scholarly journals HOW TO SOLVE QUANTUM NONLINEAR ABELIAN GAUGE THEORY IN TWO DIMENSIONS IN THE HEISENBERG PICTURE

1998 ◽  
Vol 13 (19) ◽  
pp. 3245-3254 ◽  
Author(s):  
NORIAKI IKEDA
Keyword(s):  
Gauge Theory ◽  
Canonical Quantization ◽  
Gravitational Theory ◽  
Two Dimensions ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Operator Formalism ◽  
Abelian Gauge ◽  
Abelian Gauge Theory ◽  
Heisenberg Picture

The new method based on the operator formalism proposed by Abe and Nakanishi is applied to the quantum nonlinear Abelian gauge theory in two dimensions. The soluble models in this method are extended to a wider class of quantum field theories. We obtain the exact solution in the canonical-quantization operator formalism in the Heisenberg picture, so this analysis might shed some light on the analysis of gravitational theory and nonpolynomial field theories.

GEOMETRIC QUANTIZATION AND FIELD THEORIES — THE CHIRAL ANOMALY EXAMPLE

1989 ◽  
Vol 04 (05) ◽  
pp. 483-490 ◽  
Author(s):  
P. SCHALLER ◽  
G. SCHWARZ
Keyword(s):  
Gauge Theory ◽  
Geometric Quantization ◽  
Field Theories ◽  
Chiral Anomaly ◽  
Abelian Gauge ◽  
Abelian Gauge Theory ◽  
Quantum Operator

In the framework of geometric quantization, the chiral U(1) symmetry of a non-abelian gauge theory is considered. The chiral anomaly is computed from half form contribution of the quantum operator.

scholarly journals ONE-LOOP RENORMALIZATION OF NON-ABELIAN GAUGE THEORY AND β FUNCTION BASED ON LOOP REGULARIZATION METHOD

2008 ◽  
Vol 23 (19) ◽  
pp. 2861-2913 ◽  
Author(s):  
JIAN-WEI CUI ◽  
YUE-LIANG WU
Keyword(s):  
Gauge Theory ◽  
Regularization Method ◽  
Gauge Theories ◽  
Field Theories ◽  
Abelian Gauge ◽  
Abelian Gauge Theory ◽  
Cutoff Energy ◽  
Original Field ◽  
Β Function ◽  
Renormalization Constants

All one-loop renormalization constants for non-Abelian gauge theory are computed in detail by using the symmetry-preserving loop regularization method proposed in Refs. 1 and 2. The resulting renormalization constants are manifestly shown to satisfy Ward–Takahaski–Slavnov–Taylor identities, and lead to the well-known one loop β function for non-Abelian gauge theory of QCD.3-5 The loop regularization method is realized in the dimension of original field theories, it maintains not only symmetries but also divergent behaviors of original field theories with the introduction of two energy scales. Such two scales play the roles of characterizing and sliding energy scales as well as ultraviolet and infrared cutoff energy scales. An explicit check of those identities provides a clear demonstration how the symmetry-preserving loop regularization method can consistently be applied to non-Abelian gauge theories.

scholarly journals SOLITONIC ASPECTS OF q-FIELD THEORIES

2003 ◽  
Vol 18 (04) ◽  
pp. 627-650 ◽  
Author(s):  
R. J. FINKELSTEIN
Keyword(s):  
Gauge Theory ◽  
Lie Algebra ◽  
Lie Group ◽  
Degrees Of Freedom ◽  
Field Theories ◽  
Standard Theory ◽  
Abelian Gauge ◽  
Abelian Gauge Theory ◽  
Point Particles ◽  
Non Locality

We have examined the deformation of a generic non-Abelian gauge theory obtained by replacing its Lie group by the corresponding quantum group. This deformed gauge theory has more degrees of freedom than the theory from which it is derived. By going over from point particles in the standard theory to solitonic particles in the deformed theory, it is proposed that we interpret the new degrees of freedom as being descriptive of the non-locality of the deformed theory. It also turns out that the original Lie algebra gets replaced by two dual algebras, one of which lies close to and approaches the original Lie algebra in a correspondence limit, while the second algebra is new and disappears in this same correspondence limit. The exotic field particles associated with the second algebra can be interpreted as quark-like constituents of the solitons, which are themselves described as point particles in the first algebra. These ideas are explored for q-deformed SU(2) and GL q(3).

