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 language | English (US) |
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Pages (from-to) | 467-486 |
Number of pages | 20 |
Journal | Nuclear Physics, Section B |
Volume | 337 |
Issue number | 2 |
DOIs | |
State | Published - Jun 18 1990 |
Externally published | Yes |
ASJC Scopus subject areas
- Nuclear and High Energy Physics