scholarly journals A CHIRAL SCHWINGER MODEL, ITS CONSTRAINT STRUCTURE AND APPLICATIONS TO ITS QUANTIZATION

2008 ◽  
Vol 23 (06) ◽  
pp. 855-869 ◽  
Author(s):  
PAUL BRACKEN
Keyword(s):  
Scalar Field ◽  
Canonical Quantization ◽  
Gauge Invariant ◽  
Invariant Model ◽  
Schwinger Model ◽  
Gauge Fixing ◽  
Dirac Brackets ◽  
Constraint Structure

The Jackiw–Rajaraman version of the chiral Schwinger model is studied as a function of the renormalization parameter. The constraints are obtained and they are used to carry out canonical quantization of the model by means of Dirac brackets. By introducing an additional scalar field, it is shown that the model can be made gauge invariant. The gauge invariant model is quantized by establishing a pair of gauge fixing constraints in order that the method of Dirac can be used.

FADDEEV–JACKIW FORMALISM FOR CONSTRAINED SYSTEMS WITH GRASSMANN DYNAMICAL FIELD VARIABLES

2012 ◽  
Vol 27 (24) ◽  
pp. 1250145 ◽  
Author(s):  
EDMUNDO C. MANAVELLA
Keyword(s):  
Iterative Process ◽  
Canonical Quantization ◽  
Constrained Systems ◽  
Independent Variables ◽  
Gauge Symmetries ◽  
Gauge Fixing ◽  
Quantization Formalism ◽  
Dirac Brackets ◽  
Constraint Structure ◽  
Dynamical Field

The Faddeev–Jackiw canonical quantization formalism for constrained systems with Grassmann dynamical variables within the framework of the field theory is reviewed. First, by means of a iterative process, the symplectic supermatrix is constructed and their associated constraints are found. Next, by taking into account the phase space of the system, the constraint structure is considered. It is found that, if there are no auxiliary dynamical field variables, the supermatrix whose elements are the Bose–Fermi brackets between the constraints associated with the independent dynamical field variables coincides with the symplectic supermatrix corresponding to these independent variables. An alternative procedure to obtain the first-class constraints is given. It is shown that for systems with gauge symmetries, by means of suitable gauge-fixing conditions, a nonsingular final symplectic supermatrix can be found. Then, two possible ways of calculating the Faddeev–Jackiw brackets are pointed out. The relation between the Faddeev–Jackiw and Dirac brackets is discussed. Throughout the previous developments, the Faddeev–Jackiw and Dirac algorithms are compared. Finally, the Faddeev–Jackiw canonical quantization method is applied to a simple model and the obtained results are compared with the ones corresponding to the use of the Dirac procedure on this model.

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.

CONSISTENT CANONICAL QUANTIZATION OF THE CHIRAL SCHWINGER MODEL

1991 ◽  
Vol 06 (21) ◽  
pp. 3823-3841 ◽  
Author(s):  
FUAD M. SARADZHEV
Keyword(s):  
Canonical Quantization ◽  
Bound State ◽  
Gauge Invariant ◽  
Gauge Transformations ◽  
Schwinger Model ◽  
Canonical Variables ◽  
Bound State Spectrum

For the chiral Schwinger model, the canonical quantization formulation consistent with the Gauss law constraint is developed. This requires modification of the canonical variables of the model. The formulation presented is unitary and gauge-invariant under modified gauge transformations. The bound state spectrum of the model is established.

HAMILTONIAN EMBEDDING OF EINSTEIN–HILBERT ACTION IN (1+1) DIMENSIONS

2011 ◽  
Vol 26 (26) ◽  
pp. 1995-2006
Author(s):  
M. MONEMZADEH ◽  
V. NIKOOFARD ◽  
R. RAMEZANI-ARANI
Keyword(s):  
Phase Space ◽  
Finite Order ◽  
Canonical Analysis ◽  
Extended Phase Space ◽  
Extended Phase ◽  
Gauge Invariant ◽  
Invariant Model ◽  
Constrained Model ◽  
Constraint Structure ◽  
Hilbert Action

Canonical analysis of constraint structure of Einstein–Hilbert action in (1+1) dimensions possesses a mixed constrained model. By means of finite order BFT approach in the extended phase space, it converts to a fully gauge-invariant model. Embedded Hamiltonian in this extended phase space is independent of momenta similar to the classical Hamiltonian.

