Quantum mechanics and the geometry of the Weyl character formula

Orlando Alvarez, I. M. Singer, Paul Windey

Research output: Contribution to journalArticle

20 Citations (Scopus)

Abstract

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 B
Volume337
Issue number2
DOIs
StatePublished - Jun 18 1990
Externally publishedYes

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quantum mechanics
geometry
Hilbert space
bundles
derivation
operators
ground state

ASJC Scopus subject areas

  • Nuclear and High Energy Physics

Cite this

Quantum mechanics and the geometry of the Weyl character formula. / Alvarez, Orlando; Singer, I. M.; Windey, Paul.

In: Nuclear Physics B, Vol. 337, No. 2, 18.06.1990, p. 467-486.

Research output: Contribution to journalArticle

Alvarez, Orlando ; Singer, I. M. ; Windey, Paul. / Quantum mechanics and the geometry of the Weyl character formula. In: Nuclear Physics B. 1990 ; Vol. 337, No. 2. pp. 467-486.
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