Fermions from classical probability and statistics defined by stochastic independence
- Autores: Accardi L.1, Lu Y.2
-
Afiliações:
- Università degli Studi di Roma — Tor Vergata
- Universitá degli Studi di Bari
- Edição: Volume 87, Nº 5 (2023)
- Páginas: 5-40
- Seção: Articles
- URL: https://journals.rcsi.science/1607-0046/article/view/140427
- DOI: https://doi.org/10.4213/im9389
- ID: 140427
Citar
Resumo
The case study of fermions and the attempt to deduce their structure from classical probability opens new ways for classical and quantum probability, in particular, for the notion of stochastic coupling which, on the basis of the example of fermions, we enlarge to the notion of algebraic coupling, and for the various notions of stochastic independence. These notions are shown to be strictly correlated with algebraic and stochastic couplings. This approach allows to expand considerably the notion of open system. The above statements will be illustrated with some examples. The last section shows how, from these new stochastic couplings, new statistics emerge alongside the known Maxwell–Boltzmann, Bose–Einstein and Fermi–Dirac statistics.Bibliography: 5 titles.
Texto integral
Sobre autores
Luigi Accardi
Università degli Studi di Roma — Tor Vergata
Email: accardi@volterra.mat.uniroma2.it
Yun Lu
Universitá degli Studi di Bari
Bibliografia
- L. Accardi, Yun-Gang Lu, “The $qq$-bit (I): Central limits with left $q$-Jordan–Wigner embeddings, monotone interacting Fock space, Azema random variable, probabilistic meaning of $q$”, Infin. Dimens. Anal. Quantum Probab. Relat. Top., 21:4 (2018), 1850030, 53 pp.
- R. Lenczewski, “Unification of independence in quantum probability”, Infin. Dimens. Anal. Quantum Probab. Relat. Top., 1:3 (1998), 383–405
- V. Liebscher, “On a central limit theorem for monotone noise”, Infin. Dimens. Anal. Quantum Probab. Relat. Top., 2:1 (1999), 155–167
- L. Accardi, A. Boukas, Yun-Gang Lu, A. Teretenkov, “The non-linear and quadratic quantization programs”, Infinite dimensional analysis, quantum probability and applications (Al Ain, UAE, 2021), Springer Proc. Math. Stat., 390, Springer, Cham, 2022, 3–53
- L. Accardi, “Classical and quantum conditioning: mathematical and information theoretical aspects”, Quantum bio-informatics III. From quantum informatics to bio-informatics, QP-PQ: Quantum Probab. White Noise Anal., 26, World Sci. Publ., Hackensack, NJ, 2009, 1–16