A BRST formulation for the conic constrained particle

2018 ◽  
Vol 33 (10n11) ◽  
pp. 1850055 ◽  
Author(s):  
Gabriel D. Barbosa ◽  
Ronaldo Thibes
Keyword(s):  
Brst Symmetry ◽  
Extended Phase Space ◽  
Extended Phase ◽  
Gauge Invariant ◽  
Generating Functional ◽  
Class System ◽  
First Order ◽  
Symmetry Transformations ◽  
Dirac Brackets ◽  
Constraint Structure

We describe the gauge invariant BRST formulation of a particle constrained to move in a general conic. The model considered constitutes an explicit example of an originally second-class system which can be quantized within the BRST framework. We initially impose the conic constraint by means of a Lagrange multiplier leading to a consistent second-class system which generalizes previous models studied in the literature. After calculating the constraint structure and the corresponding Dirac brackets, we introduce a suitable first-order Lagrangian, the resulting modified system is then shown to be gauge invariant. We proceed to the extended phase space introducing fermionic ghost variables, exhibiting the BRST symmetry transformations and writing the Green’s function generating functional for the BRST quantized model.

scholarly journals Chiral Schwinger model with Faddeevian anomaly and its BRST quantization

2020 ◽  
Vol 80 (2) ◽  
Author(s):  
Sanjib Ghosal ◽  
Anisur Rahaman
Keyword(s):  
Phase Space ◽  
Brst Quantization ◽  
Hamiltonian Formulation ◽  
Extended Phase Space ◽  
Extended Phase ◽  
Gauge Invariant ◽  
Schwinger Model ◽  
Gauge Fixing

Abstract We consider chiral Schwinger model with Faddeevian anomaly, and carry out the quantization of both the gauge-invariant and non-invariant version of this model has been. Theoretical spectra of this model have been determined both in the Lagrangian and Hamiltonian formulation and a necessary correlation between these two are made. BRST quantization using BFV formalism has been executed which shows spontaneous appearance of Wess–Zumino term during the process of quantization. The gauge invariant version of this model in the extended phase space is found to map onto the physical phase space with the appropriate gauge fixing condition.

GAUGE-INVARIANT REFORMULATION OF THE VECTOR SCHWINGER MODEL WITH A PHOTON MASS TERM AND ITS HAMILTONIAN, PATH INTEGRAL AND BRST FORMULATIONS

2007 ◽  
Vol 22 (32) ◽  
pp. 6183-6201 ◽  
Author(s):  
USHA KULSHRESHTHA ◽  
D. S. KULSHRESHTHA
Keyword(s):  
Path Integral ◽  
Quantum Electrodynamics ◽  
Hamiltonian Path ◽  
Mass Term ◽  
Photon Mass ◽  
Gauge Invariant ◽  
Schwinger Model ◽  
Gauge Fixing ◽  
Stueckelberg Formalism ◽  
Massless Fermions

Using the Stueckelberg formalism, we construct a gauge-invariant version of the vector Schwinger model (VSM) with a photon mass term studied by one of us recently. This model describes two-dimensional massive electrodynamics with massless fermions, where the left-handed and right-handed fermions are coupled to the electromagnetic field with equal couplings. This model describing the 2D massive electrodynamics becomes gauge-noninvariant (GNI). This is in contrast to the case of the massless VSM which is a gauge-invariant (GI) theory (as a consequence of demanding the regularization for the theory to be GI). In this work we first construct a GI theory corresponding to this model describing the 2D massive electrodynamics, using the Stueckelberg formalism and then we recover the physical contents of the original GNI theory studied earlier, under some special gauge choice. We then study the Hamiltonian, path integral and BRST formulations of this GI theory under appropriate gauge-fixing. The theory presents a new class of models in the 2D quantum electrodynamics with massless fermions but with a photon mass term.

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.

scholarly journals Canonical Quantization of the Scalar Field: The Measure Theoretic Perspective

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
José Velhinho
Keyword(s):  
Scalar Field ◽  
Canonical Quantization ◽  
Field Theories ◽  
Quantum Fields ◽  
Theoretical Methods ◽  
Local Properties ◽  
Free Scalar ◽  
Free Fields ◽  
Field Behaviour

This review is devoted to measure theoretical methods in the canonical quantization of scalar field theories. We present in some detail the canonical quantization of the free scalar field. We study the measures associated with the free fields and present two characterizations of the support of these measures. The first characterization concerns local properties of the quantum fields, whereas for the second one we introduce a sequence of variables that test the field behaviour at large distances, thus allowing distinguishing between the typical quantum fields associated with different values of the mass.

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