THE CANONICAL ALGEBRA OF SYMMETRIES FOR GAUGE THEORIES: THE EXAMPLE OF ANYONS

1994 ◽  
Vol 09 (31) ◽  
pp. 2903-2912
Author(s):  
J. M. PONS
Keyword(s):  
Gauge Theories ◽  
Canonical Formalism ◽  
Symmetry Algebra ◽  
Ideal Gas ◽  
Constrained Systems ◽  
Canonical Algebra ◽  
Constants Of Motion ◽  
Symmetry Generators ◽  
Continuous Symmetries

Some special features of the algebra of continuous symmetries for constrained systems are illustrated through the example of the nonrelativistic ideal gas of anyons. The relation between constants of motion and symmetry generators for this gauge system is completely worked out. The generators of both its rigid and gauge continuous symmetries are explicitly given in the canonical formalism. Also the interplay between these two types of symmetries within the symmetry algebra is exhibited.

scholarly journals Symmetry algebra in gauge theories of gravity

2019 ◽  
Vol 36 (4) ◽  
pp. 045002 ◽  
Author(s):  
Cristóbal Corral ◽  
Yuri Bonder
Keyword(s):  
Gauge Theories ◽  
Symmetry Algebra ◽  
Theories Of Gravity

Canonical formalism for gauge theories with application to monopole

1976 ◽  
Vol 114 (1) ◽  
pp. 61-99 ◽  
Author(s):  
Norman H. Christ ◽  
Alan H. Guth ◽  
Erick J. Weinberg
Keyword(s):  
Gauge Theories ◽  
Canonical Formalism

CURRENT COMMUTATOR ANOMALIES AND CHIRAL ANOMALIES IN THE CANONICAL FORMALISM

1988 ◽  
Vol 03 (07) ◽  
pp. 691-701 ◽  
Author(s):  
SHINOBU HOSONO ◽  
KOICHI SEO
Keyword(s):  
Electric Field ◽  
Regularization Method ◽  
Gauge Theories ◽  
Canonical Formalism ◽  
Current Commutator ◽  
Current Divergence ◽  
Dimensional Spacetime ◽  
Current Electric Field

Without recourse to the Bjorken-Johnson-Low (BJL) method, current-current and current-electric-field commutator anomalies are evaluated in chiral gauge theories in two-and four-dimensional spacetime with the help of a gauge covariant regularization method. The results are consistent with previous analyses through the BJL method, and partially confirmed Faddeev’s conjecture on the commutator anomalies of the Gauss law constraint operators within the canonical formalism. The chiral anomalies of the current divergence are derived from these commutator anomalies in the Weyl gauge where current-electric-field commutator anomalies play important roles.

scholarly journals ELECTRIC-MAGNETIC DUALITY AND THE “LOOP REPRESENTATION” IN ABELIAN GAUGE THEORIES

1996 ◽  
Vol 11 (13) ◽  
pp. 1107-1114 ◽  
Author(s):  
LORENZO LEAL
Keyword(s):  
Phase Space ◽  
Gauge Theories ◽  
Topological Algebra ◽  
Geometric Representation ◽  
Abelian Gauge ◽  
Dual Algebra ◽  
Nonlocal Operators ◽  
Canonical Algebra

Abelian gauge theories are quantized in a geometric representation that generalizes the loop representation and treats electric and magnetic operators on the same footing. The usual canonical algebra is turned into a topological algebra of nonlocal operators that resembles the order-disorder dual algebra of ’t Hooft. These dual operators provide a complete description of the physical phase space of the theories.

CONFORMAL PARASUPERSYMMETRY IN QUANTUM MECHANICS

1989 ◽  
Vol 04 (26) ◽  
pp. 2519-2529 ◽  
Author(s):  
STEPHANE DURAND ◽  
LUC VINET
Keyword(s):  
Quantum Mechanics ◽  
Energy Spectrum ◽  
Symmetry Algebra ◽  
Wave Functions ◽  
Quantum Mechanical ◽  
Quantum Mechanical System ◽  
One Dimensional ◽  
Complete Determination ◽  
Symmetry Generators

Conformal parasupersymmetry of order 2 is exemplified using a one-dimensional quantum mechanical system. Symmetry generators are seen to realize trilinear structure relations. The relevant representations of this novel symmetry algebra are constructed and shown to allow for a complete determination of the energy spectrum and wave functions of the system.

scholarly journals Symmetries versus the spectrum of $ J\bar T$-deformed CFTs

2021 ◽  
Vol 10 (3) ◽  
Author(s):  
Monica Guica
Keyword(s):  
Finite Size ◽  
Symmetry Algebra ◽  
Energy Operator ◽  
Size Spectrum ◽  
Proper Action ◽  
Gauge Transformations ◽  
Infinite Dimensional ◽  
Symmetry Generators ◽  
Energy Dependent ◽  
Equal Spacing

It has been recently shown that classical J\bar TJT‾ - deformed CFTs possess an infinite-dimensional Witt-Kac-Moody symmetry, generated by certain field-dependent coordinate and gauge transformations. On a cylinder, however, the equal spacing of the descendants’ energies predicted by such a symmetry algebra is inconsistent with the known finite-size spectrum of J\bar TJT‾ - deformed CFTs. Also, the associated quantum symmetry generators do not have a proper action on the Hilbert space. In this article, we resolve this tension by finding a new set of (classical) conserved charges, whose action is consistent with semiclassical quantization, and which are related to the previous symmetry generators by a type of energy-dependent spectral flow. The previous inconsistency between the algebra and the spectrum is resolved because the energy operator does not belong to the spectrally flowed sector.

Canonical formalism of gauge theories with reducible constraints

1985 ◽  
Vol 28 (7) ◽  
pp. 576-579
Author(s):  
P. M. Lavrov ◽  
I. V. Tyutin
Keyword(s):  
Gauge Theories ◽  
Canonical Formalism
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