scholarly journals BRST Quantization of the Proca Model Based on the BFT and the BFV Formalism

1997 ◽  
Vol 12 (23) ◽  
pp. 4217-4239 ◽  
Author(s):  
Yong-Wan Kim ◽  
Mu-In Park ◽  
Young-Jai Park ◽  
Sean J. Yoon
Keyword(s):  
Phase Space ◽  
Brst Quantization ◽  
Brst Symmetry ◽  
Mass Term ◽  
Class Constraint ◽  
Extended Phase ◽  
Breaking Effect ◽  
Linear Character ◽  
Constraint System ◽  
Gauge Fixing

The BRST quantization of the Abelian Proca model is performed using the Batalin–Fradkin–Tyutin and the Batalin-Fradkin-Vilkovisky formalism. First, the BFT Hamiltonian method is applied in order to systematically convert a second class constraint system of the model into an effectively first class one by introducing new fields. In finding the involutive Hamiltonian we adopt a new approach which is simpler than the usual one. We also show that in our model the Dirac brackets of the phase space variables in the original second class constraint system are exactly the same as the Poisson brackets of the corresponding modified fields in the extended phase space due to the linear character of the constraints comparing the Dirac or Faddeev–Jackiw formalisms. Then, according to the BFV formalism we obtain that the desired resulting Lagrangian preserving BRST symmetry in the standard local gauge fixing procedure naturally includes the Stückelberg scalar related to the explicit gauge symmetry breaking effect due to the presence of the mass term. We also analyze the nonstandard nonlocal gauge fixing procedure.

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.

scholarly journals BATALIN-TYUTIN QUANTIZATION OF THE CHERN-SIMONS-PROCA THEORY

1995 ◽  
Vol 10 (15n16) ◽  
pp. 1119-1133 ◽  
Author(s):  
EI-BYUNG PARK ◽  
YONG-WAN KIM ◽  
YOUNG-JAI PARK ◽  
YONDUK KIM ◽  
WON TAE KIM
Keyword(s):  
Mass Term ◽  
Three Dimensions ◽  
Quantum Mechanical ◽  
Class Constraint ◽  
Hamiltonian Method ◽  
Extended Phase ◽  
Constraint System ◽  
New Type ◽  
Chern Simons ◽  
Gauge Anomaly

We quantize the Chern-Simons-Proca theory in three dimensions by using the Batalin-Tyutin Hamiltonian method, which systematically embeds second-class constraint system into first-class by introducing new fields in the extended phase space. As a result, we obtain simultaneously the Stückelberg scalar term, which is needed to cancel the gauge anomaly due to the mass term, and the new type of Wess-Zumino action, which is irrelevant to the gauge symmetry. We also investigate the ir property of the Chern-Simons-Proca theory by using the Batalin-Tyutin formalism as compared to the symplectic formalism. As a result, we observe that the resulting theory is precisely the gauge-invariant Chern-Simons-Proca quantum-mechanical version of this theory.

scholarly journals Dirac’s Method for the Two-Dimensional Damped Harmonic Oscillator in the Extended Phase Space

Mathematics ◽  
2018 ◽  
Vol 6 (10) ◽  
pp. 180 ◽  
Author(s):  
Laure Gouba
Keyword(s):  
Phase Space ◽  
Harmonic Oscillator ◽  
Canonical Quantization ◽  
Extended Phase Space ◽  
Two Dimensional ◽  
Class Constraint ◽  
Extended Phase ◽  
Damped Harmonic Oscillator ◽  
Points Of View ◽  
Space Description

The system of a two-dimensional damped harmonic oscillator is revisited in the extended phase space. It is an old problem that has already been addressed by many authors that we present here with some fresh points of view and carry on a whole discussion. We show that the system is singular. The classical Hamiltonian is proportional to the first-class constraint. We pursue with the Dirac’s canonical quantization procedure by fixing the gauge and provide a reduced phase space description of the system. As a result, the quantum system is simply modeled by the original quantum Hamiltonian.

Remarks on the linking theory of shape dynamics

2018 ◽  
Vol 15 (06) ◽  
pp. 1850098
Author(s):  
P. P. Yu
Keyword(s):  
Phase Space ◽  
Vector Bundle ◽  
Short Note ◽  
Extended Phase Space ◽  
Geometric Structures ◽  
Extended Phase ◽  
Shape Dynamics ◽  
Canonical Gravity ◽  
Alternative Description ◽  
Gauge Fixing

This short note is an attempt to bring out the geometric structures in the linking theory of shape dynamics. Symplectic induction is applied to give a natural construction of the extended phase space used in the linking theory as a trivial vector bundle over the original phase space for canonical gravity. The geometry of the gauge fixing for shape dynamics is analyzed with the assistance of the Lichnerowicz–York equation lifted to the extended phase space. An alternative description is provided to show how the same geometry simply derives from symplectic induction.

