# Coherent states on Hilbert modules

@article{Ali2010CoherentSO,
title={Coherent states on Hilbert modules},
author={S. Twareque Ali and Tirthankar Bhattacharyya and Subhasish Subhasish},
journal={Journal of Physics A: Mathematical and Theoretical},
year={2010},
volume={44},
pages={275202}
}
• Published 6 July 2010
• Mathematics
• Journal of Physics A: Mathematical and Theoretical
We generalize the concept of coherent states, traditionally defined as special families of vectors on Hilbert spaces, to Hilbert modules. We show that Hilbert modules over C*-algebras are the natural settings for a generalization of coherent states defined on Hilbert spaces. We consider those Hilbert C*-modules which have a natural left action from another C*-algebra, say . The coherent states are well defined in this case and they behave well with respect to the left action by . Certain…
8 Citations
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## References

SHOWING 1-10 OF 39 REFERENCES

• Mathematics
• 2010
Coherent states, similar to the canonical coherent states of the harmonic oscillator, labeled by quaternions are established on the right and left quaternionic Hilbert spaces. On the left
• Physics
• 2005
In the spirit of some earlier work on the construction of vector coherent states (VCS) over matrix domains, we compute here such states associated to some physical Hamiltonians. In particular, we
• Mathematics
• 2004
As a substantial generalization of the technique for constructing canonical and the related nonlinear and q-deformed coherent states, we present here a method for constructing vector coherent states
• Mathematics
• 2003
A general scheme is proposed for constructing vector coherent states, in analogy with the well-known canonical coherent states, and their deformed versions, when these latter are expressed as
• Mathematics
• 2008
The operator-valued Schur class is defined to be the set of holomorphic functions S mapping the unit disk into the space of contraction operators between two Hilbert spaces. There are a number of
• Physics
• 2009
Gazeau–Klauder coherent states in noncommutative quantum mechanics are considered. We find that these states share similar properties to those of ordinary canonical coherent states in the sense that
• Physics
• 2010
We explore the notion of spatial extent and structure, already alluded to in earlier literature, within the formulation of quantum mechanics on the noncommutative plane. Introducing the notion of
Nuclear C~*-algebras were introduced by M. Takesaki and C. Lance. In this paper, we shall define the notion of combinative C~*-norm on the algebraic tensor product of C~*-algebras, and give its
I Generalized Coherent States for the Simplest Lie Groups.- 1. Standard System of Coherent States Related to the Heisenberg-Weyl Group: One Degree of Freedom.- 1.1 The Heisenberg-Weyl Group and Its