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.

scholarly journals NOTE ON TRIANGLE ANOMALY WITH IMPROVED MOMENTUM CUTOFF

2011 ◽  
Vol 26 (21) ◽  
pp. 1537-1545 ◽  
Author(s):  
G. CYNOLTER ◽  
E. LENDVAI
Keyword(s):  
Gauge Symmetry ◽  
Regularization Method ◽  
Loop Momentum ◽  
Four Dimensions ◽  
Momentum Integral

A Lorentz and gauge symmetry preserving regularization method has been proposed recently in four dimensions based on Euclidean momentum cutoff. It is shown that the triangle anomaly can be calculated unambiguously with this new improved cutoff. The anticommutator of γ5 and γμ multiplied by five γ matrices is proportional to terms that do not vanish under a divergent loop-momentum integral, but cancel otherwise.

scholarly journals Unification of force and substance

2016 ◽  
Vol 374 (2075) ◽  
pp. 20150257 ◽  
Author(s):  
Frank Wilczek
Keyword(s):  
Dynamical Systems ◽  
Gauge Symmetry ◽  
Gauge Invariance ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Physical Significance ◽  
Fundamental Physics ◽  
Present Understanding

Maxwell’s mature presentation of his equations emphasized the unity of electromagnetism and mechanics, subsuming both as ‘dynamical systems’. That intuition of unity has proved both fruitful, as a source of pregnant concepts, and broadly inspiring. A deep aspect of Maxwell’s work is its use of redundant potentials, and the associated requirement of gauge symmetry. Those concepts have become central to our present understanding of fundamental physics, but they can appear to be rather formal and esoteric. Here I discuss two things: the physical significance of gauge invariance, in broad terms; and some tantalizing prospects for further unification, building on that concept, that are visible on the horizon today. If those prospects are realized, Maxwell’s vision of the unity of field and substance will be brought to a new level. This article is part of the themed issue ‘Unifying physics and technology in light of Maxwell's equations’.

scholarly journals SYMMETRY-PRESERVING LOOP REGULARIZATION AND RENORMALIZATION OF QFTs

2004 ◽  
Vol 19 (29) ◽  
pp. 2191-2204 ◽  
Author(s):  
YUE-LIANG WU
Keyword(s):  
Regularization Method ◽  
Proper Time ◽  
Dimensional Regularization ◽  
Energy Scale ◽  
Lagrangian Formalism ◽  
Quantum Field Theories ◽  
Characteristic Energy ◽  
Interaction Terms ◽  
Dimensional Interaction ◽  
Time Formalism

A new symmetry-preserving loop regularization method proposed in Ref. 1 is further investigated. It is found that its prescription can be understood by introducing a regulating distribution function to the proper-time formalism of irreducible loop integrals. The method simulates in many interesting features to the momentum cutoff, Pauli–Villars and dimensional regularization. The loop regularization method is also simple and general for the practical calculations to higher loop graphs and can be applied to both underlying and effective quantum field theories including gauge, chiral, supersymmetric and gravitational ones as the new method does not modify either the Lagrangian formalism or the spacetime dimension of original theory. The appearance of characteristic energy scale Mc and sliding energy scale μs offers a systematic way for studying the renormalization-group evolution of gauge theories in the spirit of Wilson–Kadanoff and for exploring important effects of higher dimensional interaction terms in the infrared regime.

scholarly journals Unparticle in (1+1) dimension with one-loop correction

2014 ◽  
Vol 29 (14) ◽  
pp. 1450072 ◽  
Author(s):  
Anisur Rahaman
Keyword(s):  
Gauge Symmetry ◽  
Gauge Field ◽  
Gauge Invariance ◽  
Quantum Effect ◽  
Loop Correction ◽  
Specific Expression ◽  
Classical Level ◽  
Schwinger Model ◽  
Physical Mass ◽  
Ambiguity Parameter

The possible emergence of unparticle has been mooted recently including a mass-like term for gauge field with the Schwinger model at the classical level. A one-loop correction due to bosonization is taken into account and investigation is carried out to study its effect on the unparticle scenario. It is observed that the physical mass, viz., unparticle scale acquires a new definition, i.e. the effect of this correction enters into the unparticle scale in a significant manner. The fermionic propagator is calculated which also agrees with the new scale. It has also been noticed that a novel restoration of the lost gauge invariance reappears when the ambiguity parameter related to the current anomaly acquires a specific expression. We have also observed that a quantum effect can nullify the effect of violation of gauge symmetry caused by some classical terms.

