INVARIANT CORRELATION FUNCTIONS, SUPERCONVERGENCE SUM RULES, AND ELECTRIC-MAGNETIC DUALITY

1988 ◽  
Vol 03 (05) ◽  
pp. 1155-1182 ◽  
Author(s):  
HIDENAGA YAMAGISHI
Keyword(s):  
Sum Rules ◽  
Close Relation ◽  
Asymptotic Freedom ◽  
Sum Rule ◽  
Gauge Invariant ◽  
Yang Mills ◽  
Magnetic Components ◽  
Symmetric Decomposition ◽  
Chern Simons ◽  
Mills Field

The gauge-invariant correlation function for the Yang-Mills field strengths is shown to admit a symmetric decomposition into electric and magnetic components. The spectral weights are seen to obey a sum rule of the superconvergence type, owing to asymptotic freedom. The close relation between the dielectric function, electric-magnetic duality, and the algebra of generalized Chern-Simons charges is illustrated for the linearized Yang-Mills-Higgs system.

scholarly journals Yang-Mills theory, 2 + 1 and 3 + 1 dimensions

2003 ◽  
Vol 18 (33n35) ◽  
pp. 2415-2422 ◽  
Author(s):  
V. P. NAIR
Keyword(s):  
String Tension ◽  
Simons Theory ◽  
Nonzero Temperature ◽  
Gauge Invariant ◽  
Yang Mills ◽  
Magnetic Mass ◽  
Chern Simons ◽  
Chern Simons Theory

I review the analysis of (2+1)-dimensional Yang-Mills (YM2+1) theory via the use of gauge-invariant matrix variables. The vacuum wavefunction, string tension, the propagator mass for gluons, its relation to the magnetic mass for YM3+1at nonzero temperature and the extension of our analysis to the Yang-Mills-Chern-Simons theory are discussed. A possible extension to 3 + 1 dimensions is also briefly considered.

scholarly journals Chern-Simons-Antoniadis-Savvidy Forms and Non-Abelian Anomaly

2019 ◽  
Vol 8 (1) ◽  
pp. 11-15
Author(s):  
Suhaivi Hamdan ◽  
Erwin Erwin ◽  
Saktioto Saktioto
Keyword(s):  
Field Strength ◽  
Gauge Transformation ◽  
Integral Form ◽  
Gauge Fields ◽  
Gauge Invariant ◽  
Time Coordinate ◽  
Form Analysis ◽  
Yang Mills ◽  
Chern Simons ◽  
Gauge Variation

Kuat medan tensor yang ditransformasikan secara homogen terhadap perluasan transformasi gauge memenuhi bentuk sifat invarian gauge. Analisa invarian gauge dalam bantuk integeralnya memperlihatkan hubungan dengan koordinat ruang-waktu yang menunjukan bentuk baru dari topologi Lagrangian. Sifat invarian dari bentuk Pontryagin-Chern terhadap kuat medan tensor non-Abelian dan lemma Poincare dapat digunakan untuk mengkontruksi bentuk ChSAS yang menunjukan sifat quasi-invarian dibawah transformasi gauge. Artikel ini bertujuan untuk membuktikan bahwa kuat medan tensor Yang-Mills dari bentuk ChSAS memilik variasi gauge anomali non-Abelian seperti pada bentuk Chern-Simons. Integrasi bentuk ChSAS menghasilkan dimensi-4, 6 dan 8 variasi gauge genap dan memperlihatkan hubungan dengan bentuk Chern-Simons dimensi-3 dan 5 untuk variasi gauge ganjil. Bentuk ChSAS memperlihatkan variabel lebih kompleks yang menujukan sifat berosilasi. Tensors field strength transformation homogeneously to extend gauge transformation fulfilling charateristic gauge invariant form. Analysis gauge invariant in integral form shows corresponding with space-time coordinate that prove new topology Lagrangians form. Furthermore invariant charateristic of Pontryagin-Chern to non-Abelian tensor gauge fields and lemma Poincare used to contruct ChSAS forms which shows quasi-inavriant under gauge transformation. This paper aims to prove Yang-Mills tensor gauge field of ChSAS forms has variation non-Abelian anomaly like Chern-Simons forms. The integration ChSAS forms resulted 4, 6 and 8-dimensional even gauge variation which also correspond 3 and 5-dimensional odd gauge variation Chern-Simons forms. The ChSAS forms also showed complex variable and osilation.  Keywords: Pontryagin-Chern, Kuat medan tensor non-Abelian, Chern-Simans-Antoniadis-Savvidy, Anomali Non-Abelian.

