2011/12/01 by V. P. Belavkin, Viacheslav P. Belavkin, Belavkin, Viacheslav P. +2
Computer Science · Mathematics · Physics and Astronomy · #81S25 #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Information Theory (cs.IT) #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #Random Matrices and Applications #cs.IT #math-ph #math.IT #math.MP #math.QA #msc:81S25 #quant-ph
paper · pdf · doi:10.48550/arxiv.1112.0147
A similar version is due to appear in the proceedings of the 13th workshop: non-commutative harmonic analysis. 18 pages
arxiv created 2011/12/01 · openalex publication_date 2011/12/01 · arxiv updated 2011/12/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we first introduce the Fock-Guichardet formalism for the quantum stochastic integration, then the four fundamental processes of the dynamics are introduced in the canonical basis as the operator-valued measures of the QS integration over a space-time. Then rigorous analysis of the QS integrals is carried out, and continuity of the QS derivative is proved. Finally, Q-adapted dynamics is discussed, including Bosonic Q=1, Fermionic Q=-1, and monotone Q=0 quantum dynamics. These may be of particular interest to quantum field theory, quantum open systems, and quantum theory of stochastic processes.