Ebook: Geometry, Topology and Quantization
Author: Pratul Bandyopadhyay (auth.)
- Tags: Theoretical Mathematical and Computational Physics, Quantum Physics, Elementary Particles Quantum Field Theory, Nuclear Physics Heavy Ions Hadrons, Differential Geometry
- Series: Mathematics and Its Applications 386
- Year: 1996
- Publisher: Springer Netherlands
- Edition: 1
- Language: English
- pdf
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.
Content:
Front Matter....Pages i-x
Manifold and Differential Forms....Pages 1-33
Spinor Structure and Twistor Geometry....Pages 35-66
Quantization....Pages 67-97
Quantization and Gauge Field....Pages 99-125
Fermions and Topology....Pages 127-181
Topological Field Theory....Pages 183-216
Back Matter....Pages 217-230
Content:
Front Matter....Pages i-x
Manifold and Differential Forms....Pages 1-33
Spinor Structure and Twistor Geometry....Pages 35-66
Quantization....Pages 67-97
Quantization and Gauge Field....Pages 99-125
Fermions and Topology....Pages 127-181
Topological Field Theory....Pages 183-216
Back Matter....Pages 217-230
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