SUPERSYMMETRY AND THE FOUR-DIMENSIONAL COUNTERPART OF DIMENSIONAL REGULARIZATION

1992 ◽  
Vol 07 (01) ◽  
pp. 41-59
Author(s):  
J. NOVOTNÝ
Keyword(s):  
Gauge Invariance ◽  
Dimensional Reduction ◽  
Dimensional Regularization ◽  
Explicit Calculation ◽  
Regularization Scheme

A supersymmetric generalization of the natural four-dimensional counterpart of canonical dimensional regularization developed recently is discussed for SUSY QED. The gauge invariance of the regularization scheme is proved and the method illustrated by simple examples of explicit calculation of one-loop supergraphs. The relation to the regularization by dimensional reduction is briefly discussed.

ONE-LOOP TOPOLOGICAL MASS IN QED2+1 WITHIN A BROAD CLASS OF GAUGE INVARIANT REGULARIZATION SCHEMES

1992 ◽  
Vol 07 (28) ◽  
pp. 2575-2582 ◽  
Author(s):  
J. NOVOTNÝ
Keyword(s):  
Broad Class ◽  
Dimensional Regularization ◽  
Mass Term ◽  
Explicit Calculation ◽  
Alternative Formulation ◽  
Gauge Invariant ◽  
Regularization Scheme ◽  
The One ◽  
Invariant Regularization ◽  
Topological Mass

An explicit calculation of the one-loop topological mass term within a broad class of gauge invariant regularization schemes developed recently is presented for (2+1)-dimensional QED. This provides an uniform description of the results obtained recently in the literature and an explanation of their regularization scheme dependence. The Pauli-Villars and dimensional regularization are discussed in more detail in this context and an alternative formulation of dimensional regularization in (2+1) dimensions is described.

scholarly journals A prescription for projectors to compute helicity amplitudes in D dimensions

2021 ◽  
Vol 81 (5) ◽  
Author(s):  
Long Chen
Keyword(s):  
Dimensional Regularization ◽  
Tensor Decomposition ◽  
Regularization Scheme ◽  
Lorentz Index ◽  
Dimensional Splitting ◽  
Lorentz Tensor ◽  
Helicity Amplitudes ◽  
Amplitude Level ◽  
Infrared Singularities

AbstractThis article discusses a prescription to compute polarized dimensionally regularized amplitudes, providing a recipe for constructing simple and general polarized amplitude projectors in D dimensions that avoids conventional Lorentz tensor decomposition and avoids also dimensional splitting. Because of the latter, commutation between Lorentz index contraction and loop integration is preserved within this prescription, which entails certain technical advantages. The usage of these D-dimensional polarized amplitude projectors results in helicity amplitudes that can be expressed solely in terms of external momenta, but different from those defined in the existing dimensional regularization schemes. Furthermore, we argue that despite being different from the conventional dimensional regularization scheme (CDR), owing to the amplitude-level factorization of ultraviolet and infrared singularities, our prescription can be used, within an infrared subtraction framework, in a hybrid way without re-calculating the (process-independent) integrated subtraction coefficients, many of which are available in CDR. This hybrid CDR-compatible prescription is shown to be unitary. We include two examples to demonstrate this explicitly and also to illustrate its usage in practice.

scholarly journals Modern Technique for Real Photon Radiative Correction Calculations

2021 ◽  
Vol 24 (2) ◽  
pp. 184-191
Author(s):  
I. A. Shershan ◽  
T. V. Shishkina
Keyword(s):  
Gauge Boson ◽  
Cross Sections ◽  
Dimensional Regularization ◽  
Real Photon ◽  
Boson Production ◽  
Radiative Corrections ◽  
Hard Photon ◽  
Regularization Scheme ◽  
Modern Technique ◽  
Bremsstrahlung Contribution

The problem of the bremsstrahlung contribution calculation as a part of the radiative corrections in the case of single gauge boson production was discussed. It was shown that the hard photon bremsstrahlung contribution can be divided into the finite and divergent terms. The exact calculation of soft photon bremsstrahlung and infrared part of hard photon bremsstrahlung was presented in frame of the dimensional regularization scheme. Numerical analysis of radiative corrections to the cross sections of single gauge boson production was performed.

scholarly journals SUPER-τ3QED AND THE DIMENSIONAL REDUCTION OF N=1SUPER-QED2+2

1996 ◽  
Vol 11 (08) ◽  
pp. 1367-1389 ◽  
Author(s):  
M.A. DE ANDRADE ◽  
O.M. DEL CIMA
Keyword(s):  
Vector Field ◽  
Imaginary Part ◽  
Gauge Invariance ◽  
Dimensional Reduction ◽  
Complex Vector ◽  
Gauge Invariant ◽  
Invariant Action ◽  
Supersymmetric Version ◽  
Supersymmetric Gauge ◽  
Weyl Symmetry

