The sums of Rogers, Schur and Ramanujan and the Bose-Fermi correspondence in $1+1$-dimensional quantum field theory

Details The sums of Rogers, Schur and Ramanujan and the Bose-Fermi correspondence in $1+1$-dimensional quantum field theory The sums of Rogers, Schur and Ramanujan and the Bose-Fermi correspondence in $1+1$-dimensional quantum field theory

1993-04-14

arxiv.org/abs/hep-th/9304056v2

in Recent Progress in Statistical Mechanics and Quantum Field Theory, ed. P. Bouwknegt et al, World Scientific , (Singapore 19

Physics

High Energy Physics

High Energy Physics - Theory

28/17 pages in harvmac, ITP-SB-93-19. [a few refs added]

Scientific paper

We discuss the relation of the two types of sums in the Rogers-Schur-Ramanujan identities with the Bose-Fermi correspondence of massless quantum field theory in $1+1$ dimensions. One type, which generalizes to sums which appear in the Weyl-Kac character formula for representations of affine Lie algebras and in expressions for their branching functions, is related to bosonic descriptions of the spectrum of the field theory (associated with the Feigin-Fuchs construction in conformal field theory). Fermionic descriptions of the same spectrum are obtained via generalizations of the other type of sums. We here summarize recent results for such fermionic sum representations of characters and branching functions. (To appear in C.N. Yang's 70th birthday Festschrift.)

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