Completeness and orthonormality of the Volkov states and the Volkov propagator in configuration space

Piazza, A. Di

doi:10.1103/physrevd.97.056028

Cited by 31 publications

(24 citation statements)

References 101 publications

(126 reference statements)

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“…Now, we have explicitly shown in Ref. [71] (see also Refs. [66][67][68]) that the operator G can be written in the form…”

Section: Notationmentioning

confidence: 85%

“…The notation employed below is the same as in Ref. [71] but it is convenient to report here the main definitions. As we have mentioned in the Introduction, the present paper focuses on studying radiative corrections in a general plane-wave field.…”

Section: Notationmentioning

confidence: 99%

“…[3]), the corresponding states being known as Volkov states. An alternative, equivalent technique is the so-called operator technique, first proposed by Schwinger [65] and then developed for the case of a background plane wave [66][67][68][69][70][71], which does not require the explicit solution of the Dirac equation in the plane-wave field.…”

Section: Introductionmentioning

confidence: 99%

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One-loop vertex correction in a plane wave

Piazza

Lopez-Lopez

2020

Phys. Rev. D

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We compute the general expression of the one-loop vertex correction in an arbitrary plane-wave background field for the case of two on-shell external electrons and an off-shell external photon. The properties of the vertex corrections under gauge transformations of the plane-wave background field and of the radiation field are studied. Concerning the divergences of the vertex correction, the infrared one is cured by assigning a finite mass to the photon, whereas the ultraviolet one is shown to be renormalized exactly as in vacuum. Finally, the corresponding expression of the vertex correction within the locally constant crossed field approximation is also derived and the high-field asymptotic is shown to scale according to the Ritus-Narozhny conjecture, although the terms featuring the leading-order dependence on the field are found not to contribute to physical transition amplitudes.

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“…Now, we have explicitly shown in Ref. [71] (see also Refs. [66][67][68]) that the operator G can be written in the form…”

Section: Notationmentioning

confidence: 85%

Section: Notationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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One-loop vertex correction in a plane wave

Piazza

Lopez-Lopez

2020

Phys. Rev. D

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“…The standard representation of the Volkov propagator reads [2] (see also Ref. [77] for an expression of the propagator in terms of special functions where the integral over the four-momentum is taken explicitly)…”

Section: Statesmentioning

confidence: 99%

Quasiclassical representation of the Volkov propagator and the tadpole diagram in a plane wave

Di Piazza,

Fronimos

2022

Preprint

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The solution of the Dirac equation in the presence of an arbitrary plane wave, corresponding to the so-called Volkov states, has provided an enormous insight in strong-field QED.In [Phys. Rev. A 103, 076011 (2021)] a new "fully quasiclassical" representation of the Volkov states has been found, which is equivalent to the one known in the literature but which more transparently shows the quasiclassical nature of the quantum dynamics of an electron in a plane-wave field. Here, we derive the corresponding expression of the propagator by constructing it using the fully quasiclassical form of the Volkov states. The found expression allows one, together with the fully quasiclassical expression of the Volkov states, to compute probabilities in strong-field QED in an intense plane wave by manipulating only 2-by-2 rather than 4-by-4 Dirac matrices as in the usual approach. Moreover, apart from the exponential functions featuring the classical action of an electron in a plane wave, the fully quasiclassical Volkov propagator only depends on the electron kinetic four-momentum in the plane wave, which is a gauge-invariant quantity. Finally, we also compute the tadpole diagram in a plane wave starting from the Volkov propagator and we show that, although it is divergent, its contribution can be always absorbed via a renormalization of the external field. I. INTRODUCTIONThe investigation of quantum electrodynamical processes occurring in the presence of intense laser fields has significantly improved our theoretical understanding of the strong-field regime of QED [1][2][3][4][5][6][7][8][9]. Strong-field QED signatures in the emission spectra of ultrarelativistic electrons colliding with an intense laser beam have also been observed in recent experiments [10,11]. In the strong-field regime of QED the leptons involved in the processes experience in their rest frames

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“…The aim of this paper is to extend those calculations to the full Lorentz (or R ξ ) class of gauges. See also [20] for a discussion of gauge transformations and the Volkov propagator.…”

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One loop Volkov propagator in the Lorentz class of gauges

Lavelle

McMullan

2019

Physics Letters B

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We calculate the ultraviolet divergences in a weak field expansion of the Volkov propagator. This is done for the full Lorentz class of gauges. The expected gauge invariance of the vacuum mass shift in each sideband is recovered. However, the renormalisation of the background induced mass shift is shown to be gauge dependent. In particular, we show that it vanishes in Landau gauge. We find that only in that gauge does the vacuum renormalisation remove all ultraviolet divergences.

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Completeness and orthonormality of the Volkov states and the Volkov propagator in configuration space

Cited by 31 publications

References 101 publications

One-loop vertex correction in a plane wave

One-loop vertex correction in a plane wave

Quasiclassical representation of the Volkov propagator and the tadpole diagram in a plane wave

One loop Volkov propagator in the Lorentz class of gauges

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