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).
KeywordsHilbert Space Banach Algebra Canonical Transformation Unbounded Operator Canonical Commutation Relation
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