Representations of commutations relations for p-adic systems of infinitely many degrees of freedom

DOI10.1063/1.529942zbMath0835.47053OpenAlexW2061400603MaRDI QIDQ3991687

E. I. Zelenov

Publication date: 28 June 1992

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.529942

zbMATH Keywords

Weyl algebraFock representations\(C^*\)-formalism\(p\)-adic numbers fieldexistence of free-field unitary quantization of symplectic transformationsrepresentations of commutations relationssystems of infinitely many degrees of freedom

Mathematics Subject Classification ID

Commutators, derivations, elementary operators, etc. (47B47) Applications of functional analysis in quantum physics (46N50) Commutation relations and statistics as related to quantum mechanics (general) (81S05) Operator theory over fields other than (mathbb{R}), (mathbb{C}) or the quaternions; non-Archimedean operator theory (47S10)

Related Items

Algebraic Weyl system and application ⋮ On the uniqueness of invariant states ⋮ \(p\)-adic model of quantum mechanics and quantum channels ⋮ Power series everywhere convergent on R and all Qp ⋮ Description of unitary representations of the group of infinite 𝑝-adic integer matrices

Cites Work

• p-adic quantum mechanics for \(p=2\)
• P-adic Schrödinger-type equation
• p-adic quantum mechanics
• \(p\)-adic quantum mechanics and coherent states. II: Oscillator eigenfunctions
• Sur certains groupes d'opérateurs unitaires
• On representations of the canonical commutation relations
• A theorem of Stone and von Neumann
• Hamiltonian Formalism and the Canonical Commutation Relations in Quantum Field Theory
• Quantum mechanics on p-adic fields
• Generalized functions over the field ofp-adic numbers
• Transforms for Operators and Symplectic Automorphisms over a Locally Compact Abelian Group.