After briefly reviewing classical and quantum aspects of probability, basic concepts of the noncommutative calculus of probability (called also free calculus of probability) and its possible application to model the fundamental level of physics are presented. It is shown that the pair (M, *), where M is a (noncommutative) von Neumann algebra, and a state on it, is both a dynamical object and a probabilistic object. In this way, dynamics and probability can be unified in noncommutative geometry. Some philosophical consequences of such an approach are indicated
We deal with the general structure of (noncommutative) stochastic processes by using the standard te...
Quantum theory can be regarded as a noncommutative generalization of classical probability. From thi...
We deal with the general structure of the stochastic processes by using the standard techniques of O...
Noncommutative geometry is quickly developing branch of mathematics finding important application in...
The paper can be regarded as a short and informal introduction to noncommutative calculi of probabil...
Noncommutative mathematics is a significant new trend of mathematics. Initially motivated by the dev...
The mathematics of classical probability theory was subsumed into classical measure theory by Kolmog...
Quantum mechanics is essentially a statistical theory. Classical mechanics, however, is usually not ...
Quantum probability and the theory of operator algebras are both concerned with the study of noncomm...
We continue our program of unifying general relativity and quantum mechanics in terms of a noncommut...
Space, time and probabilities not only form the arena of many physical theories, but also the arena ...
International audiencehis monograph is a progressive introduction to non-commutativity in probabilit...
In this paper we discuss the relevance of the algebraic approach to quantum phenomena first introduc...
openThe thesis is about the peculiar probabilistic structure of quantum mechanics. Typically, a rand...
© 2015, Springer Science+Business Media New York. Noncommutative measure and probability theory deve...
We deal with the general structure of (noncommutative) stochastic processes by using the standard te...
Quantum theory can be regarded as a noncommutative generalization of classical probability. From thi...
We deal with the general structure of the stochastic processes by using the standard techniques of O...
Noncommutative geometry is quickly developing branch of mathematics finding important application in...
The paper can be regarded as a short and informal introduction to noncommutative calculi of probabil...
Noncommutative mathematics is a significant new trend of mathematics. Initially motivated by the dev...
The mathematics of classical probability theory was subsumed into classical measure theory by Kolmog...
Quantum mechanics is essentially a statistical theory. Classical mechanics, however, is usually not ...
Quantum probability and the theory of operator algebras are both concerned with the study of noncomm...
We continue our program of unifying general relativity and quantum mechanics in terms of a noncommut...
Space, time and probabilities not only form the arena of many physical theories, but also the arena ...
International audiencehis monograph is a progressive introduction to non-commutativity in probabilit...
In this paper we discuss the relevance of the algebraic approach to quantum phenomena first introduc...
openThe thesis is about the peculiar probabilistic structure of quantum mechanics. Typically, a rand...
© 2015, Springer Science+Business Media New York. Noncommutative measure and probability theory deve...
We deal with the general structure of (noncommutative) stochastic processes by using the standard te...
Quantum theory can be regarded as a noncommutative generalization of classical probability. From thi...
We deal with the general structure of the stochastic processes by using the standard techniques of O...