Hi,
It would be great if someone could post some lecture notes about the representations of the canonical commutation (CCR)
and anticommutation (CAR)relations. In textbooks the only representation presented is that based on the Fock space.
I ran into some mathematical physics papers by I. Segal, A. Wightman, H. Araki and others, and some textbooks by G. Emch (Algebraic methods in statistical mechanics and QFT)and O. Bratelli (Operator Algebras and Quantum Statistical Mechanics), but they are almost impossible to read, unless you are an expert in functional analysis.
The only thing I got is that there are infinitely many unitarilly nonequivalent representations of CCR and CAR.
A set of notes that presents a classification of the representations, written more for physicists than mathematicians, would be very useful. The style of Paul Roman's "Some Modern Mathematics for Physicists and Other Outsiders", i.e. math explained for physicists, would be the ideal.
Thanks,
Andrew
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