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.

LOCALIZATION OF NONLOCAL LAGRANGIANS AND MASS GENERATION FOR NON-ABELIAN GAUGE FIELDS

2008 ◽  
Vol 23 (26) ◽  
pp. 4289-4313
Author(s):  
ALEXEY SEVOSTYANOV
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Gauge Fields ◽  
Green Functions ◽  
Coupling Constant ◽  
Mass Generation ◽  
Abelian Gauge ◽  
Yang Mills ◽  
Dimensional Space Time ◽  
Three Dimensional Space

We introduce and study the four-dimensional analogue of a mass generation mechanism for non-Abelian gauge fields suggested in the paper, Phys. Lett. B403, 297 (1997), in the case of three-dimensional space–time. The construction of the corresponding quantized theory is based on the fact that some nonlocal actions may generate local expressions for Green functions. An example of such a theory is the ordinary Yang–Mills field where the contribution of the Faddeev–Popov determinant to the Green functions can be made local by introducing additional ghost fields. We show that the quantized Hamiltonian for our theory unitarily acts in a Hilbert space of states and prove that the theory is renormalizable to all orders of perturbation theory. One-loop coupling constant and mass renormalizations are also calculated.

scholarly journals EXACT SOLUTIONS OF THE REISSNER–NORDSTRÖM TYPE IN EINSTEIN–YANG–MILLS SYSTEMS WITH ARBITRARY GAUGE GROUPS AND SPACE–TIME DIMENSIONS

1996 ◽  
Vol 11 (28) ◽  
pp. 4999-5014 ◽  
Author(s):  
GERD RUDOLPH ◽  
TORSTEN TOK ◽  
IGOR P. VOLOBUEV
Keyword(s):  
Dimensional Space ◽  
Space Time ◽  
Abelian Gauge ◽  
Gauge Groups ◽  
Yang Mills ◽  
Gravitational Fields ◽  
Dimensional Reduction Method ◽  
Dimensional Space Time ◽  
Spatial Rotations ◽  
Arbitrary Gauge

We present a class of solutions in Einstein–Yang–Mills systems with arbitrary gauge groups and space–time dimensions, which are symmetric under the action of the group of spatial rotations. Our approach is based on the dimensional reduction method for gauge and gravitational fields and relates symmetric Einstein–Yang–Mills solutions to certain solutions of two-dimensional Einstein–Yang–Mills–Higgs-dilaton theory. Application of this method to four-dimensional spherically symmetric (pseudo-)Riemannian space–time yields, in particular, new solutions describing both a magnetic and an electric charge at the center of a black hole. Moreover, we give an example of a solution with non-Abelian gauge group in six-dimensional space–time. We also comment on the stability of the obtained solutions.

scholarly journals About renormalized effective action for the Yang-Mills theory in four-dimensional space-time

2018 ◽  
Vol 191 ◽  
pp. 06001
Author(s):  
A.V. Ivanov
Keyword(s):  
Infinite Series ◽  
Effective Action ◽  
Dimensional Space ◽  
Space Time ◽  
Coupling Constant ◽  
Asymptotic Approach ◽  
Yang Mills ◽  
Dimensional Space Time ◽  
Bare Coupling Constant ◽  
Renormalization Theory

This work is related to the asymptotic approach in the renormalization theory and its problems. As the main example, the Yang-Mills theory in four-dimensional space-time is considered. It has been shown earlier [16] that using the asymptotic of the bare coupling constant one can find an expression for the renormalized effective action, however, this formula has problems (divergence ln " and infinite series). This work shows the relation of these values and provides an answer for the renormalized effective action.

MAGNETOFLUID UNIFICATION IN YANG–MILLS LAGRANGIAN

2009 ◽  
Vol 24 (18n19) ◽  
pp. 3630-3637 ◽  
Author(s):  
A. SULAIMAN ◽  
A. FAJARUDIN ◽  
T. P. DJUN ◽  
L. T. HANDOKO
Keyword(s):  
Gauge Symmetry ◽  
Gauge Field ◽  
Lagrangian Approach ◽  
General Description ◽  
Abelian Gauge ◽  
Yang Mills ◽  
Relativistic Fluid ◽  
Physical Consequences

The magnetofluid unification is constructed using lagrangian approach by imposing a non-Abelian gauge symmetry to the matter inside the fluid. The model provides a general description for relativistic fluid interacting with either Abelian or non-Abelian gauge field. The differences with the hybrid magnetofluid model are discussed, and some physical consequences of this formalism are briefly worked out.

scholarly journals SPIN GAUGE THEORY OF GRAVITY IN CLIFFORD SPACE: A REALIZATION OF KALUZA–KLEIN THEORY IN FOUR-DIMENSIONAL SPACE–TIME

2006 ◽  
Vol 21 (28n29) ◽  
pp. 5905-5956 ◽  
Author(s):  
MATEJ PAVŠIČ
Keyword(s):  
Dimensional Space ◽  
Space Time ◽  
Dirac Field ◽  
Spin Connection ◽  
Yang Mills ◽  
Object A ◽  
Klein Theory ◽  
Dimensional Space Time ◽  
The Right ◽  
Kaluza Klein

