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) |
|---|---|
| Pages (from-to) | 467-486 |
| Number of pages | 20 |
| Journal | Nuclear Physics B |
| Volume | 337 |
| Issue number | 2 |
| DOIs | |
| State | Published - Jun 18 1990 |
| Externally published | Yes |
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ASJC Scopus subject areas
- Nuclear and High Energy Physics
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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 journal › Article
}
TY - JOUR
T1 - Quantum mechanics and the geometry of the Weyl character formula
AU - Alvarez, Orlando
AU - Singer, I. M.
AU - Windey, Paul
PY - 1990/6/18
Y1 - 1990/6/18
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=0011499358&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0011499358&partnerID=8YFLogxK
U2 - 10.1016/0550-3213(90)90278-L
DO - 10.1016/0550-3213(90)90278-L
M3 - Article
AN - SCOPUS:0011499358
VL - 337
SP - 467
EP - 486
JO - Nuclear Physics B
JF - Nuclear Physics B
SN - 0550-3213
IS - 2
ER -