{"product_id":"geometry-topology-and-quantization-9789401062824","title":"Geometry, Topology and Quantization","description":"\u003cp\u003e • Author(s): P. Bandyopadhyay\u003cbr\u003e • Publisher: Springer\u003cbr\u003e • Publisher Imprint: Springer\u003cbr\u003e • BISAC: Physics - Mathematical \u0026amp; Computational\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThis 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.\u003c\/p\u003e","brand":"Springer","offers":[{"title":"Paperback","offer_id":45281770504343,"sku":"9789401062824","price":7277.0,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9789401062824.webp?v=1769300184","url":"https:\/\/atlanticbooks.com\/products\/geometry-topology-and-quantization-9789401062824","provider":"Atlantic Books","version":"1.0","type":"link"}