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Geometry, Topology and Quantization (Paperback, Softcover reprint of the original 1st ed. 1996)
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Geometry, Topology and Quantization (Paperback, Softcover reprint of the original 1st ed. 1996)
Series: Mathematics and Its Applications, 386
Expected to ship within 10 - 15 working days
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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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