R – Conformal Symmetries in 2 D Nonlocal Quantum Field Theory , Categorical Representation Theory , and Virasoro Algebra

D ec 1 99 7 q R – CONFORMAL SYMMETRIES IN 2 D NONLOCAL QUANTUM FIELD THEORY , CATEGORICAL REPRESENTATION THEORY , AND VIRASORO ALGEBRA

R – Conformal Symmetries . Ii . Geometric Quantization and Hidden Symmetries of Verma Modules over Virasoro Algebra

This article being a continuation of the first part [1] is addressed to specialists in representation theory, infinite dimensional geometry, quantum algebra, mathematical physics and informatics of interactive systems. The interrelations of the infinite dimensional geometry of the homogeneous Kähler manifold M = Diff+(S )/S (see e.g. [2] and numerous refs wherein), its quotient M1 = Diff+(S )/P...

The emergence of the Virasoro and w∞ algebras through the renormalized powers of quantum white noise

We introduce a new renormalization for the powers of the Dirac delta function. We show that this new renormalization leads to a second quantized version of the Virasoro sector w∞ of the extended conformal algebra with infinite symmetries W∞ of Conformal Field Theory ( [4]-[7], [11], [13], [14]). In particular we construct a white noise (boson) representation of the w∞ generators and commutation...

Quantum Virasoro algebra with central charge c = 1 on the event horizon of a 2 D - Rindler spacetime

Using the holographic machinery built up in a previous work, we show that the hidden SL(2,R) symmetry of a scalar quantum field propagating in a Rindler spacetime admits an enlargement in terms of a unitary positive-energy representation of Virasoro algebra defined in the Fock representation. That representation has central charge c = 1. The Virasoro algebra of operators gets a manifest geometr...

Quantum Virasoro algebra with central charge c = 1 on the horizon of a 2 D - Rindler spacetime

Using the holographic machinery built up in a previous work, we show that the hidden SL(2,R) symmetry of a scalar quantum field propagating in a Rindler spacetime admits an enlargement in terms of a unitary positive-energy representation of Virasoro algebra defined in the Fock representation. That representation has central charge c = 1. The Virasoro algebra of operators gets a manifest geometr...