One-loop divergences

2021 ◽  
pp. 363-387
Author(s):  
Iosif L. Buchbinder ◽  
Ilya L. Shapiro
Keyword(s):  
General Result ◽  
Asymptotic Freedom ◽  
Yukawa Model ◽  
Yang Mills ◽  
Starting Point ◽  
The One ◽  
Mills Field ◽  
Matter Fields

This chapter focuses on one-loop calculations and related issues such as practical renormalization and the derivation of beta functions. The general result for the one-loop divergences from chapter 13 is applied to a sequence of practical calculations. The starting point is the derivation of vacuum divergences of free matter fields. The beta functions in the vacuum sector are calculated. Asymptotic freedom is discussed. In addition, examples of one-loop divergences in interacting theories are elaborated, including the Yang-Mills field coupled to fermions and scalars, and the Yukawa model.

FADDEEV–POPOV GHOSTS

2010 ◽  
Vol 25 (06) ◽  
pp. 1079-1089 ◽  
Author(s):  
LUDVIG DMITRIEVICH FADDEEV
Keyword(s):  
Gauge Invariance ◽  
Degrees Of Freedom ◽  
Lorentz Invariance ◽  
Local Fields ◽  
Theoretical Physics ◽  
Covariant Quantization ◽  
Widespread Application ◽  
Gauge Invariant ◽  
Yang Mills ◽  
Mills Field

In the terminology of theoretical physics, the term "ghost" is used to identify an object that has no real physical meaning. The name "Faddeev–Popov ghosts" is given to the fictitious fields that were originally introduced in the construction of a manifestly Lorentz covariant quantization of the Yang–Mills field. Later, these objects acquired more widespread application, including in string theory. The necessity of ghosts is associated with gauge invariance. In gauge invariant theories, one usually has to deal with local fields, whose number exceeds that of physical degrees of freedom. For example in electrodynamics, in order to maintain manifest Lorentz invariance, one uses a four component vector potential Aμ(x), whereas the photon has only two polarizations. Thus, one needs a suitable mechanism in order to get rid of the unphysical degrees of freedom. Introducing fictitious fields, the ghosts, is one way of achieving this goal.

scholarly journals Gauge invariant variables and the Yang–Mills–Chern–Simons theory

2000 ◽  
Vol 566 (1-2) ◽  
pp. 331-347 ◽  
Author(s):  
Dimitra Karabali ◽  
Chanju Kim ◽  
V.P. Nair
Keyword(s):  
Simons Theory ◽  
Gauge Invariant ◽  
Yang Mills ◽  
Chern Simons ◽  
Chern Simons Theory

scholarly journals The first law of heterotic stringy black hole mechanics at zeroth order in α′

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Zachary Elgood ◽  
Dimitrios Mitsios ◽  
Tomás Ortín ◽  
David Pereñíguez
Keyword(s):  
Black Hole ◽  
Field Strength ◽  
Effective Field ◽  
Gauge Invariant ◽  
Yang Mills ◽  
First Order ◽  
Entropy Formula ◽  
Gauge Symmetries ◽  
Ring Solution ◽  
Chern Simons

Abstract We prove the first law of black hole mechanics in the context of the Heterotic Superstring effective action compactified on a torus to leading order in α′, using Wald’s formalism, covariant Lie derivatives and momentum maps. The Kalb-Ramond field strength of this theory has Abelian Chern-Simons terms which induce Nicolai-Townsend transformations of the Kalb-Ramond field. We show how to deal with all these gauge symmetries deriving the first law in terms of manifestly gauge-invariant quantities. In presence of Chern-Simons terms, several definitions of the conserved charges exist, but the formalism picks up only one of them to play a role in the first law. We study explicitly a non-extremal, charged, black ring solution of pure $$ \mathcal{N} $$ N = 1, d = 5 supergravity embedded in the Heterotic Superstring effective field theory.This work is a first step towards the derivation of the first law at first order in α′ where, more complicated, non-Abelian, Lorentz (“gravitational”) and Yang-Mills Chern-Simons terms are included in the Kalb-Ramond field strength. The derivation of a first law is a necessary step towards the derivation of a manifestly gauge-invariant entropy formula which is still lacking in the literature. In its turn, this entropy formula is needed to compare unambiguously macroscopic and microscopic black hole entropies.

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