W-ALGEBRA REALIZATIONS AND W-GRAVITY ANOMALIES

1991 ◽  
Vol 06 (32) ◽  
pp. 2995-3003 ◽  
Author(s):  
C. M. HULL ◽  
L. PALACIOS
Keyword(s):  
Path Integral ◽  
Current Algebra ◽  
Gravity Anomalies ◽  
Normal Ordering ◽  
Path Integral Quantization ◽  
Transformation Rules ◽  
Higher Derivative ◽  
Quantum Current ◽  
Boson Model ◽  
Background Charge

The coupling of scalars fields to chiral W3 gravity is reviewed. In general the quantum current algebra generated by the spin-two and three currents does not close when the "natural" regularization (corresponding to the normal ordering with respect to the modes of ∂ϕi) is used, and the non-closure reflects matter-dependent anomalies in the path integral quantization. We consider the most general modification of the current, involving higher derivative "background charge" terms, and find the conditions for them to form a closed algebra in the "natural" regularization. These conditions can be satisfied only for the two-boson model. In that case, it is possible to cancel all the matter-dependent anomalies by adding finite local counter terms to the action and modifying the transformation rules of the fields.

$\mathcal W$-GRAVITY ANOMALIES WITH GHOST LOOPS AND BACKGROUND CHARGES

1993 ◽  
Vol 08 (14) ◽  
pp. 2419-2436 ◽  
Author(s):  
C. M. HULL
Keyword(s):  
Path Integral ◽  
Gravity Anomalies ◽  
Path Integral Quantization ◽  
Exact Quantum ◽  
Complete Set ◽  
Background Charge

The path-integral quantization of chiral [Formula: see text] gravity is considered and the complete set of anomalies arising from both matter and ghost integrations is calculated. The effects of background charge are included and the results are related to the operator quantization. For those matter theories with exact quantum [Formula: see text] symmetry, the ghost contributions precisely cancel the matter-dependent anomalies. The results are extended to nonchiral [Formula: see text] gravity.

LIGHT-FRONT HAMILTONIAN AND PATH INTEGRAL QUANTIZATION OF VECTOR SCHWINGER MODEL WITH A PHOTON MASS TERM

2012 ◽  
Vol 27 (27) ◽  
pp. 1250157 ◽  
Author(s):  
USHA KULSHRESHTHA
Keyword(s):  
Path Integral ◽  
Light Cone ◽  
Mass Term ◽  
Light Front ◽  
Light Cone Gauge ◽  
Schwinger Model ◽  
Path Integral Quantization ◽  
New Class ◽  
Gauge Fixing ◽  
Form Theory

Vector Schwinger model with a mass term for the photon, describing 2D electrodynamics with massless fermions, studied by us recently [U. Kulshreshtha, Mod. Phys. Lett. A22, 2993 (2007); U. Kulshreshtha and D. S. Kulshreshtha, Int. J. Mod. Phys. A22, 6183 (2007); U. Kulshreshtha, PoS LC2008, 008 (2008)], represents a new class of models. This theory becomes gauge-invariant when studied on the light-front. This is in contrast to the instant-form theory which is gauge-non-invariant. In this work, we study the light-front Hamiltonian and path integral quantization of this theory under appropriate light-cone gauge-fixing. The discretized light-cone quantization of the theory where we wish to make contact with the experimentally observational aspects of the theory would be presented in a separate paper.

PATH INTEGRAL QUANTIZATION OF SUPERSTRING

2010 ◽  
Vol 25 (02) ◽  
pp. 135-141
Author(s):  
H. A. ELEGLA ◽  
N. I. FARAHAT
Keyword(s):  
Phase Space ◽  
Differential Equations ◽  
Path Integral ◽  
Equations Of Motion ◽  
Singular System ◽  
Constrained Systems ◽  
Classical Structure ◽  
Path Integral Quantization ◽  
Total Differential

Motivated by the Hamilton–Jacobi approach of constrained systems, we analyze the classical structure of a four-dimensional superstring. The equations of motion for a singular system are obtained as total differential equations in many variables. The path integral quantization based on Hamilton–Jacobi approach is applied to quantize the system, and the integration is taken over the canonical phase space coordinates.

scholarly journals Quantum Current Algebra Symmetries and Integrable Many-Particle Schrödinger Type Quantum Hamiltonian Operators

Symmetry ◽  
2019 ◽  
Vol 11 (8) ◽  
pp. 975
Author(s):  
Dominik Prorok ◽  
Anatolij Prykarpatski
Keyword(s):  
Representation Theory ◽  
Current Algebra ◽  
Fock Space ◽  
Integrable Quantum ◽  
Quantum Hamiltonian ◽  
Quantum Symmetries ◽  
Sutherland Model ◽  
Quantum Current ◽  
Hamiltonian Operators

Based on the G. Goldin’s quantum current algebra symmetry representation theory, have succeeded in explaining a hidden relationship between the quantum many-particle Hamiltonian operators, defined in the Fock space, their factorized structure and integrability. Interesting for applications quantum oscillatory Hamiltonian operators are considered, the quantum symmetries of the integrable quantum Calogero-Sutherland model are analyzed in detail.

scholarly journals QUANTIZATION OF SINGULAR SYSTEMS WITH SECOND-ORDER LAGRANGIANS

2002 ◽  
Vol 17 (36) ◽  
pp. 2383-2391 ◽  
Author(s):  
SAMI I. MUSLIH
Keyword(s):  
Path Integral ◽  
Singular Systems ◽  
Second Order ◽  
Integral Formulation ◽  
Path Integral Formulation ◽  
Path Integral Quantization

The path integral formulation of singular systems with second-order Lagrangians is constructed by using the canonical method. The path integral quantization of Podolsky electrodynamics is studied.

ON THE PATH INTEGRAL QUANTIZATION OF CHIRAL BOSONS

1989 ◽  
Vol 04 (01) ◽  
pp. 249-255 ◽  
Author(s):  
F. A. SCHAPOSNIK ◽  
J. E. SOLOMIN
Keyword(s):  
Path Integral ◽  
Degree Of Freedom ◽  
Lagrangian Formalism ◽  
Proper Treatment ◽  
Gauge Transformations ◽  
Path Integral Quantization ◽  
Gauge Degree ◽  
Chiral Bosons

We show that, in the covariant Lagrangian formalism, a proper treatment of the gauge degree of freedom in a model of chiral bosons proposed by Siegel uncovers the presence of a Jacobian (a "Wess-Zumino action"): the group of gauge transformations gets quantized and the anomaly is absorbed.

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