Geometry of time-spaces : non-commutative algebraic geometry, applied to quantum theory

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Bibliographic Information

Geometry of time-spaces : non-commutative algebraic geometry, applied to quantum theory

Olav Arnfinn Laudal

World Scientific, c2011

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Note

Includes bibliographical references (p. 137-139) and index

Description and Table of Contents

Description

This is a monograph about non-commutative algebraic geometry, and its application to physics. The main mathematical inputs are the non-commutative deformation theory, moduli theory of representations of associative algebras, a new non-commutative theory of phase spaces, and its canonical Dirac derivation. The book starts with a new definition of time, relative to which the set of mathematical velocities form a compact set, implying special and general relativity. With this model in mind, a general Quantum Theory is developed and shown to fit with the classical theory. In particular the "toy"-model used as example, contains, as part of the structure, the classical gauge groups u(1), su(2) and su(3), and therefore also the theory of spin and quarks, etc.

Table of Contents

  • Introduction
  • Phase Spaces and the Dirac Derivation
  • Non-Commutative Deformations and the Structure of the Moduli Space of Simple Representations
  • Geometry of Time-Spaces and the General Dynamical Law
  • Interaction, Decoherence and Decay.

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