Central extensions and stochastic processes associated with the Lie algebra of the renormalized higher powers of white noise

• Autorzy: Luigi Accardi , Andreas Boukas
• Języki publikacji: EN

Abstrakty

EN

In the first part of the paper we discuss possible definitions of Fock representation of the *-Lie algebra of the Renormalized Higher Powers of White Noise (RHPWN). We propose one definition that avoids the no-go theorems and we show that the vacuum distribution of the analogue of the field operator for the n-th renormalized power of WN defines a continuous binomial process. In the second part of the paper we present without proof our recent results on the central extensions of RHPWN, its subalgebras and the $w_{∞}$ Lie algebra of conformal field theory. In the third part of the paper we describe our results on the non-trivial central extensions of the Heisenberg algebra. This is a 4-dimensional Lie algebra, hence belonging to a list which is well known and has been studied by several research groups. However the canonical nature of this algebra, i.e. the fact that it is the unique (up to a complex scaling) non-trivial central extension of the Heisenberg algebra, seems to be new. We also find the possible vacuum distributions corresponding to a family of injective *-homomorphisms of different non-trivial central extensions of the Heisenberg algebra into the Schrödinger algebra.

Kategorie tematyczne

• 81T30: String and superstring theories; other extended objects (e.g., branes)
• 60H40: White noise theory
• 81S05: Canonical quantization, commutation relations and statistics
• 81T40: Two-dimensional field theories, conformal field theories, etc.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2010
• Tom: 89
• Numer: 1
• Strony: 13-43

Daty

wydano

2010

Twórcy

autor

Luigi Accardi

• Centro Vito Volterra, Università di Roma Tor Vergata, via Columbia 2, 00133 Roma, Italy

autor

Andreas Boukas

• Department of Mathematics and Natural Sciences, American College of Greece, Aghia Paraskevi 15342, Athens, Greece

Identyfikatory

DOI

10.4064/bc89-0-1