Coherent states associated to the real Jacobi group

2007 ◽  
Author(s):  
S. Berceanu ◽  
Piotr Kielanowski ◽  
Anatol Odzijewicz ◽  
Martin Schlichenmeier ◽  
Theodore Voronov
Keyword(s):  
Coherent States ◽  
The Real ◽  
Jacobi Group

Squeezing in the Real and Imaginary Spin Coherent States

2005 ◽  
Vol 22 (3) ◽  
pp. 521-524 ◽  
Author(s):  
Yan Dong ◽  
Wang Xiao-Guang ◽  
Wu Ling-An
Keyword(s):  
Coherent States ◽  
The Real ◽  
Spin Coherent States

scholarly journals Coherent states and geometry on the Siegel–Jacobi disk

2014 ◽  
Vol 11 (04) ◽  
pp. 1450035 ◽  
Author(s):  
Stefan Berceanu
Keyword(s):  
Coherent State ◽  
Scalar Curvature ◽  
Coherent States ◽  
Discrete Series ◽  
Series Representation ◽  
State Representation ◽  
Discrete Series Representation ◽  
Jacobi Group ◽  
Two Parameters ◽  
Ricci Form

The coherent state representation of the Jacobi group [Formula: see text] is indexed with two parameters, [Formula: see text], describing the part coming from the Heisenberg group, and k, characterizing the positive discrete series representation of SU(1,1). The Ricci form, the scalar curvature and the geodesics of the Siegel–Jacobi disk [Formula: see text] are investigated. The significance in the language of coherent states of the transform which realizes the fundamental conjecture on the Siegel–Jacobi disk is emphasized. The Berezin kernel, Calabi's diastasis, the Kobayashi embedding and the Cauchy formula for the Siegel–Jacobi disk are presented.

scholarly journals Harmonic Maaß–Jacobi forms of degree 1 with higher rank indices

2016 ◽  
Vol 12 (07) ◽  
pp. 1871-1897 ◽  
Author(s):  
Charles H. Conley ◽  
Martin Westerholt-Raum
Keyword(s):  
Central Extension ◽  
Casimir Operator ◽  
Jacobi Forms ◽  
The Real ◽  
Arbitrary Rank ◽  
Jacobi Group ◽  
Higher Rank ◽  
Real Analytic

We define and investigate real analytic weak Jacobi forms of degree 1 and arbitrary rank. En route we calculate the Casimir operator associated to the maximal central extension of the real Jacobi group, which for rank exceeding 1 is of order 4. In ranks exceeding 1, the notions of H-harmonicity and semi-holomorphicity are the same.

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