Part of the Theoretical and Mathematical Physics book series (TMP)


There exists a formulation of a dynamical physical system that is particularly suitable for the handling of systems with infinitely many degrees of freedom, which is the case after having taken the thermodynamic limit. It is particularly handy for the study of the collective phenomena. This formulation is sometimes called the algebraic approach to statistical mechanics and field theory. Extensive mathematical and technical information about this approach can be found in Bratteli, Robinson (1979). For a book with a view focused on the applications in many body systems we refer, as one example, to Sewell (1986).


Hilbert Space Banach Algebra Canonical Transformation Unbounded Operator Canonical Commutation Relation 
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  1. 26.
    Bratteli O., Robinson D.W.: Operator algebras and statistical mechanics I, II, (I) 1979, (II, 2nd Edition) 1996, Springer-Verlag, Berlin Heidelberg New York Google Scholar
  2. 152.
    Sewell G.L.: Quantum theory of collective phenomena, Oxford University Press, 1986; second edition 1989 Google Scholar

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© Springer-Verlag London Limited 2011

Authors and Affiliations

  1. 1.Institute for Theoretical PhysicsK.U.LeuvenLeuvenBelgium

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