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OverviewThis 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. Full Product DetailsAuthor: P. BandyopadhyayPublisher: Springer Imprint: Springer Edition: Softcover reprint of the original 1st ed. 1996 Volume: 386 Dimensions: Width: 16.00cm , Height: 1.30cm , Length: 24.00cm Weight: 0.397kg ISBN: 9789401062824ISBN 10: 940106282 Pages: 230 Publication Date: 22 November 2012 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Manufactured on demand ![]() We will order this item for you from a manufactured on demand supplier. Table of ContentsPreface. 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. Index.ReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |