Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Communications in Mathematical Physics

Unification of fermion and Boson stochastic calculus

R. L. Hudson, Kalyanapuram Rangachari Parthasarathy

Published Sep 1, 1986• 90 citations
Publisher
DOI
10.1007/bf01210951

Related papers

Boson stochastic calculus

Kalyanapuram Rangachari Parthasarathy

Pramana•Oct 1, 1985•16 citations

Quantum stochastic calculus and a boson Levy theorem

Franco Fagnola

Lecture notes in mathematics•Jan 1, 1990•2 citations

Boson—Fermion Correspondence on the Circle via Quantum Stochastic Calculus

R. L. Hudson

International Journal of Theoretical Physics•Mar 1, 2000•0 citations

A boson field stochastic calculus and quantum filtering in Fock space

V. P. Belavkin

•Dec 1, 1989•2 citations

Classical Stochastic Processes from Quantum Stochastic Calculus

R. L. Hudson

Journal of Mathematical Sciences•Aug 1, 2001•2 citations

Fermion stochastic calculus in Dirac-Fock space

David Applebaum

A quantum stochastic calculus for fermions is developed where the basic integrators are based on Dirac fields and the charge operator. The associated Ito formula has seven non-trivial correction terms. Conditions are found for the solutions of stochastic differential equations to be unitary and it is shown that the corresponding quantum stochastic flow manifests a broken symmetry whereby the particle and antiparticle noises no longer balance each other. An abstract theory of such flows is then developed. By employing the unification between boson and fermion stochastic calculi, we are able to develop the entire theory using boson Fock spaces.

Journal of Physics A Mathematical and General•Jan 21, 1995•6 citations
A quantum stochastic calculus for fermions is developed where the basic integrators are based on Dirac fields and the charge operator. The associated Ito formula has seven non-trivial correction terms. Conditions are found for the solutions of stochastic differential equations to be unitary and it is shown that the corresponding quantum stochastic flow manifests a broken symmetry whereby the particle and antiparticle noises no longer balance each other. An abstract theory of such flows is then developed. By employing the unification between boson and fermion stochastic calculi, we are able to develop the entire theory using boson Fock spaces.