Quantum mechanics and the geometry of the Weyl character formula

Orlando Alvarez, I. M. Singer, Paul Windey

Research output: Contribution to journalArticlepeer-review

20 Scopus citations


General field theoretic methods are developed which will allow a path integral derivation of the character formula for loop groups. The methods are introduced in the classical Weyl character case. The irreducible representations of a compact semi-simple Lie group G are realized as the ground states of a supersymmetric quantum mechanical system. The Hilbert space for the quantum mechanical system is the space of sections of a holomorphic line bundle L over the complex manifold G/T, where T is the maximal torus of G. The Weyl character formula is derived by an explicit path integral computation of the index of the Dolbeault operator ∂L.

Original languageEnglish (US)
Pages (from-to)467-486
Number of pages20
JournalNuclear Physics, Section B
Issue number2
StatePublished - Jun 18 1990
Externally publishedYes

ASJC Scopus subject areas

  • Nuclear and High Energy Physics


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