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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Geometry, Topology and Quantization

Geometry, Topology and Quantization

Bandyopadhyay, P.

Hardcover

Series: Mathematics and Its Applications, Book 386

Geometry

ISBN10: 0792343050
ISBN13: 9780792343059
Publisher: Springer Nature
Published: Oct 31 1996
Pages: 230
Weight: 1.14
Height: 0.56 Width: 6.14 Depth: 9.21
Language: English
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.

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