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 FINITE ORDER BFFT METHOD

2003 ◽  
Vol 18 (30) ◽  
pp. 5613-5625 ◽  
Author(s):  
M. MONEMZADEH ◽  
A. SHIRZAD
Keyword(s):  
Phase Space ◽  
Finite Order ◽  
Infinite Series ◽  
Poisson Brackets ◽  
Extended Phase Space ◽  
Extended Phase ◽  
The Matrix ◽  
Chiral Bosons ◽  
Physical Quantities

We propose a method in the context of BFFT approach that leads to truncation of the infinite series regarded as constraints in the extended phase space, as well as other physical quantities (such as Hamiltonian). This has been done for cases where the matrix of Poisson brackets among the constraints is symplectic or constant. The method is applied to the Proca model, single self dual chiral bosons and chiral Schwinger models as examples.

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.

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.

TRANSITION STATE THEORY IN EXTENDED PHASE SPACE

1993 ◽  
Vol 07 (19) ◽  
pp. 1263-1268
Author(s):  
H. DEKKER ◽  
A. MAASSEN VAN DEN BRINK
Keyword(s):  
Phase Space ◽  
Transition State Theory ◽  
Unstable Mode ◽  
Planck Equation ◽  
State Theory ◽  
Extended Phase Space ◽  
Extended Phase ◽  
Theoretical Concepts ◽  
Rate Processes ◽  
Mode Energy

Turnover theory (of the escape Γ) à la Grabert will be based solely on Kramers' Fokker–Planck equation for activated rate processes. No recourse to a microscope model or Langevin dynamics will be made. Apart from the unstable mode energy E, the analysis requires new theoretical concepts such as a constrained Gaussian transformation (CGT) and dynamically extended phase space (EPS).

scholarly journals Reality of the Wigner Functions and Quantization

2009 ◽  
Vol 2009 ◽  
pp. 1-5 ◽  
Author(s):  
Sadollah Nasiri ◽  
Samira Bahrami
Keyword(s):  
Phase Space ◽  
Quantum Statistical Mechanics ◽  
Direct Consequence ◽  
Extended Phase Space ◽  
Extended Phase ◽  
Reality Condition ◽  
Energy Quantization ◽  
Extended Action ◽  
Space Formulation ◽  
Quantum Statistical

Here we use the extended phase space formulation of quantum statistical mechanics proposed in an earlier work to define an extended lagrangian for Wigner's functions (WFs). The extended action defined by this lagrangian is a function of ordinary phase space variables. The reality condition of WFs is employed to quantize the extended action. The energy quantization is obtained as a direct consequence of the quantized action. The technique is applied to find the energy states of harmonic oscillator, particle in the box, and hydrogen atom as the illustrative examples.

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.

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