The vacuum polarization in two-dimensional noncommutative QED

2003 ◽  
Vol 81 (8) ◽  
pp. 997-1003 ◽  
Author(s):  
F T Brandt ◽  
D.G.C. McKeon
Keyword(s):  
Vector Field ◽  
Gauge Field ◽  
Vacuum Polarization ◽  
Two Dimensions ◽  
Tree Level ◽  
Polarization Tensor ◽  
Two Dimensional ◽  
First Order ◽  
The One ◽  
Vacuum Polarization Tensor

The one-loop vacuum polarization tensor in noncommutative spinor QED in two dimensions is computed. A first-order formalism is used to simplify the interaction vertices for the vector field. Although the form of the gauge field-spinor interaction is chosen so as to vanish at tree level, as the noncommuting parameter goes to zero, the vacuum polarization is nontrivial in this limit. PACS No.: 12.20.–m

VACUUM POLARIZATION TENSOR IN THREE-DIMENSIONAL QUANTUM ELECTRODYNAMICS

1992 ◽  
Vol 07 (21) ◽  
pp. 5307-5316 ◽  
Author(s):  
B.M. PIMENTEL ◽  
A.T. SUZUKI ◽  
J.L. TOMAZELLI
Keyword(s):  
Quantum Electrodynamics ◽  
Vacuum Polarization ◽  
Three Dimensional ◽  
Boson Mass ◽  
Polarization Tensor ◽  
Regularization Technique ◽  
Abelian Case ◽  
Gauge Boson Mass ◽  
The One ◽  
Vacuum Polarization Tensor

We evaluate the one-loop vacuum polarization tensor for three-dimensional quantum electrodynamics (QED), using an analytic regularization technique, implemented in a gauge-invariant way. We show thus that a gauge boson mass is generated at this level of radiative correction to the photon propagator. We also point out in our conclusions that the generalization for the non Abelian case is straightforward.

AMBIGUITIES AND SYMMETRY RELATIONS IN FIVE-DIMENSIONAL PERTURBATIVE CALCULATIONS: THE EXPLICIT EVALUATION OF THE QED5 VACUUM POLARIZATION TENSOR

2013 ◽  
Vol 28 (27) ◽  
pp. 1350135
Author(s):  
M. V. S. FONSECA ◽  
T. J. GIRARDI ◽  
G. DALLABONA ◽  
O. A. BATTISTEL
Keyword(s):  
Quantum Electrodynamics ◽  
Vacuum Polarization ◽  
Space Time ◽  
General Character ◽  
Polarization Tensor ◽  
Time Dimension ◽  
Perturbative Calculations ◽  
Explicit Evaluation ◽  
The One ◽  
Vacuum Polarization Tensor

An explicit evaluation of the D = 4+1 quantum electrodynamics (QED) vacuum polarization tensor is presented. The calculations are made preserving all the intrinsic arbitrariness involved in such type of problem. The internal momenta are assumed arbitrary in order to preserve the possibility of dependence on such kind of choice, due to the superficial degree of divergence involved. An arbitrary scale is introduced in the separation of terms having different degrees of divergences in order to preserve the possibility of scale ambiguities. In the performed steps the effects of regularizations are avoided by using an adequate strategy to handle the problem of divergences in Quantum Field Theory perturbative calculations. Given this attitude it is possible to get clean and sound conclusions about the consistency requirements involved in perturbative calculations D = 4+1 space–time dimension. At the final a symmetry preserving and ambiguities free result is obtained allowing the renormalization of the photon propagator at the one-loop level. The simplicity added to the general character of the adopted procedure allows us to believe that the referred strategy can be used without restrictions of applicability in perturbative calculations made in theories formulated in a space–time having extra dimensions relative to the physical one (D = 3+1) producing consistent results, in odd and even dimensions, in spite of the nonrenormalizable character.

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.

SOLVING THE TWO-DIMENSIONAL INVERSE FRACTAL PROBLEM WITH THE WAVELET TRANSFORM

Fractals ◽  
1996 ◽  
Vol 04 (04) ◽  
pp. 469-475 ◽  
Author(s):  
ZBIGNIEW R. STRUZIK
Keyword(s):  
Wavelet Transform ◽  
Scale Invariance ◽  
Wavelet Decomposition ◽  
Two Dimensions ◽  
The Self ◽  
Continuous Wavelet ◽  
Two Dimensional ◽  
One Dimensional ◽  
Affine Functions ◽  
The One

The methodology of the solution to the inverse fractal problem with the wavelet transform1,2 is extended to two-dimensional self-affine functions. Similar to the one-dimensional case, the two-dimensional wavelet maxima bifurcation representation used is derived from the continuous wavelet decomposition. It possesses translational and scale invariance necessary to reveal the invariance of the self-affine fractal. As many fractals are naturally defined on two-dimensions, this extension constitutes an important step towards solving the related inverse fractal problem for a variety of fractal types.

scholarly journals ELECTRODYNAMICS IN A BACKGROUND CHIRAL FIELD

2011 ◽  
Vol 26 (38) ◽  
pp. 2879-2887
Author(s):  
F. T. BRANDT ◽  
D. G. C. MCKEON ◽  
A. PATRUSHEV
Keyword(s):  
Vector Field ◽  
Euclidean Space ◽  
Effective Action ◽  
Exact Expression ◽  
Two Dimensions ◽  
Perturbative Expansion ◽  
Dimensional Euclidean Space ◽  
Chiral Field ◽  
Axial Field ◽  
The One

We consider the one-loop effective action in four-dimensional Euclidean space for a background chiral field coupled to a spinor field. It proves possible to find an exact expression for this action if the mass m of the spinor vanishes. If m does not vanish, one can make a perturbative expansion in powers of the axial field that contributes to the chiral field, while treating the contribution of the vector field exactly when it is a constant. The analogous problem in two dimensions is also discussed.

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.

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