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The exponential map for the unitary group SU(2,2)

A O Barut, J R Zeni and A Laufer

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In this article, we extend our previous results for the orthogonal group SO(2,4) to its homomorphic group SU(2,2). Here we present a closed finite formula for the exponential of a 4*4 traceless matrix, which can be viewed as the generator (Lie algebra elements) of the SL(4,C) group. We apply this result to the SU(2,2) group, the lie algebra of which can be represented by Dirac matrices, and discuss how the exponential map for SU(2,2) can be written by means of Dirac matrices.


PACS

02.20.-a Group theory

02.10.Ud Linear algebra

03.65.Fd Algebraic methods

02.10.Yn Matrix theory

MSC

65Q05 Difference and functional equations, recurrence relations

15A18 Eigenvalues, singular values, and eigenvectors

20K30 Automorphisms, homomorphisms, endomorphisms, etc.

22E47 Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.) (See also 17B10)

05C30 Enumeration of graphs and maps

17B45 Lie algebras of linear algebraic groups (See also 14Lxx and 20Gxx)

Subjects

Mathematical physics

Quantum information and quantum mechanics

Dates

Issue 20 (21 October 1994)



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