Probability and Fock Spaces

Charles R. Giardina

Sandro Sozzo

Sergey A. Rashkovskiy, Andrei Yu. Khrennikov

This paper is devoted to linear space representations of contextual probabilities-in generalized Fock space. This gives the possibility to use the calculus of creation and annihilation operators to express probabilistic dynamics in the Fock space (in particular, the wide class of classical kinetic equations). In this way, we reproduce the Doi-Peliti formalism. The context-dependence of probabilities can be quantified with the aid of the generalized formula of total probability-by the magnitude of the interference term. This article is part of the theme issue 'Contextuality and probability in quantum mechanics and beyond'.

Mićo Đurđević

Within the framework of the Fock space formalism of the nonrelativistic quantum field theory the problem of hidden variables is studied. It is shown that one can construct, both for fermionic and bosonic Fock spaces, a local completely causal underlying theory which reproduces all quantum probabilities. This is done by suitable generalization of the probability concepts.

Antonio Liguori, Mihail Mintchev

Naofumi Muraki

An example of independence, conditional expectation and martingales in quantum probability theory is constructed on the permutational Fock space which is a kind of discrete "Fock space" generated by an the permutations from the natural numbers.Besides a discrete time analogue of quantum Ito's formula for the permutational Fock space is obtained.