CONSTRAINT STRUCTURE AND QUANTIZATION OF A NON-ABELIAN GAUGE THEORY BY MEANS OF DIRAC BRACKETS

2009 ◽  
Vol 24 (32) ◽  
pp. 2611-2621
Author(s):  
PAUL BRACKEN
Keyword(s):  
Gauge Theory ◽  
Canonical Quantization ◽  
Abelian Gauge ◽  
Hamiltonian Density ◽  
Abelian Gauge Theory ◽  
Gauge Fixing ◽  
Dirac Brackets ◽  
Constraint Structure

An SO(3) non-Abelian gauge theory is introduced. The Hamiltonian density is determined and the constraint structure of the model is derived. The first-class constraints are obtained and gauge-fixing constraints are introduced into the model. Finally, using the constraints, the Dirac brackets can be determined and a canonical quantization is found using Dirac's procedure.

Regge behavior of spontaneously broken non-Abelian gauge theory

1978 ◽  
Vol 17 (2) ◽  
pp. 585-597 ◽  
Author(s):  
J. B. Bronzan ◽  
R. L. Sugar
Keyword(s):  
Gauge Theory ◽  
Abelian Gauge ◽  
Abelian Gauge Theory ◽  
Regge Behavior

scholarly journals Static force potential of a non-Abelian gauge theory in a finite box in Coulomb gauge

2021 ◽  
Vol 103 (5) ◽  
Author(s):  
Tomohiro Furukawa ◽  
Keiichi Ishibashi ◽  
H. Itoyama ◽  
Satoshi Kambayashi
Keyword(s):  
Gauge Theory ◽  
Coulomb Gauge ◽  
Static Force ◽  
Abelian Gauge ◽  
Abelian Gauge Theory ◽  
Force Potential

Non-Abelian gauge theory from the Poisson bracket

2018 ◽  
Vol 33 (30) ◽  
pp. 1850182
Author(s):  
Mu Yi Chen ◽  
Su-Long Nyeo
Keyword(s):  
Gauge Theory ◽  
Poisson Bracket ◽  
Commutation Relation ◽  
Maxwell Equations ◽  
Dynamical Variable ◽  
Gauge Fields ◽  
Abelian Gauge ◽  
Abelian Gauge Theory ◽  
Generalized Poisson ◽  
Lie Algebraic Structure

The Hamiltonian of a nonrelativistic particle coupled to non-Abelian gauge fields is defined to construct a non-Abelian gauge theory. The Hamiltonian which includes isospin as a dynamical variable dictates the dynamics of the particle and isospin according to the Poisson bracket that incorporates the Lie algebraic structure of isospin. The generalized Poisson bracket allows us to derive Wong’s equations, which describe the dynamics of isospin, and the homogeneous (sourceless) equations for non-Abelian gauge fields by following Feynman’s proof of the homogeneous Maxwell equations.It is shown that the derivation of the homogeneous equations for non-Abelian gauge fields using the generalized Poisson bracket does not require that Wong’s equations be defined in the time-axial gauge, which was used with the commutation relation. The homogeneous equations derived by using the commutation relation are not Galilean and Lorentz invariant. However, by using the generalized Poisson bracket, it can be shown that the homogeneous equations are not only Galilean and Lorentz invariant but also gauge independent. In addition, the quantum ordering ambiguity that arises from using the commutation relation can be avoided when using the Poisson bracket.From the homogeneous equations, which define the “electric field” and “magnetic field” in terms of non-Abelian gauge fields, we construct the gauge and Lorentz invariant Lagrangian density and derive the inhomogeneous equations that describe the interaction of non-Abelian gauge fields with a particle.

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