Algebraic structures spanned by differential-like operators on toy Fock spaces

2017/01/03 by Jerzy Szulga, Szulga, Jerzy
Mathematics · #42C10 #60H07 #Advanced Operator Algebra Research #Algebraic and Geometric Analysis #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #Primary 47L30 #Secondary 46L53 #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1701.00789

openalex publication_date 2017/01/03 · openalex created_date 2017/03/23 · openalex updated_date 2026/07/28

Abstract

We study multiplicative systems of linear mappings acting on the toy Fock space, a.k.a. Rademacher chaos or Walsh-Fourier series, related to the creation, annihilation, and conservation operators in quantum probability. Like differential operators they entail analogs of the Leibnitz Formula and the Chain Rule, derived with the help of Riesz products (or discrete coherent vectors). Two symmetries among these operators entail groups and algebras of varying signatures and mixed commutativity, generalizing Pauli spin matrices and quaternions. In particular, anticommutative Rademacher systems are constructed.

Citations

• Quantum Probability for Probabilists
• Quaternions and matrices of quaternions

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