Infinite infrared regularization and a state space for the Heisenberg algebra | Zendy

Andreas U. Schmidt | Zendy

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Infinite infrared regularization and a state space for the Heisenberg algebra

Author(s) -

Andreas U. Schmidt

Publication year - 2002

Publication title -

journal of mathematical physics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.708

H-Index - 119

eISSN - 1089-7658

pISSN - 0022-2488

DOI - 10.1063/1.1425427

Subject(s) - regularization (linguistics) , infrared , mathematical physics , algebra over a field , mathematics , physics , pure mathematics , quantum mechanics , computer science , artificial intelligence

We present a method for the construction of a Krein space completion forspaces of test functions, equipped with an indefinite inner product induced bya kernel which is more singular than a distribution of finite order. Thisgeneralizes a regularization method for infrared singularities in quantum fieldtheory, introduced by G. Morchio and F. Strocchi, to the case of singularitesof infinite order. We give conditions for the possibility of this procedure interms of local differential operators and the Gelfand- Shilov test functionspaces, as well as an abstract sufficient condition. As a model case weconstruct a maximally positive definite state space for the Heisenberg algebrain the presence of an infinite infrared singularity.Comment: 18 pages, typos corrected, journal-ref added, reference adde

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