scholarly journals Motion of a scalar field coupled to a Yang Mills field reformulated locally with some gauge invariant variables

2000 ◽  
Vol 2000 (03) ◽  
pp. 022-022
Author(s):  
Eric Chopin
Keyword(s):  
Scalar Field ◽  
Gauge Invariant ◽  
Yang Mills ◽  
Mills Field

Field models

2021 ◽  
pp. 42-69
Author(s):  
Iosif L. Buchbinder ◽  
Ilya L. Shapiro
Keyword(s):  
Electromagnetic Field ◽  
Scalar Field ◽  
Spinor Field ◽  
Vector Fields ◽  
Sigma Model ◽  
Complex Scalar ◽  
Yang Mills ◽  
Scalar Field Models ◽  
Complex Scalar Field ◽  
Mills Field

This chapter provides constructions of Lagrangians for various field models and discusses the basic properties of these models. Concrete examples of field models are constructed, including real and complex scalar field models, the sigma model, spinor field models and models of massless and massive free vector fields. In addition, the chapter discusses various interactions between fields, including the interactions of scalars and spinors with the electromagnetic field. A detailed discussion of the Yang-Mills field is given as well.

scholarly journals Decay of a Yang-Mills field coupled to a scalar field

1979 ◽  
Vol 67 (1) ◽  
pp. 51-67 ◽  
Author(s):  
Robert T. Glassey ◽  
Walter A. Strauss
Keyword(s):  
Scalar Field ◽  
Yang Mills ◽  
Mills Field

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.

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 MAPPING A MASSLESS SCALAR FIELD THEORY ON A YANG–MILLS THEORY: CLASSICAL CASE

2009 ◽  
Vol 24 (30) ◽  
pp. 2425-2432 ◽  
Author(s):  
MARCO FRASCA
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Field Equations ◽  
Scalar Field Theory ◽  
Classical Level ◽  
Gradient Expansion ◽  
Yang Mills ◽  
Mills Field

We analyze a recent proposal to map a massless scalar field theory onto a Yang–Mills theory at classical level. It is seen that this mapping exists at a perturbative level when the expansion is a gradient expansion. In this limit the theories share the spectrum, at the leading order, that is the one of a harmonic oscillator. Gradient expansion is exploited maintaining Lorentz covariance by introducing a fifth coordinate and turning the theory to Euclidean space. These expansions give common solutions to scalar and Yang–Mills field equations that are so proved to exist by construction, confirming that the selected components of the Yang–Mills field are indeed an extremum of the corresponding action functional.

scholarly journals Chirality, a new key for the definition of the connection and curvature of a Lie-Kac superalgebra

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Jean Thierry-Mieg
Keyword(s):  
Scalar Field ◽  
Lie Algebra ◽  
Bianchi Identity ◽  
Parallel Transport ◽  
Lie Superalgebra ◽  
Natural Generalization ◽  
Yang Mills ◽  
Complex Functions ◽  
Definition Of ◽  
Mills Field

Abstract A natural generalization of a Lie algebra connection, or Yang-Mills field, to the case of a Lie-Kac superalgebra, for example SU(m/n), just in terms of ordinary complex functions and differentials, is proposed. Using the chirality χ which defines the supertrace of the superalgebra: STr(…) = Tr(χ…), we construct a covariant differential: D = χ(d + A) + Φ, where A is the standard even Lie-subalgebra connection 1-form and Φ a scalar field valued in the odd module. Despite the fact that Φ is a scalar, Φ anticommutes with (χA) because χ anticommutes with the odd generators hidden in Φ. Hence the curvature F = DD is a superalgebra-valued linear map which respects the Bianchi identity and correctly defines a chiral parallel transport compatible with a generic Lie superalgebra structure.

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