scholarly journals Canonical formulation of a new action for a nonrelativistic particle coupled to gravity

2020 ◽  
Vol 101 (12) ◽  
Author(s):  
Rabin Banerjee ◽  
Pradip Mukherjee
Keyword(s):  
Nonrelativistic Particle ◽  
Canonical Formulation

scholarly journals QUANTUM GRAVITY BY THE COMPLEX CANONICAL FORMULATION

1992 ◽  
Vol 01 (03n04) ◽  
pp. 439-523 ◽  
Author(s):  
HIDEO KODAMA
Keyword(s):  
General Relativity ◽  
Quantum Gravity ◽  
Conventional Treatment ◽  
Quantum States ◽  
Hamiltonian Constraint ◽  
Canonical Formulation ◽  
Recent Developments ◽  
Canonical Approach ◽  
New Formulation ◽  
Basic Features

The basic features of the complex canonical formulation of general relativity and the recent developments in the quantum gravity program based on it are reviewed. The exposition is intended to be complementary to the review articles already available and some original arguments are included. In particular the conventional treatment of the Hamiltonian constraint and quantum states in the canonical approach to quantum gravity is criticized and a new formulation is proposed.

scholarly journals Canonical Formulation of Superstring

1985 ◽  
Vol 73 (2) ◽  
pp. 476-495 ◽  
Author(s):  
T. Hori ◽  
K. Kamimura
Keyword(s):  
Canonical Formulation

Quantum statistical physics: Functional integration formalism

2021 ◽  
pp. 64-89
Author(s):  
Jean Zinn-Justin
Keyword(s):  
Phase Space ◽  
Integral Representation ◽  
Density Matrix ◽  
Thermal Equilibrium ◽  
Degrees Of Freedom ◽  
Functional Integral ◽  
Complex Variables ◽  
Path Integral Representation ◽  
Canonical Formulation ◽  
Grand Canonical

The functional integral representation of the density matrix at thermal equilibrium in non-relativistic quantum mechanics (QM) with many degrees of freedom, in the grand canonical formulation is introduced. In QM, Hamiltonians H(p,q) can be also expressed in terms of creation and annihilation operators, a method adapted to the study of perturbed harmonic oscillators. In the holomorphic formalism, quantum operators act by multiplication and differentiation on a vector space of analytic functions. Alternatively, they can also be represented by kernels, functions of complex variables that correspond in the classical limit to a complex parametrization of phase space. The formalism is adapted to the description of many-body boson systems. To this formalism corresponds a path integral representation of the density matrix at thermal equilibrium, where paths belong to complex spaces, instead of the more usual position–momentum phase space. A parallel formalism can be set up to describe systems with many fermion degrees of freedom, with Grassmann variables replacing complex variables. Both formalisms can be generalized to quantum gases of Bose and Fermi particles in the grand canonical formulation. Field integral representations of the corresponding quantum partition functions are derived.

The interaction of molecular multipoles with the electromagnetic field in the canonical formulation of non-covariant quantum electrodynamics

1970 ◽  
Vol 319 (1539) ◽  
pp. 549-563 ◽  
Keyword(s):  
Electromagnetic Field ◽  
Physical Interpretation ◽  
Quantum Electrodynamics ◽  
Unitary Transformation ◽  
Canonical Quantization ◽  
Multipole Moments ◽  
Gauge Invariant ◽  
Covariant Quantum ◽  
Canonical Formulation ◽  
Gauge Conditions

The procedure devised by Dirac for the canonical quantization of systems described by degenerate lagrangians is used to construct the hamiltonian for molecules interacting with the electromagnetic field. The hamiltonian obtained is expressed in terms of the gauge invariant field strengths and the electric and magnetic multipole moments of the molecules. The Coulomb gauge is introduced but other gauge conditions could be used. Finally, a physical interpretation of the unitary transformation that may be used to generate the multipole hamiltonian is given.

scholarly journals A new action for nonrelativistic particle in curved background

2019 ◽  
Vol 797 ◽  
pp. 134834 ◽  
Author(s):  
Rabin Banerjee ◽  
Pradip Mukherjee
Keyword(s):  
Nonrelativistic Particle

Implementation of a Multivariable Control

2000 ◽  
Author(s):  
Louis J. Larkin ◽  
James Philpott
Keyword(s):  
Fixed Point ◽  
Control System ◽  
Programming Language ◽  
Multivariable Control ◽  
Engine Control ◽  
Engine Control System ◽  
Canonical Formulation ◽  
Technology Demonstrator

A multivariable control (MVC) was designed and implemented for the Joint Technology Demonstrator Engine (JTDE) XTE65-2. The engine control system utilized an existing MC68000 processor that used fixed point ADA for its programming language and was limited in throughput and memory. A canonical formulation for the MVC compensator was used to minimize memory and calculation load on the processor. Use of this formulation resulted in a number of numerical difficulties. This paper relates the issues associated with the implementation of a MVC in this environment, and some approaches to solve these difficulties.

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