Open Systems & Information Dynamics

, Volume 13, Issue 4, pp 415–426

Exploring Representation Theory of Unitary Groups via Linear Optical Passive Devices

Article

DOI: 10.1007/s11080-006-9023-1

Cite this article as:
Aniello, P., Lupo, C. & Napolitano, M. Open Syst Inf Dyn (2006) 13: 415. doi:10.1007/s11080-006-9023-1
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Abstract

In this paper, we investigate some mathematical structures underlying the physics of linear optical passive (LOP) devices. We show, in particular, that with the class of LOP transformations on N optical modes one can associate a unitary representation of U(N) in the N-mode Fock space, representation which can be decomposed into irreducible sub-representations living in the subspaces characterized by a fixed number of photons. These (sub-)representations can be classified using the theory of representations of semi-simple Lie algebras. The remarkable case where N = 3 is studied in detail.

Copyright information

© Springer Science+Business Media, LLC 2006

Authors and Affiliations

  1. 1.Dipartimento di Scienze Fisiche dell’Università di Napoli Federico II Istituto Nazionale di Fisica Nucleare (INFN), Sezione di NapoliComplesso Universitario di Monte S. AngeloNapoliItaly
  2. 2.Dipartimento di Scienze Fisiche dell’Università di Napoli Federico II Complesso Universitario di Monte S. AngeloNapoliItaly