Invariant metric on the extended Siegel-Jacobi upper half space

JOURNAL OF GEOMETRY AND PHYSICS

卷:162

Article

Berceanu, Stefan¹ 

[1] Horia Hulubei Natl Inst Phys & Nucl Engn, Dept Theoret Phys, POB MG-6, Magurele 077125, Romania

关键词: Jacobi group;    Jacobi algebra;    Siegel-Jacobi upper half space;    Extended Siegel-Jacobi upper half space;    Invariant metrics;    Coherent states;   

DOI  :  10.1016/j.geomphys.2020.104049

来源: Elsevier

【 摘 要 】

The real Jacobi group G(n)(J)(R), defined as the semidirect product of the Heisenberg group H-n(R) with the symplectic group Sp(n, R), admits a matrix embedding in Sp(n + 1, R). The modified pre-Iwasawa decomposition of Sp(n, R) allows us to introduce a convenient coordinatization S-n of G(n)(J)(R), which for G(1)(J)(R) coincides with the S-coordinates. Invariant one-forms on G(n)(J)(R) are determined. The formula of the 4-parameter invariant metric on G(n)(J)(R) obtained as sum of squares of 6 invariant one-forms is extended to G(n)(J)(R), n is an element of N. We obtain a three parameter invariant metric on the extended Siegel-Jacobi upper half space (X) over tilde (J)(n) approximate to (X) over tilde (J)(n) x R by adding the square of an invariant one-form to the two-parameter roR) balanced metric on the Siegel-Jacobi upper half space XnJ = GnJ(R)/U(n)xR. (C) 2020 Elsevier B.V. All rights reserved.

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