Noncommutative Unification of Dynamics and Probability

• Authors: Michał Heller

Title variants

PL

Nieprzemienna unifikacja dynamiki i prawdopodobieństwa

EN

Noncommutative Unification of Dynamics and Probability

• Languages of publication: PL

Abstracts

PL

Noncommutative geometry is quickly developing branch of mathematics finding important application in physics, especially in the domain of the search for the fundamental physical theory. It comes as a surprise that noncommutative generalizations of probabilistic measure and dynamics are unified into the same mathematical structure, i.e., noncommutative von Neumann algebra with a distinguished linear form on it. The so-called free probability calculus and the Tomita-Takesaki theorem, on which this unification is based, are briefly presented. It is argued that the unitary evolution, known from quantum mechanics, could be a trace of noncommutativity on a deeper level. Philosophical significance of these results is also discussed.

• Publisher: University of Warsaw, Institute of Philosophy
• Journal: Filozofia Nauki
• Year: 2004
• Volume: 12
• Issue: 1
• Pages: 7-17

Dates

published

2004-03-01

Contributors

author

Michał Heller