Generalized Weyl correspondence and Moyal multiplier algebras
| Autor: | M. A. Soloviev |
|---|---|
| Rok vydání: | 2012 |
| Předmět: |
Generalized function
Topological algebra Wigner quasiprobability distribution Statistical and Nonlinear Physics Multiplier (Fourier analysis) Algebra symbols.namesake Star product symbols Weyl transformation Noncommutative quantum field theory Mathematics::Representation Theory Mathematical Physics Moyal bracket Mathematics |
| Zdroj: | Theoretical and Mathematical Physics. 173:1359-1376 |
| ISSN: | 1573-9333 0040-5779 |
| DOI: | 10.1007/s11232-012-0119-1 |
| Popis: | We show that the Weyl correspondence and the concept of a Moyal multiplier can be naturally extended to generalized function classes that are larger than the class of tempered distributions. This generalization is motivated by possible applications to noncommutative quantum field theory. We prove that under reasonable restrictions on the test function space E ⊂ L2, any operator in L2 with a domain E and continuous in the topologies of E and L2 has a Weyl symbol, which is defined as a generalized function on the Wigner-Moyal transform of the projective tensor square of E. We also give an exact characterization of the Weyl transforms of the Moyal multipliers for the Gel’fand-Shilov spaces Sββ. |
| Databáze: | OpenAIRE |
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