Introduction to Random Time and Quantum Randomness

by Chung, Kai Lai; Zambrini, Jean-Claude

• ISBN13: 9789812383884
• ISBN10: 9812383883
• Edition: Revised
• Format: Hardcover
• Copyright: 2003-07-01
• Publisher: World Scientific Pub Co Inc

Summary

This book is made up of two essays on the role of time in probability and quantum physics. In the first one, K. L. Chung explains why, in his view, probability theory starts where random time appears. This idea is illustrated in various probability schemes and the deep impact of those random times on the theory of the stochastic process is shown.

Table of Contents

Monographs of the Portuguese Mathematical Society	p. v
Monografias da Sociedade Portuguesa de Matematica	p. vii
Guide	p. ix
Foreword to Part 1	p. 1
Introduction to Random Time
Prologue	p. 3
Stopping time	p. 11
Martingale stopped	p. 18
Random past and future	p. 28
Other times	p. 36
From first to last	p. 47
Gapless time	p. 58
Markov chain in continuum time	p. 64
The trouble with the infinite	p. 69
References	p. 76
Foreword to Part 2	p. 79
Introduction to Quantum Randomness
Classical prologue	p. 85
Standard quantum mechanics	p. 93
Probabilities in standard quantum mechanics	p. 108
Feynman's approach to quantum probabilities	p. 118
Lagrangian mechanics	p. 118
Feynman's space-time reinterpretation of quantum mechanics	p. 123
Schrodinger's Euclidean quantum mechanics	p. 143
A probabilistic interpretation of Feynman's approach	p. 143
Feynman's results revisited	p. 157
Beyond Feynman's approach	p. 171
More quantum symmetries	p. 171
Introduction to functional calculus	p. 190
Time for a dialogue	p. 196
References	p. 205
Index	p. 209
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