A theory in which four-dimensional space–time is generalized to a larger space, namely a 16-dimensional Clifford space (C-space) is investigated. Curved Clifford space can provide a realization of Kaluza–Klein. A covariant Dirac equation in curved C-space is explored. The generalized Dirac field is assumed to be a polyvector-valued object (a Clifford number) which can be written as a superposition of four independent spinors, each spanning a different left ideal of Clifford algebra. The general transformations of a polyvector can act from the left and/or from the right, and form a large gauge group which may contain the group U (1) × SU (2) × SU (3) of the standard model. The generalized spin connection in C-space has the properties of Yang–Mills gauge fields. It contains the ordinary spin connection related to gravity (with torsion), and extra parts describing additional interactions, including those described by the antisymmetric Kalb–Ramond fields.

scholarly journals ON UNITARITY OF A LINEARIZED YANG–MILLS FORMULATION FOR MASSLESS AND MASSIVE GRAVITY WITH PROPAGATING TORSION

2010 ◽  
Vol 25 (26) ◽  
pp. 4911-4932
Author(s):  
ROLANDO GAITAN DEVERAS
Keyword(s):  
Degrees Of Freedom ◽  
Dimensional Space ◽  
Massive Gravity ◽  
Dynamical Variable ◽  
General Covariance ◽  
Yang Mills ◽  
Dimensional Space Time ◽  
Perturbative Regime ◽  
Massive Theory ◽  
Extended Theories

A perturbative regime based on contortion as a dynamical variable and metric as a (classical) fixed background, is performed in the context of a pure Yang–Mills formulation for gravity in a (2+1)-dimensional space–time. In the massless case, we show that the theory contains three degrees of freedom and only one is a nonunitary mode. Next, we introduce quadratical terms dependent on torsion, which preserve parity and general covariance. The linearized version reproduces an analogue Hilbert–Einstein–Fierz–Pauli unitary massive theory plus three massless modes, two of them represents nonunitary ones. Finally, we confirm the existence of a family of unitary Yang–Mills-extended theories which are classically consistent with Einstein's solutions coming from nonmassive and topologically massive gravity. The unitarity of these Yang–Mills-extended theories is shown in a perturbative regime. A possible way to perform a nonperturbative study is remarked.

scholarly journals LOOP VARIABLES WITH CHAN–PATON FACTORS

2004 ◽  
Vol 19 (01) ◽  
pp. 59-70 ◽  
Author(s):  
B. SATHIAPALAN
Keyword(s):  
Gauge Invariance ◽  
Continuum Limit ◽  
Open String ◽  
Equation Of Motion ◽  
Low Energy ◽  
Scale Transformation ◽  
Abelian Gauge ◽  
Rotation Symmetry ◽  
Yang Mills ◽  
Massless Fields

The loop variable method that has been developed for the U(1) bosonic open string is generalized to include non-Abelian gauge invariance by incorporating "Chan–Paton" gauge group indices. The scale transformation symmetry k(s)→λ(s)k(s) that was responsible for gauge invariance in the U(1) case continues to be a symmetry. In addition there is a non-Abelian "rotation" symmetry. Both symmetries crucially involve the massive modes. However, it is plausible that only a linear combination, which is the usual Yang–Mills transformation on massless fields, has a smooth (worldsheet) continuum limit. We also illustrate how an infinite number of terms in the equation of motion in the cutoff theory add up to give a term that has a smooth continuum limit, and thus contributes to the low energy Yang–Mills equation of motion.

scholarly journals Gauge Invariance and Mass Gap in (2+1)-Dimensional Yang–Mills Theory

1997 ◽  
Vol 12 (06) ◽  
pp. 1161-1171 ◽  
Author(s):  
Dimitra Karabali ◽  
V. P. Nair
Keyword(s):  
Gauge Invariance ◽  
Gauge Theories ◽  
Abelian Gauge ◽  
Gauge Invariant ◽  
Yang Mills ◽  
Mass Gap ◽  
Spatial Dimensions

In terms of a gauge-invariant matrix parametrization of the fields, we give an analysis of how the mass gap could arise in non-Abelian gauge theories in two spatial dimensions.

scholarly journals NON-ABELIAN GAUGE THEORIES AS A CONSEQUENCE OF PERTURBATIVE QUANTUM GAUGE INVARIANCE

1999 ◽  
Vol 14 (21) ◽  
pp. 3421-3432 ◽  
Author(s):  
A. ASTE ◽  
G. SCHARF
Keyword(s):  
Gauge Theory ◽  
Gauge Invariance ◽  
Gauge Theories ◽  
Fundamental Concept ◽  
Abelian Gauge ◽  
Abelian Gauge Theory ◽  
Yang Mills ◽  
Vector Bosons ◽  
Perturbative Quantum

We show for the case of interacting massless vector bosons, how the structure of Yang–Mills theories emerges automatically from a more fundamental concept, namely perturbative quantum gauge invariance. It turns out that the coupling in a non-Abelian gauge theory is necessarily of Yang–Mills type plus divergence- and coboundary-couplings. The extension of the method to massive gauge theories is briefly discussed.

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