Derivative expansion of the effective action and vacuum instability for QED in 2+1 dimensions

Cangemi, Daniel; D’Hoker, Eric; Dunne, Gerald V.

doi:10.1103/physrevd.51.r2513

Cited by 85 publications

(144 citation statements)

References 20 publications

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“…The combination of all the different models under a common description is made possible by using the 'coarse graining' provided by a low-momentum approximation. Our approach consists of constructing a 'classical' effective theory for the gauge field A µ , which can be interpreted as arising after integrating out the massive matter fields [4], keeping a finite number of derivatives acting on F µν . We may call the theory for A µ at this stage 'classical', since A µ is not yet quantized.…”

Section: Introductionmentioning

confidence: 99%

Effective theory for parity-conserving three-dimensional QED

1996

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We consider a higher derivative effective theory for an Abelian gauge field in three dimensions, which represents the result of integrating out heavy matter fields interacting with a classical gauge field in a parity-conserving way.We retain terms containing up to two derivatives of F µν , but make no assumption about the strength of this field. We then quantize the gauge field, * ijra@thphys.ox.ac.uk † fosco@cab.cnea.edu.ar ‡ fmazzi@df.uba.ar 1 and compute the one-loop effective action for a constant F µν . The result is explicitly evaluated for the case of a constant magnetic field.

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Section: Introductionmentioning

confidence: 99%

Effective theory for parity-conserving three-dimensional QED

1996

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“…Apart from the effective action in a constant field, the string-inspired method has also been extensively applied to the calculation of the full one-loop QED effective action in an arbitrary background field, using the derivative expansion [39,40,41].…”

Section: The "String-inspired" Approachmentioning

confidence: 99%

QED in the worldline representation

Schubert

2007

AIP Conference Proceedings

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Abstract. Simultaneously with inventing the modern relativistic formalism of quantum electrodynamics, Feynman presented also a first-quantized representation of QED in terms of worldline path integrals. Although this alternative formulation has been studied over the years by many authors, only during the last fifteen years it has acquired some popularity as a computational tool. I will shortly review here three very different techniques which have been developed during the last few years for the evaluation of worldline path integrals, namely (i) the "string-inspired formalism", based on the use of worldline Green functions, (ii) the numerical "worldline Monte Carlo formalism", and (iii) the semiclassical "worldline instanton" approach.Keywords: Quantum electrodynamics, perturbation theory, worldline, string inspired formalism PACS: 11.15. Bt,11.15.Kt,11.25.Db,12.20.Ds FEYNMAN'S WORLDLINE REPRESENTATION OF QEDIn 1950 Feynman presented, in an appendix to one of his groundbreaking papers on the modern, manifestly relativistic formalism of perturbative QED [1], also a first-quantized formulation of scalar QED, "for its own interest as an alternative to the formulation of second quantization". There he provides a simple rule for constructing the complete scalar QED S-matrix by representing virtual scalars and photons in terms of relativistic particle path integrals, and coupling them in all possible ways. Restricting ourselves, for simplicity, to the purely photonic part of the S-matrix (no external scalars), and moreover to the "quenched" contribution (only one virtual scalar), this "worldline representation" can be given most compactly in terms of the (quenched) effective action Γ[A]:Here T denotes the proper-time of the scalar particle in the loop, m its mass, and x(T )=x(0) Dx(τ) a path integral over all closed loops in spacetime with fixed periodicity in the proper-time. The worldline action S[x(τ)] has three parts,(see fig. 1). Of these, the kinetic term S 0 describes the free propagation of the scalar, S ext its interaction with the external field, and S int the corrections due to internal photon exchanges in the loop. The connection to a standard Feynman diagrammatic description is made simply by expanding out the two interaction exponentials.

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“…Recently a new sample of papers devoted to DSB in external electromagnetic field have been published [8], [9]. It shed a new light onto the universal character of magnetic catalysis, which means that magnetic field breaks chiral symmetry for any value of its strength.…”

Section: Introductionmentioning

confidence: 99%

Dynamical symmetry breaking in Nambu-Jona-Lasinio model under the influence of external electromagnetic and gravitational fields

Elizalde¹,

Shil'nov²

1998

AIP Conference Proceedings

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Abstract. Dynamical symmetry breaking is investigated for a four-fermion NambuJona-Lasinio model in external electromagnetic and gravitational fields. An effective potential is calculated in the leading order of the large-N expansion using the propertime Schwinger formalism.Phase transitions accompanying a chiral symmetry breaking in the Nambu-JonaLasinio model are studied in detail. A magnetic calalysis phenomenon is shown to exist in curved spacetime but it turns out to lose its universal character because the chiral symmetry is restored above some critical positive value of the spacetime curvature.

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Derivative expansion of the effective action and vacuum instability for QED in 2+1 dimensions

Cited by 85 publications

References 20 publications

Effective theory for parity-conserving three-dimensional QED

Effective theory for parity-conserving three-dimensional QED

QED in the worldline representation

Dynamical symmetry breaking in Nambu-Jona-Lasinio model under the influence of external electromagnetic and gravitational fields

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