scholarly journals C-projection and monopole condensation in QCD

2014 ◽  
Vol 29 ◽  
pp. 1460210
Author(s):  
Y. M. Cho
Keyword(s):  
Effective Action ◽  
Gauge Invariance ◽  
Integral Expression ◽  
Gauge Invariant ◽  
Invariant Integral ◽  
Infra Red ◽  
The Stability ◽  
The One

We show that the monopole condensation is responsible for the confinement. To demonstrate this we present a new gauge invariant integral expression of the one-loop QCD effective action which has no infra-red divergence, and show that the color reflection invariance ("the C-projection") assures the gauge invariance and the stability of the monopole condensation.

MONOPOLE CONDENSATION AND MASS GAP IN SU(3) QCD

2014 ◽  
Vol 29 (03n04) ◽  
pp. 1450013 ◽  
Author(s):  
Y. M. CHO
Keyword(s):  
Effective Potential ◽  
Effective Action ◽  
Infrared Divergence ◽  
Integral Expression ◽  
Gauge Invariant ◽  
Mass Gap ◽  
Invariant Integral ◽  
The One

We demonstrate the monopole condensation in SU(3) QCD. We first discuss the gauge independent and Weyl symmetric Abelian (Cho-Duan-Ge) decomposition of the SU(3) QCD, and present a new gauge invariant integral expression of the one-loop effective action which has no infrared divergence. Integrating it gauge invariantly imposing the color reflection invariance ("the C-projection") we show that the effective potential generates the stable monopole condensation which generates the mass gap.

scholarly journals On the one-loop calculations with Reggeized quarks

2017 ◽  
Vol 32 (40) ◽  
pp. 1750207 ◽  
Author(s):  
Maxim Nefedov ◽  
Vladimir Saleev
Keyword(s):  
Field Theory ◽  
Renormalization Group ◽  
Effective Field Theory ◽  
Effective Action ◽  
Gauge Invariance ◽  
Effective Field ◽  
Loop Correction ◽  
Gauge Invariant ◽  
The One ◽  
Regge Limit

The technique of one-loop calculations for the processes involving Reggeized quarks is described in the framework of gauge invariant effective field theory for the Multi-Regge limit of QCD, which has been introduced by Lipatov and Vyazovsky. The rapidity divergences, associated with the terms enhanced by log(s), appear in the loop corrections in this formalism. The covariant procedure of regularization of rapidity divergences, preserving the gauge invariance of effective action is described. As an example application, the one-loop correction to the propagator of Reggeized quark and [Formula: see text]-scattering vertex are computed. Obtained results are used to construct the Regge limit of one-loop [Formula: see text] amplitude. The cancellation of rapidity divergences and consistency of the EFT prediction with the full QCD result is demonstrated. The rapidity renormalization group within the EFT is discussed.

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.

scholarly journals ONE-PARTICLE AND COLLECTIVE ELECTRON SPECTRA IN HOT AND DENSE QED AND THEIR GAUGE DEPENDENCE

1998 ◽  
Vol 13 (21) ◽  
pp. 1719-1728 ◽  
Author(s):  
O. K. KALASHNIKOV
Keyword(s):  
Gauge Invariance ◽  
Electron Spectrum ◽  
Particle Spectrum ◽  
Gauge Invariant ◽  
Long Wavelength ◽  
Gauge Dependence ◽  
Electron Spectra ◽  
Zero Momentum ◽  
Collective Spectrum ◽  
The One

The one-particle electron spectrum is found for hot and dense QED and its properties are investigated in comparison with the collective spectrum. It is shown that the one-particle spectrum (in any case its zero momentum limit) is gauge-invariant, but the collective spectrum, being qualitatively different, is always gauge-dependent. The exception is the case m,μ=0 for which the collective spectrum long wavelength limit demonstrates the gauge invariance as well.

scholarly journals Background independent exact renormalisation

2021 ◽  
Vol 81 (2) ◽  
Author(s):  
Kevin Falls
Keyword(s):  
Path Integral ◽  
Effective Action ◽  
Beta Function ◽  
Background Field ◽  
Flow Equation ◽  
Renormalisation Group ◽  
Gauge Invariant ◽  
Yang Mills ◽  
The One ◽  
Group Flow

AbstractA geometric formulation of Wilson’s exact renormalisation group is presented based on a gauge invariant ultraviolet regularisation scheme without the introduction of a background field. This allows for a manifestly background independent approach to quantum gravity and gauge theories in the continuum. The regularisation is a geometric variant of Slavnov’s scheme consisting of a modified action, which suppresses high momentum modes, supplemented by Pauli–Villars determinants in the path integral measure. An exact renormalisation group flow equation for the Wilsonian effective action is derived by requiring that the path integral is invariant under a change in the cutoff scale while preserving quasi-locality. The renormalisation group flow is defined directly on the space of gauge invariant actions without the need to fix the gauge. We show that the one-loop beta function in Yang–Mills and the one-loop divergencies of General Relativity can be calculated without fixing the gauge. As a first non-perturbative application we find the form of the Yang–Mills beta function within a simple truncation of the Wilsonian effective action.