THE sp(3) BRST HAMILTONIAN FORMALISM FOR THE YANG–MILLS FIELDS

2008 ◽  
Vol 23 (10) ◽  
pp. 737-750 ◽  
Author(s):  
CARMEN IONESCU
Keyword(s):  
Brst Symmetry ◽  
Hamiltonian Formalism ◽  
General Rule ◽  
Extended Phase Space ◽  
Extended Phase ◽  
Yang Mills ◽  
First Approximation ◽  
Gauge Term ◽  
Generalized Symmetry ◽  
Gauge Fixing

The paper presents in all its nontrivial details the sp(3) BRST Hamiltonian formalism. It is based on structuring the extended phase space on many levels. In this picture, the standard BRST symmetry appears as being only the first approximation of a generalized symmetry, acting as a horizontal (same level) operator. The gauge-fixing problem is completely solved by formulating a theorem and a general rule which allow the choice of a simple gauge term. As an example, the Hamiltonian sp(3) quantization of the Yang–Mills model is exhaustively presented.

scholarly journals On the BRST Quantization of the Massless Bosonic Particle in Twistor-Like Formulation

1997 ◽  
Vol 12 (18) ◽  
pp. 3259-3273 ◽  
Author(s):  
Igor Bandos ◽  
Alexey Maznytsia ◽  
Igor Rudychev ◽  
Dmitri Sorokin
Keyword(s):  
Dynamical System ◽  
Phase Space ◽  
Path Integral ◽  
Brst Quantization ◽  
Extended Phase Space ◽  
Particle Path ◽  
Extended Phase ◽  
Conversion Procedure ◽  
Particle Propagator ◽  
Hamiltonian Analysis

We study some features of bosonic-particle path-integral quantization in a twistor-like approach by the use of the BRST–BFV-quantization prescription. In the course of the Hamiltonian analysis we observe links between various formulations of the twistor-like particle by performing a conversion of the Hamiltonian constraints of one formulation to another. A particular feature of the conversion procedure applied to turn the second-class constraints into first-class constraints is that the simplest Lorentz-covariant way to do this is to convert a full mixed set of the initial first- and second-class constraints rather than explicitly extracting and converting only the second-class constraints. Another novel feature of the conversion procedure applied below is that in the case of the D = 4 and D = 6 twistor-like particle the number of new auxiliary Lorentz-covariant coordinates, which one introduces to get a system of first-class constraints in an extended phase space, exceeds the number of independent second-class constraints of the original dynamical system. We calculate the twistor-like particle propagator in D = 3,4,6 space–time dimensions and show that it coincides with that of a conventional massless bosonic particle.

scholarly journals BV AND BFV FORMULATION OF A GAUGE THEORY OF QUADRATIC LIE ALGEBRAS IN 2D AND A CONSTRUCTION OF W3 TOPOLOGICAL GRAVITY

1994 ◽  
Vol 09 (23) ◽  
pp. 2157-2165 ◽  
Author(s):  
ÖMER F. DAYI
Keyword(s):  
Gauge Theory ◽  
Phase Space ◽  
Lie Algebras ◽  
Brst Symmetry ◽  
Field Method ◽  
Continuous Variable ◽  
Two Dimensions ◽  
Gauge Fixing ◽  
Topological Gravity ◽  
The One

The recently proposed generalized field method for solving the master equation of Batalin and Vilkovisky is applied to a gauge theory of quadratic Lie algebras in two dimensions. The charge corresponding to BRST symmetry derived from this solution in terms of the phase space variables by using the Noether procedure, and the one found due to the BFV-method are compared and found to coincide. W3-algebra, formulated in terms of a continuous variable is exploit in the mentioned gauge theory to construct a W3 topological gravity. Moreover, its gauge fixing is briefly discussed.

THE DEGENERATE SECTOR OF ASHTEKAR'S PHASE SPACE

1998 ◽  
Vol 13 (35) ◽  
pp. 2839-2843 ◽  
Author(s):  
YONGGE MA ◽  
CANBIN LIANG
Keyword(s):  
Phase Space ◽  
Class Constraint ◽  
Constraint System

We study the phase space of Ashtekar's (3+l)-gravity which involves degenerate triads. A new first-class constraint system is found, which describes a degenerate sector of the phase space. The implications of this constraint system in the dynamics of degenerate triads are also discussed.

scholarly journals QUANTUM AND CLASSICAL GAUGE SYMMETRIES IN A MODIFIED QUANTIZATION SCHEME

2001 ◽  
Vol 16 (10) ◽  
pp. 1775-1788 ◽  
Author(s):  
KAZUO FUJIKAWA ◽  
HIROAKI TERASHIMA
Keyword(s):  
Gauge Symmetry ◽  
Brst Symmetry ◽  
Mass Term ◽  
Large Mass ◽  
Quantization Scheme ◽  
Mass Limit ◽  
Classical Action ◽  
Gauge Invariant ◽  
Gauge Fixing ◽  
Nonlinear Gauge

The use of the mass term as a gauge fixing term has been studied by Zwanziger, Parrinello and Jona-Lasinio, which is related to the nonlinear gauge [Formula: see text] of Dirac and Nambu in the large mass limit. We have recently shown that this modified quantization scheme is in fact identical to the conventional local Faddeev–Popov formula without taking the large mass limit, if one takes into account the variation of the gauge field along the entire gauge orbit and if the Gribov complications can be ignored. This suggests that the classical massive vector theory, for example, is interpreted in a more flexible manner either as a gauge invariant theory with a gauge fixing term added, or as a conventional massive nongauge theory. As for massive gauge particles, the Higgs mechanics, where the mass term is gauge-invariant, has a more intrinsic meaning. It is suggested that we extend the notion of quantum gauge symmetry (BRST symmetry) not only to classical gauge theory but also to a wider class of theories whose gauge symmetry is broken by some extra terms in the classical action. We comment on the implications of this extended notion of quantum gauge symmetry.

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