The Riesz-Clifford Functional Calculus for Non-Commuting Operators and Quantum Field Theory
Vladimir V. Kisil, Enrique Ram\'irez de Arellano
TL;DR
This paper develops a Riesz-like hyperholomorphic functional calculus for non-commuting operators using Clifford analysis, with applications to quantum field theory, advancing mathematical tools for quantum physics.
Contribution
It introduces a novel Riesz-Clifford functional calculus tailored for non-commuting operators, bridging Clifford analysis and quantum field theory.
Findings
Established a new hyperholomorphic calculus framework.
Applied the calculus to quantum field theory models.
Provided mathematical tools for quantization processes.
Abstract
We present a Riesz-like hyperholomorphic functional calculus for a set of non-commuting operators based on the Clifford analysis. Applications to the quantum field theory are described. Keywords: Functional calculus, Weyl calculus, Riesz calculus, Clifford analysis, quantization, quantum field theory. AMSMSC Primary:47A60, Secondary: 81T10
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