A study of gauge-invariant non-local interactions

1954 ◽  
Vol 223 (1155) ◽  
pp. 468-481 ◽  
Keyword(s):  
Quantum Theory ◽  
Gauge Invariance ◽  
Local Interactions ◽  
Gauge Invariant ◽  
Invariance Properties ◽  
Finite Theory ◽  
Non Local ◽  
The One ◽  
Dimensional Integral

The paper investigates the possibility of introducing ‘non-local’ interactions, i. e. interactions represented by four-dimensional integral operations, in order to eliminate divergences in the quantum theory of interacting fields. In particular, a type of equation is discussed which preserves all the required invariance properties, including gauge invariance and macroscopic causality. It turns out that equations of this type still give divergent results. The origin of these divergences is discussed, and it is shown that if there is any way of formulating a finite theory it would have to be very different from the one investigated here.

scholarly journals The one-loop effective action of noncommutative super Yang–Mills is gauge invariant

2001 ◽  
Vol 504 (1-2) ◽  
pp. 131-140 ◽  
Author(s):  
Mario Pernici ◽  
Alberto Santambrogio ◽  
Daniela Zanon
Keyword(s):  
Effective Action ◽  
Gauge Invariant ◽  
Yang Mills ◽  
The One

scholarly journals EFFECTIVE ACTION OF SPONTANEOUSLY BROKEN GAUGE THEORIES

1998 ◽  
Vol 13 (01) ◽  
pp. 95-124 ◽  
Author(s):  
S.-H. HENRY TYE ◽  
YAN VTOROV-KAREVSKY
Keyword(s):  
Effective Potential ◽  
Effective Action ◽  
Gauge Theories ◽  
Perturbation Expansion ◽  
Gauge Invariant ◽  
Abelian Case ◽  
Covariant Gauge ◽  
The One ◽  
Higgs Fields ◽  
Field Redefinition

The effective action of a Higgs theory should be gauge-invariant. However, the quantum and/or thermal contributions to the effective potential seem to be gauge-dependent, posing a problem for its physical interpretation. In this paper, we identify the source of the problem and argue that in a Higgs theory perturbative contributions should be evaluated with the Higgs fields in the polar basis, not in the Cartesian basis. Formally, this observation can be made from the derivation of the Higgs theorem, which we provide. We show explicitly that, properly defined, the effective action for the Abelian Higgs theory is gauge-invariant to all orders in perturbation expansion when evaluated in the covariant gauge in the polar basis. In particular, the effective potential is gauge-invariant. We also show the equivalence between the calculations in the covariant gauge in the polar basis and the unitary gauge. These points are illustrated explicitly with the one-loop calculations of the effective action. With a field redefinition, we obtain the physical effective potential. The SU(2) non-Abelian case is also discussed.

OPERATOR REGULARIZATION AND THE DIVERGENCE OF THE SUPERCURRENT

1987 ◽  
Vol 02 (03) ◽  
pp. 785-796 ◽  
Author(s):  
D. G. C. McKEON ◽  
T. N. SHERRY
Keyword(s):  
Effective Action ◽  
Gauge Invariance ◽  
Green's Functions ◽  
Green’S Functions ◽  
Perturbative Expansion ◽  
Feynman Diagrams ◽  
Spinor Particle ◽  
Yang Mills ◽  
Loop Level ◽  
The One

Operator regularization is introduced as a procedure to compute Green's functions perturbatively. At the one-loop level the effective action is regularized by means of the ζ-function. A perturbative expansion due to Schwinger allows one to compute from the ζ-function one-loop one-particle irreducible Green's functions. By regulating in this way, we do not have to compute Feynman diagrams, we avoid having to introduce a regulating parameter into the initial Lagrangian and we do not encounter any divergent integrals. This procedure is illustrated for N = 1 super Yang-Mills theory in which the one-loop one-particle irreducible Green's function associated with the decay of the supercurrent into a vector and a spinor particle is treated. Gauge invariance is automatically maintained and the usual anomaly in the divergence of the super-current is recovered.

Sign in / Sign up

Export Citation Format

Share Document