UV-divergent part of the vacuum polarization tensor in the temporal gauge with the LM prescription. BRS identities

The UV-divergent part of the one-loop contribution to the vacuum polarization tensor [Formula: see text] is shown to satisfy the BRS identities governing its dependence on the time-like vector n and the auxiliary space-like vector n′ introduced by the generalized Leibbrandt-Mandelstam (LM) prescription. As far as we know the BRS identity for the n′ dependence cannot be obtained within the pragmatic approach to the LM prescription. In order to circumvent the problem the LM prescription is incorporated into a BRS-invariant action. The BRS identity for n′ provides an example of a situation where terms of order η combine with loop integrals that are singular as η→0 yielding a finite contribution.

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SECOND-ORDER CORRECTIONS TO QED COUPLING AT LOW TEMPERATURE

International Journal of Modern Physics A ◽

10.1142/s0217751x08041712 ◽

2008 ◽

Vol 23 (29) ◽

pp. 4709-4719 ◽

Cited By ~ 5

Author(s):

SAMINA S. MASOOD ◽

MAHNAZ HASEEB

Keyword(s):

Low Temperatures ◽

Vacuum Polarization ◽

Second Order ◽

Electromagnetic Properties ◽

Electron Mass ◽

Polarization Tensor ◽

Coupling Constant ◽

Electric Permittivity ◽

Thermal Medium ◽

Vacuum Polarization Tensor

We calculate the second-order corrections to vacuum polarization tensor of photons at low temperatures, i.e. T ≪ 1010 K (T ≪ me). The thermal contributions to the QED coupling constant are evaluated at temperatures below the electron mass that is T < me. Renormalization of QED at these temperatures has explicitly been checked. The electromagnetic properties of such a thermal medium are modified. Parameters like electric permittivity and magnetic permeability of such a medium are no more constant and become functions of temperature.

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Derivative corrections to the Heisenberg-Euler effective action

Journal of High Energy Physics ◽

10.1007/jhep09(2021)070 ◽

2021 ◽

Vol 2021 (9) ◽

Cited By ~ 1

Author(s):

Felix Karbstein

Keyword(s):

Electric Fields ◽

Effective Action ◽

Vacuum Polarization ◽

Strong Field ◽

Background Field ◽

Polarization Tensor ◽

Quantum Vacuum ◽

Electron Positron ◽

Vacuum Polarization Tensor ◽

Electron Positron Pair

Abstract We show that the leading derivative corrections to the Heisenberg-Euler effective action can be determined efficiently from the vacuum polarization tensor evaluated in a homogeneous constant background field. After deriving the explicit parameter-integral representation for the leading derivative corrections in generic electromagnetic fields at one loop, we specialize to the cases of magnetic- and electric-like field configurations characterized by the vanishing of one of the secular invariants of the electromagnetic field. In these cases, closed-form results and the associated all-orders weak- and strong-field expansions can be worked out. One immediate application is the leading derivative correction to the renowned Schwinger-formula describing the decay of the quantum vacuum via electron-positron pair production in slowly-varying electric fields.

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Perturbative Chern-Simons theory in the light-cone gauge. The one-loop vacuum polarization tensor in a gauge-invariant formalism

Nuclear Physics B ◽

10.1016/0550-3213(92)90303-s ◽

1992 ◽

Vol 377 (3) ◽

pp. 593-621 ◽

Cited By ~ 14

Author(s):

G. Leibbrandt ◽

C.P. Martin

Keyword(s):

Light Cone ◽

Vacuum Polarization ◽

Simons Theory ◽

Polarization Tensor ◽

Gauge Invariant ◽

Light Cone Gauge ◽

The One ◽

Chern Simons ◽

Vacuum Polarization Tensor ◽

Chern Simons Theory

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CONSISTENCY OF THE HYBRID REGULARIZATION WITH HIGHER COVARIANT DERIVATIVE AND INFINITELY MANY PAULI–VILLARS

International Journal of Modern Physics A ◽

10.1142/s0217751x01005031 ◽

2001 ◽

Vol 16 (22) ◽

pp. 3755-3783

Author(s):

KOH-ICHI NITTOH

Keyword(s):

Covariant Derivative ◽

Vacuum Polarization ◽

Gauge Theories ◽

Polarization Tensor ◽

Logarithmic Divergence ◽

Yang Mills ◽

Higher Covariant Derivative ◽

Group Functions ◽

Supersymmetric Gauge ◽

Vacuum Polarization Tensor

We study the regularization and renormalization of the Yang–Mills theory in the framework of the manifestly invariant formalism, which consists of a higher covariant derivative with an infinitely many Pauli–Villars fields. Unphysical logarithmic divergence, which is the problematic point on the Slavnov method, does not appear in our scheme, and the well-known value of the renormalization group functions are derived. The cancellation mechanism of the quadratic divergence is also demonstrated by calculating the vacuum polarization tensor of the order of Λ0 and Λ-4. These results are the evidence that our method is valid for intrinsically divergent theories and is expected to be available for the theory which contains the quantity depending on the space–time dimensions, like supersymmetric gauge theories.

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FEYNMAN DIAGRAMS AND DIFFERENTIAL EQUATIONS

International Journal of Modern Physics A ◽

10.1142/s0217751x07037147 ◽

2007 ◽

Vol 22 (24) ◽

pp. 4375-4436 ◽

Cited By ~ 93

Author(s):

MARIO ARGERI ◽

PIERPAOLO MASTROLIA

Keyword(s):

Differential Equations ◽

Boundary Conditions ◽

Difference Equations ◽

Vacuum Polarization ◽

Feynman Diagrams ◽

Polarization Tensor ◽

Photon Propagator ◽

Feynman Integrals ◽

Technical Aspects ◽

Vacuum Polarization Tensor

We review in a pedagogical way the method of differential equations for the evaluation of D-dimensionally regulated Feynman integrals. After dealing with the general features of the technique, we discuss its application in the context of one- and two-loop corrections to the photon propagator in QED, by computing the Vacuum Polarization tensor exactly in D. Finally, we treat two cases of less trivial differential equations, respectively associated to a two-loop three-point, and a four-loop two-point integral. These two examples are the playgrounds for showing more technical aspects about: Laurent expansion of the differential equations in D (around D = 4); the choice of the boundary conditions; and the link among differential and difference equations for Feynman integrals.

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