Geometry, Topology and Quantization (Hardcover, 1996 ed.)

This is a monograph on geometrical and topological features which arise in various quantization procedures. Quantization schemes consider the feasibility of arriving at a quantum system from a classical one and these involve three major procedures viz. i) geometric quantization, ii) Klauder quantization, and iii) stochastic quanti zation. In geometric quantization we have to incorporate a hermitian line bundle to effectively generate the quantum Hamiltonian operator from a classical Hamil tonian. Klauder quantization also takes into account the role of the connection one-form along with coordinate independence. In stochastic quantization as pro posed by Nelson, Schrodinger equation is derived from Brownian motion processes; however, we have difficulty in its relativistic generalization. It has been pointed out by several authors that this may be circumvented by formulating a new geometry where Brownian motion proceses are considered in external as well as in internal space and, when the complexified space-time is considered, the usual path integral formulation is achieved. When this internal space variable is considered as a direc tion vector introducing an anisotropy in the internal space, we have the quantization of a Fermi field. This helps us to formulate a stochastic phase space formalism when the internal extension can be treated as a gauge theoretic extension. This suggests that massive fermions may be considered as Skyrme solitons. The nonrelativistic quantum mechanics is achieved in the sharp point limit."

General

Imprint:	Springer
Country of origin:	Netherlands
Series:	Mathematics and Its Applications, 386
Release date:	2001
First published:	1996
Authors:	P. Bandyopadhyay
Dimensions:	235 x 155 x 14mm (L x W x T)
Format:	Hardcover
Pages:	230
Edition:	1996 ed.
ISBN-13:	978-0-7923-4305-9
Categories:	Books > Science & Mathematics > Mathematics > Applied mathematics > Mathematics for scientists & engineers Books > Science & Mathematics > Physics > Quantum physics (quantum mechanics) > General Promotions
LSN:	0-7923-4305-0
Barcode:	9780792343059

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