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Physical Applications of Algebras of Unbounded Operators

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Contributions in Mathematical Physics

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Abstract

During the past 20 years a long series of papers concerning algebras of unbounded operators appeared in the literature, papers which, though being originally motivated by physical arguments, contain almost no physics at all. On the contrary the mathematical aspects of these algebras have been analyzed in many details and this analysis produced, up to now, the monographes [32] and [2]. Some physics appeared first in [28] and [31], in the attempt to describe systems with a very large (1024) number of degrees of freedom, following some general ideas originally proposed in the famous Haag and Kastler’s paper, [27], on QM∞.

After a brief historical introduction on the standard algebraic approach to quantum mechanics of large systems, QM∞, we review some basic mathematical aspects and few physical applications of algebras of unbounded operators.

This paper is dedicated to Gerard Emch for his 70th birthday

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Author information

Authors and Affiliations

  1. Dipartimento di Metodi e Modelli Matematici, Facoltà di Ingegneria, Università di Palermo, Viale delle Scienze, I-90128, Palermo, Italy

    F. Bagarello

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  1. F. Bagarello
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Editors and Affiliations

  1. Department of Mathematics and Statistics, Concordia University, 1455, de Maisonneuve Blvd. West, Montreal, Quebec, Canada, H3G1 M8

    S. Twareque Ali

  2. Jawaharlal Nehru Centre for Advanced Scientific Research, P.O. Jakkur, 560064, Bangalore, India

    Kalyan B. Sinha

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© 2007 Hindustan Book Agency

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Bagarello, F. (2007). Physical Applications of Algebras of Unbounded Operators. In: Ali, S.T., Sinha, K.B. (eds) Contributions in Mathematical Physics. Hindustan Book Agency, Gurgaon. https://doi.org/10.1007/978-93-86279-33-0_4

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