Formal group laws for affine Kac-Moody groups and group quantization

DOI10.1007/BF01221252zbMath0637.22011MaRDI QIDQ1098947

Jose Navarro-Salas, Victor Aldaya

Publication date: 1987

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

Kac-Moody algebrasrepresentationswave functionsgroup lawinvariant vector fieldsconnection formlocal groupquantization formalismaffine Kac- Moody groupcentral extensions of loop groupspolarization subalgebra

Mathematics Subject Classification ID

Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10) Infinite-dimensional Lie (super)algebras (17B65) Applications of Lie groups to the sciences; explicit representations (22E70) Infinite-dimensional Lie groups and their Lie algebras: general properties (22E65) Group structures and generalizations on infinite-dimensional manifolds (58B25) Geometric quantization (53D50)

Related Items (12)

GENERALIZED CONFORMAL SYMMETRY AND EXTENDED OBJECTS FROM THE FREE PARTICLE ⋮ Quantum dynamics on (super)groups: Constraints and the ‘‘BRST’’ supergroup ⋮ Irrational conformal field theory ⋮ Kac-Moody group representations and generalization of the Sugawara construction of the Virasoro algebra ⋮ Group-theoretical construction of the quantum relativistic harmonic oscillator ⋮ Gauge principle revisited: Towards a unification of space–time and internal gauge interactions ⋮ Group-cohomology refinement to classify G-symplectic manifolds ⋮ Algebraic quantization on a group and nonabelian constraints ⋮ Group quantization on configuration space: Gauge symmetries and linear fields ⋮ Quantization on the Virasoro group ⋮ Lie group representations and quantization ⋮ EXTENDED DIFFEOMORPHISM ALGEBRAS IN (QUANTUM) GRAVITATIONAL PHYSICS

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• Current algebras and Wess-Zumino model in two dimensions
• Quantization, symmetry, and natural polarization
• Quantization as a consequence of the symmetry group: An approach to geometric quantization
• Quantization and unitary representations
• Introduction to Lie Algebras and Representation Theory

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