Buch, Englisch, Band 386, 230 Seiten, HC runder Rücken kaschiert, Format (B × H): 160 mm x 241 mm, Gewicht: 1150 g
Buch, Englisch, Band 386, 230 Seiten, HC runder Rücken kaschiert, Format (B × H): 160 mm x 241 mm, Gewicht: 1150 g
Reihe: Mathematics and Its Applications
ISBN: 978-0-7923-4305-9
Verlag: Springer Netherlands
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.
Zielgruppe
Research
Autoren/Hrsg.
Fachgebiete
- Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
- Naturwissenschaften Biowissenschaften Angewandte Biologie Biomathematik
- Naturwissenschaften Physik Quantenphysik Kernphysik
- Naturwissenschaften Physik Quantenphysik Teilchenphysik
- Mathematik | Informatik Mathematik Geometrie Nicht-Euklidische Geometrie
Weitere Infos & Material
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.
