scholarly journals Vacuum polarization tensor in inhomogeneous magnetic fields

2011 ◽  
Vol 84 (6) ◽  
Author(s):  
Holger Gies ◽  
Lars Roessler
Keyword(s):  
Magnetic Fields ◽  
Vacuum Polarization ◽  
Polarization Tensor ◽  
Vacuum Polarization Tensor

scholarly journals A NUMERICAL EVALUATION OF VACUUM POLARIZATION TENSOR IN CONSTANT EXTERNAL MAGNETIC FIELDS

2013 ◽  
Vol 28 (20) ◽  
pp. 1350100 ◽  
Author(s):  
KEN-ICHI ISHIKAWA ◽  
DAIJI KIMURA ◽  
KENTA SHIGAKI ◽  
ASAKO TSUJI
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Landau Level ◽  
Vacuum Polarization ◽  
Form Factors ◽  
Heavy Ion ◽  
Kinematic Parameter ◽  
Polarization Tensor ◽  
Photon Momentum ◽  
Vacuum Polarization Tensor

Hattori–Itakura have recently derived the full Landau-level summation form for the photon vacuum polarization tensor in constant external magnetic fields at the one-loop level. The Landau-level summation form is essential when the photon momentum exceeds the threshold of the pair creation of charged particles in a magnetic field stronger than the squared mass of the charged particle. The tensor has three different form factors depending on the tensor direction with respect to the external magnetic field. The renormalization is nontrivial because these form factors are expressed in terms of double or triple summation forms. We give a numerical UV subtraction method which can be applied to numerically evaluate the form factors in constant external magnetic fields. We numerically investigate the photon vacuum polarization tensor in the form of the Landau-level summation and estimate the systematic errors coming from truncation of the Landau-level summation in a parameter region realized in heavy ion collision experiments. We find that the error is practically controllable at an O(10-2) level for electrons and muons in strong magnetic fields expected in heavy ion collisions in the experimentally feasible kinematic parameter regions.

scholarly journals SECOND-ORDER CORRECTIONS TO QED COUPLING AT LOW TEMPERATURE

2008 ◽  
Vol 23 (29) ◽  
pp. 4709-4719 ◽  
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.

scholarly journals Derivative corrections to the Heisenberg-Euler effective action

2021 ◽  
Vol 2021 (9) ◽  
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.

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

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.

scholarly journals FEYNMAN DIAGRAMS AND DIFFERENTIAL EQUATIONS

2007 ◽  
Vol 22 (24) ◽  
pp. 4375-4436 ◽  
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.

Asymptotic behavior of the vacuum polarization tensor

1980 ◽  
Vol 22 (10) ◽  
pp. 2534-2541 ◽  
Author(s):  
Reinhard Oehme ◽  
Wolfhart Zimmermann
Keyword(s):  
Asymptotic Behavior ◽  
Vacuum Polarization ◽  
Polarization Tensor ◽  
Vacuum Polarization Tensor
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