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Geometry, Topology and Quantization

Geometry, Topology and Quantization
Catalogue Information
Field name Details
Dewey Class 530.1
Title Geometry, Topology and Quantization ([EBook] /) / by Pratul Bandyopadhyay.
Author Bandyopadhyay, Pratul
Other name(s) SpringerLink (Online service)
Publication Dordrecht : : Springer Netherlands : : Imprint: Springer, , 1996.
Physical Details X, 230 p. : online resource.
Series Mathematics and its applications ; 386
ISBN 9789401154260
Summary Note 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.:
Contents note 1 Manifold and Differential Forms -- 2 Spinor Structure and Twistor Geometry -- 3 Quantization -- 4 Quantization And Gauge Field -- 5 Fermions and Topology -- 6 Topological Field Theory -- References.
System details note Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site http://dx.doi.org/10.1007/978-94-011-5426-0
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