In this work the supersymmetric gauge-invariant action for the massive Abelian N=1 super-QED 2+2 in the Atiyah-Ward space-time (D=2+2) is formulated. The questions concerning the scheme of the gauge invariance in D=2+2 by means of gauging the massive N=1 super-QED 2+2 are investigated. We study how to ensure the gauge invariance at the expense of the introduction of a complex vector superfield. We discuss the Wess-Zumino gauge and thereupon we conclude that, in this gauge, only the imaginary part of the complex vector field, Bμ, gauges a U(1) symmetry. whereas its real part gauges a Weyl symmetry. We build up the gauge-invariant massive term by introducing a pair of chiral and antichiral superfields with opposite U(1) charges. We carry out a dimensional reduction à la Scherk of the massive N=1 super-QED 2+2 action from D=2+2 to D=1+2. Truncations are needed in order to suppress nonphysical modes, and we end up with a parity-preserving N=1 super-QED 1+2 (rather than N=2) in D=1+2. Finally, we show that the N=1 super-QED 1+2 we have obtained is the supersymmetric version of τ3 QED .

scholarly journals REGULARIZATION PARAMETER INDEPENDENT ANALYSIS IN NAMBU–JONA-LASINIO MODEL

2013 ◽  
Vol 28 (31) ◽  
pp. 1350164 ◽  
Author(s):  
T. INAGAKI ◽  
D. KIMURA ◽  
H. KOHYAMA ◽  
A. KVINIKHIDZE
Keyword(s):  
Regularization Parameter ◽  
Dimensional Regularization ◽  
Low Energy ◽  
Leading Order ◽  
Regularization Scheme ◽  
Independent Analysis

Nambu–Jona-Lasinio model used to investigate low energy phenomena is nonrenormalizable, therefore the results depend on the regularization parameter in general. A possibility of the finite in four-dimensional limit and even the in regularization parameter (this is dimension in the dimensional regularization scheme) independent analysis is shown in the leading order of the 1/Nc expansion.

scholarly journals GEOMETRICALLY RELATING MOMENTUM CUT-OFF AND DIMENSIONAL REGULARIZATION

2012 ◽  
Vol 10 (02) ◽  
pp. 1250081 ◽  
Author(s):  
SUSAMA AGARWALA
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Hopf Algebras ◽  
Dimensional Regularization ◽  
Mass Scale ◽  
Feynman Diagrams ◽  
Field Theories ◽  
Coupling Constant ◽  
Regularization Scheme ◽  
Β Function

The β function for a scalar field theory describes the dependence of the coupling constant on the renormalization mass scale. This dependence is affected by the choice of regularization scheme. I explicitly relate the β functions of momentum cut-off regularization and dimensional regularization on scalar field theories by a gauge transformation using the Hopf algebras of the Feynman diagrams of the theories.

scholarly journals Symmetry preserving regularization with a cutoff

Open Physics ◽  
2011 ◽  
Vol 9 (5) ◽  
Author(s):  
Gabor Cynolter ◽  
Endre Lendvai
Keyword(s):  
Gauge Symmetry ◽  
Gauge Invariance ◽  
Regularization Method ◽  
Dimensional Regularization ◽  
Loop Momentum

AbstractA Lorentz and gauge symmetry preserving regularization method is proposed in 4 dimensions based on a momentum cutoff. We use the conditions of gauge invariance or equivalently the freedom to shift the loop momentum to define the evaluation of the terms carrying even number of Lorentz indices, e.g. proportional to k µ k ν. The remaining scalar integrals are calculated with a four dimensional momentum cutoff. The finite terms (independent of the cutoff) are free of ambiguities coming from subtractions in non-trivial cases. Finite parts of the result are equal to that of dimensional regularization.

Feynman integrals and hypergeometric functions

2014 ◽  
Vol 05 (supp01) ◽  
pp. 1441001
Author(s):  
Héctor Luna García ◽  
Luz María García
Keyword(s):  
Hypergeometric Functions ◽  
Dimensional Regularization ◽  
Feynman Integrals ◽  
Regularization Scheme

We review Davydychev method for calculating Feynman integrals for massive and no massive propagators, by employing Mellin–Barnes transformation and the dimensional regularization scheme, same that lead to hypergeometric functions. In particular, an example is calculated explicitly from such a method.

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