Document type

Journal articles

Document subtype

Full paper

Title

Non-commutative probability and non-commutative processes: Beyond the Heisenberg algebra

Participants in the publication

R. Vilela Mendes (Author)

CMAFcIO

Summary

A probability space is a pair (A, ?) where A is an algebra and ? is a state on the algebra. In classical probability, A is the algebra of linear combinations of indicator functions on the sample space, and in quantum probability, A is the Heisenberg or Clifford algebra. However, other algebras are of interest in noncommutative probability. After a short review of the framework of classical and quantum probability, other noncommutative probability spaces are discussed, in particular those associated with noncommutative space-time.

Where published

Journal of Mathematical Physics

Publication Identifiers

ISSN - 0022-2488,1089-7658

Publisher

AIP Publishing

Document Identifiers

DOI - https://doi.org/10.1063/1.5089500

URL - http://dx.doi.org/10.1063/1.5089500

Journal articles

Document subtype

Full paper

Title

Non-commutative probability and non-commutative processes: Beyond the Heisenberg algebra

Participants in the publication

R. Vilela Mendes (Author)

CMAFcIO

Summary

A probability space is a pair (A, ?) where A is an algebra and ? is a state on the algebra. In classical probability, A is the algebra of linear combinations of indicator functions on the sample space, and in quantum probability, A is the Heisenberg or Clifford algebra. However, other algebras are of interest in noncommutative probability. After a short review of the framework of classical and quantum probability, other noncommutative probability spaces are discussed, in particular those associated with noncommutative space-time.

Date of Publication

2019-09

2019-09

Where published

Journal of Mathematical Physics

Publication Identifiers

ISSN - 0022-2488,1089-7658

Publisher

AIP Publishing

Volume

60

60

Number

9

9

Starting page

093501

093501

Document Identifiers

DOI - https://doi.org/10.1063/1.5089500

URL - http://dx.doi.org/10.1063/1.5089500

APA

R. Vilela Mendes, (2019). Non-commutative probability and non-commutative processes: Beyond the Heisenberg algebra. Journal of Mathematical Physics, 60, ISSN 0022-2488,1089-7658. eISSN . http://dx.doi.org/10.1063/1.5089500

IEEE

R. Vilela Mendes, "Non-commutative probability and non-commutative processes: Beyond the Heisenberg algebra" in Journal of Mathematical Physics, vol. 60, 2019. 10.1063/1.5089500

BIBTEX

@article{46387, author = {R. Vilela Mendes}, title = {Non-commutative probability and non-commutative processes: Beyond the Heisenberg algebra}, journal = {Journal of Mathematical Physics}, year = 2019, volume = 60 }

R. Vilela Mendes, (2019). Non-commutative probability and non-commutative processes: Beyond the Heisenberg algebra. Journal of Mathematical Physics, 60, ISSN 0022-2488,1089-7658. eISSN . http://dx.doi.org/10.1063/1.5089500

IEEE

R. Vilela Mendes, "Non-commutative probability and non-commutative processes: Beyond the Heisenberg algebra" in Journal of Mathematical Physics, vol. 60, 2019. 10.1063/1.5089500

BIBTEX

@article{46387, author = {R. Vilela Mendes}, title = {Non-commutative probability and non-commutative processes: Beyond the Heisenberg algebra}, journal = {Journal of Mathematical Physics}, year = 2019, volume = 60 }