. Phys.

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We study particle theories that have a tower of worldline internal degrees of freedom. Such a theory can arise when the worldsheet of closed strings is dimensionally reduced to a worldline, in which case the tower is infinite with regularly spaced masses. But our discussion is significantly more general than this, and there is scope to consider all kinds of internal degrees of freedom carried by the propagating particle. For example it is possible to consider towers corresponding to other geometries, or towers with no obvious geometric interpretation that still yield a modular invariant theory. Truncated towers generate non-local particle theories that share with string theory the property of having a Gross-Mende-like saddle point in their amplitudes. This provides a novel framework for constructing exotic theories which may have desirable properties such as finiteness and modular invariance.

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“…In [76] this approach is shown to be an efficient alternative to Feynman diagrams for calculations such as linear and non-linear Compton scattering and the electron self energy and its tensor decomposition. For a similar but distinct approach to the open fermion line see [77].…”

Section: The Open Fermion Linementioning

confidence: 99%

Quantum mechanical path integrals in the first quantised approach to quantum field theory

Edwards,

Schubert

2019

Preprint

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Perturbative quantum field theory usually uses second quantisation and Feynman diagrams. The worldline formalism provides an alternative approach based on first quantised particle path integrals, similar in spirit to string perturbation theory. Here we review the history, main features and present applications of the formalism. Our emphasis is on recent developments such as the path integral representation of open fermion lines, the description of colour using auxiliary worldline fields, incorporation of higher spin, and extension of the formalism to non-commutative space.

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Worldline Path-Integral Representations for Standard Model Propagators and Effective Actions

Cited by 10 publications

References 49 publications

Worldline master formulas for the dressed electron propagator. Part I. Off-shell amplitudes

Worldline master formulas for the dressed electron propagator. Part I. Off-shell amplitudes

Worldline theories with towers of internal states

Quantum mechanical path integrals in the first quantised approach to quantum field theory

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