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.

Shape Dynamics and the Linking Theory

2018 ◽  
Author(s):  
Flavio Mercati
Keyword(s):  
Phase Space ◽  
Degrees Of Freedom ◽  
Line Element ◽  
Hamiltonian Formulation ◽  
Operational Definition ◽  
Extended Phase Space ◽  
Extended Phase ◽  
Problem Of Time ◽  
Definition Of ◽  
Matter Fields

This chapter explains in detail the current Hamiltonian formulation of SD, and the concept of Linking Theory of which (GR) and SD are two complementary gauge-fixings. The physical degrees of freedom of SD are identified, the simple way in which it solves the problem of time and the problem of observables in quantum gravity are explained, and the solution to the problem of constructing a spacetime slab from a solution of SD (and the related definition of physical rods and clocks) is described. Furthermore, the canonical way of coupling matter to SD is introduced, together with the operational definition of four-dimensional line element as an effective background for matter fields. The chapter concludes with two ‘structural’ results obtained in the attempt of finding a construction principle for SD: the concept of ‘symmetry doubling’, related to the BRST formulation of the theory, and the idea of ‘conformogeometrodynamics regained’, that is, to derive the theory as the unique one in the extended phase space of GR that realizes the symmetry doubling idea.

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.

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.

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.

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.

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