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.

QED VERTEX PART IN NONLOCAL REGULARIZATION

1994 ◽  
Vol 09 (14) ◽  
pp. 1283-1290 ◽  
Author(s):  
P.C. RAJE BHAGEERATHI ◽  
KURUVILLA EAPEN
Keyword(s):  
Dimensional Regularization ◽  
Vertex Part ◽  
Gauge Invariant ◽  
Regularization Scheme ◽  
Nonlocal Regularization ◽  
Invariant Regularization

Evens et al.1 have given a gauge invariant regularization scheme for QED which they have named nonlocal regularization. We have evaluated the QED vertex part in this scheme of regularization. This result agrees with the expression obtained using dimensional regularization apart from numerical constants.

scholarly journals On the connection between quark propagation and hadronization

2020 ◽  
Vol 80 (9) ◽  
Author(s):  
Alberto Accardi ◽  
Andrea Signori
Keyword(s):  
Sum Rules ◽  
Mass Term ◽  
Final State ◽  
Mass Generation ◽  
Gauge Invariant ◽  
Dynamical Generation ◽  
Dynamical Quark Mass ◽  
Complete Set ◽  
Fragmentation Functions ◽  
The One

AbstractWe investigate the properties and structure of the recently discussed “fully inclusive jet correlator”, namely, the gauge-invariant field correlator characterizing the final state hadrons produced by a free quark as this propagates in the vacuum. Working at the operator level, we connect this object to the single-hadron fragmentation correlator of a quark, and exploit a novel gauge invariant spectral decomposition technique to derive a complete set of momentum sum rules for quark fragmentation functions up to twist-3 level; known results are recovered, and new sum rules proposed. We then show how one can explicitly connect quark hadronization and dynamical quark mass generation by studying the inclusive jet’s gauge-invariant mass term. This mass is, on the one hand, theoretically related to the integrated chiral-odd spectral function of the quark, and, on the other hand, is experimentally accessible through the E and $${\widetilde{E}}$$ E ~ twist-3 fragmentation function sum rules. Thus, measurements of these fragmentation functions in deep inelastic processes provide one with an experimental gateway into the dynamical generation of mass in Quantum Chromodynamics.

WARD IDENTITY FOR NONLOCAL QED

1998 ◽  
Vol 13 (05) ◽  
pp. 797-829 ◽  
Author(s):  
P. C. RAJE BHAGEERATHI ◽  
KURUVILLA EAPEN
Keyword(s):  
Ward Identity ◽  
Vertex Part ◽  
Gauge Invariant ◽  
Regularization Scheme ◽  
Usual Form ◽  
Nonlocal Regularization ◽  
Invariant Regularization

Evens et al.1 have given a gauge-invariant regularization scheme for QED which they have named nonlocal regularization. The present authors2 have worked out the QED vertex part in this scheme of regularization. In this paper we present a Ward identity for nonlocal QED to the order of two loops (order e4). In the limit of QED (Λ→∞), this identity reduces to the usual form of the Ward identity.

scholarly journals DUALITY THROUGH THE SYMPLECTIC EMBEDDING FORMALISM

2007 ◽  
Vol 22 (21) ◽  
pp. 3605-3620 ◽  
Author(s):  
E. M. C. ABREU ◽  
A. C. R. MENDES ◽  
C. NEVES ◽  
W. OLIVEIRA ◽  
F. I. TAKAKURA
Keyword(s):  
Phase Space ◽  
Gauge Invariance ◽  
Zero Mode ◽  
Mass Term ◽  
Gauge Invariant ◽  
Embedding Method ◽  
Symplectic Embedding ◽  
The One ◽  
Topological Term

In this work we show that we can obtain dual equivalent actions following the symplectic formalism with the introduction of extra variables which enlarge the phase space. We show that the results are equal as the one obtained with the recently developed gauging iterative Noether dualization method. We believe that, with the arbitrariness property of the zero mode, the symplectic embedding method is more profound since it can reveal a whole family of dual equivalent actions. We illustrate the method demonstrating that the gauge-invariance of the electromagnetic Maxwell Lagrangian broken by the introduction of an explicit mass term and a topological term can be restored to obtain the dual equivalent and gauge-invariant version of the theory.

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.

scholarly journals GLUON-W-MESON SCATTERING VIA DIFFERENT RENORMALIZATION SCHEMES

1999 ◽  
Vol 14 (15) ◽  
pp. 993-1005 ◽  
Author(s):  
M. M. DEMINOV ◽  
A. A. SLAVNOV
Keyword(s):  
Dimensional Regularization ◽  
Ward Identities ◽  
Gauge Invariant ◽  
The One ◽  
Villars Regularization

The one-loop gluon-W-meson amplitude is calculated by means of the gauge-invariant generalized Pauli–Villars regularization and with the help of dimensional regularization. It is shown that in the former case the amplitude satisfies generalized Ward identities, whereas in the latter case the amplitude differs from the former by the constant.

scholarly journals ONE-LOOP EFFECTIVE POTENTIAL FOR SCALAR AND VECTOR FIELDS ON HIGHER-DIMENSIONAL NONCOMMUTATIVE FLAT MANIFOLDS

2001 ◽  
Vol 16 (23) ◽  
pp. 1479-1486 ◽  
Author(s):  
A. A. BYTSENKO ◽  
A. E. GONÇALVES ◽  
S. ZERBINI
Keyword(s):  
Zeta Function ◽  
Vector Fields ◽  
Dimensional Regularization ◽  
Massless Scalar ◽  
Quantum Field Theories ◽  
Dimensional Manifold ◽  
Logarithmic Term ◽  
Scalar And Vector Fields ◽  
The One ◽  
Flat Manifolds

The non-planar contribution to the effective potentials for massless scalar and vector quantum field theories on D-dimensional manifold with p compact noncommutative extra dimensions is evaluated by means of dimensional regularization implemented by zeta function techniques. It is found that, the zeta function associated with the one-loop operator may not be regular at the origin. Thus, the related heat kernel trace has a logarithmic term in the short t asymptotic expansion. Consequences of this fact are briefly discussed.

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.

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