Vacuum polarization of weak interaction theory in Krein space quantization

2019 ◽  
Vol 34 (07n08) ◽  
pp. 1950050
Author(s):  
B. Forghan
Keyword(s):  
Hilbert Space ◽  
Weak Interaction ◽  
Regularization Method ◽  
Vacuum Polarization ◽  
Krein Space ◽  
Dimensional Regularization ◽  
Interaction Theory ◽  
Kreĭn Space ◽  
Krein Space Quantization

In this paper, one of the most important diagrams of weak interaction (vacuum polarization) is studied in Krein space quantization (KSQ). This diagram has divergent terms in Hilbert space which must be eliminated using a traditional regularization method like dimensional regularization whereas in KSQ the result is automatically finite and does not need renormalization.

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.

THE EXTRA GAUGE SYMMETRY OF STRING DEFORMATIONS IN ELECTROMAGNETISM WITH CHARGES AND DIRAC MONOPOLES

1992 ◽  
Vol 07 (19) ◽  
pp. 4693-4705 ◽  
Author(s):  
H. KLEINERT
Keyword(s):  
Gauge Symmetry ◽  
Gauge Invariance ◽  
Quantum Physics ◽  
Magnetic Monopoles ◽  
Quantization Condition ◽  
Gauge Transformations ◽  
Charge Quantization ◽  
Particle Orbits ◽  
Local Gauge Invariance ◽  
Physical Consequences

We point out that electromagnetism with Dirac magnetic monopoles harbors an extra local gauge invariance called monopole gauge invariance. The gauge transformations act on a gauge field of monopoles [Formula: see text] and are independent of the ordinary electromagnetic gauge invariance. The extra invariance expresses the physical irrelevance of the shape of the Dirac strings attached to the monopoles. The independent nature of the new gauge symmetry is illustrated by comparison with two other systems, superfluids and solids, which are not gauge-invariant from the outset but which nevertheless possess a precise analog of the monopole gauge invariance in their vortex and defect structure, respectively. The extra monopole gauge invariance is shown to be responsible for the Dirac charge quantization condition 2eg/ħc=integer, which can now be proved for any fixed particle orbits, i.e. without invoking fluctuating orbits which would correspond to the standard derivation using Schrödinger wave functions. The only place where quantum physics enters in our theory is by admitting the action to jump by 2πħ×integer without physical consequences when moving the string at fixed particle orbits.

scholarly journals Non-Abelian Gauge Symmetry in the Causal Epstein–Glaser Approach

1997 ◽  
Vol 12 (24) ◽  
pp. 4461-4476 ◽  
Author(s):  
Tobias Hurth
Keyword(s):  
Perturbation Theory ◽  
Gauge Symmetry ◽  
Gauge Invariance ◽  
Fock Space ◽  
Dimensional Space ◽  
Abelian Gauge ◽  
Yang Mills ◽  
Tree Graphs ◽  
Adiabatic Switching ◽  
Dimensional Space Time

Non-Abelian gauge symmetry in (3 + 1)-dimensional space–time is analyzed in the causal Epstein–Glaser framework. In this formalism, the technical details concerning the well-known UV and IR problem in quantum field theory are separated and reduced to well-defined problems, namely the causal splitting and the adiabatic switching of operator-valued distributions. Non-Abelian gauge invariance in perturbation theory is completely discussed in the well-defined Fock space of free asymptotic fields. The LSZ formalism is not used in this construction. The linear operator condition of asymptotic gauge invariance is sufficient for the unitarity of the S matrix in the physical subspace and the usual Slavnov–Taylor identities. We explicitly derive the most general specific coupling compatible with this condition. By analyzing only tree graphs in the second order of perturbation theory we show that the well-known Yang–Mills couplings with anticommuting ghosts are the only ones which are compatible with asymptotic gauge invariance. The required generalizations for linear gauges are given.

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