Marek Bożejko

Anyonic Fock spaces, q-CCR relations for |q| = 1 and relations with Yang-Baxter operators

1. Free and deformed Fock spaces q-Fock spaces for real q( If q=1 , we have Bosonic Fock spaces, if q=-1, Fermionic Fock spaces).
2. Yang-Baxter operators and generalized Fock spaces.
3. Anyonic q-Fock spaces and construction of q-Gaussian and q-Poisson processes for |q|=1.
4. Applications to new factors of type II and III.

References:

1. M. Bożejko, Deformed Fock spaces, Hecke operators and monotone Fock space of Muraki, Demonstratio Mathematica, vol. XLV, 2012, 399-413.
2. M. Bożejko, B. Kummerer, R. Speicher, q-Gaussian processes: non-commutative and classical aspects, Comm. Math. Phys., 185(1), (1997), 129–154.
3. M. Bożejko, E. Lytvynov, J. Wysoczański, Noncommutative Levy processes for generalized (particularly anyon) statistics, Comm. Math. Phys. 313, Issue 2 (2012), 535–569.
4. M. Bożejko, E. Lytvynov, I.Rodionova, An extended Fock space and noncommutative Meixner-type orthogonal polynomials, Uspiekhi Mat. Nauk, 70(5), 2015, 47 pp. ,there is also russian version.
5. M. Bożejko, R. Speicher, An example of a generalized Brownian motion, Commun. Math. Phys. 137 (1991), 519–531.