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.

Exploring representation theory of unitary groups via linear optical passive devices / Aniello, P.; Lupo, C.; Napolitano, M.. - In: OPEN SYSTEMS & INFORMATION DYNAMICS. - ISSN 1230-1612. - 13:4(2006), pp. 415-426. [10.1007/s11080-006-9023-1]

Exploring representation theory of unitary groups via linear optical passive devices

C. Lupo;
2006-01-01

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.
2006
Exploring representation theory of unitary groups via linear optical passive devices / Aniello, P.; Lupo, C.; Napolitano, M.. - In: OPEN SYSTEMS & INFORMATION DYNAMICS. - ISSN 1230-1612. - 13:4(2006), pp. 415-426. [10.1007/s11080-006-9023-1]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11589/248842
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