Coherent states for arbitrary Lie group
TLDR
In this paper, the concept of coherent states originally closely related to the nilpotent group of Weyl is generalized to arbitrary Lie groups and its features are investigated for the simplest Lie groups.Abstract:
The concept of coherent states originally closely related to the nilpotent group of Weyl is generalized to arbitrary Lie group. For the simplest Lie groups the system of coherent states is constructed and its features are investigated.read more
Citations
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Coherent states: Theory and some Applications
TL;DR: In this article, a general algorithm for constructing coherent states of dynamical groups for a given quantum physical system is presented, and the result is that the coherent states are isomorphic to a coset space of group geometrical space.
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'Nonclassical' states in quantum optics: a 'squeezed' review of the first 75 years
TL;DR: A review of studies performed in the field of non-classical states can be found in this article, with a focus on the evolution of Gaussian wave packets for an oscillator, a free particle and a particle moving in uniform constant electric and magnetic fields.
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Quantum spin squeezing
TL;DR: In this article, the sensitivity of a state with respect to SU(2) rotations is analyzed for both entanglement detection and high-precision metrology, and various definitions of spin squeezing parameters are presented.
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The classical limit for quantum mechanical correlation functions
TL;DR: For quantum systems of finitely many particles as well as for boson quantum field theories, the classical limit of the expectation values of products of Weyl operators, translated in time by the quantum mechanical Hamiltonian and taken in coherent states centered inx-andp-space around −1/2 (coordinates of a point in classical phase space) are shown to become the exponentials of coordinate functions of the classical orbit in phase space.
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Riemannian structure on manifolds of quantum states
J. P. Provost,G. Vallee +1 more
TL;DR: In this paper, it is shown on examples that the distance between nearby states is related to quantum fluctuations; in particular, in the particular case of the harmonic oscillator group the condition of zero curvature appears to be identical to that of non dispersion of wave packets.
References
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The Quantum Theory of Optical Coherence
TL;DR: In this paper, a succession of correlation functions for the complex field strengths is defined, and a fully coherent field is defined as one whose correlation functions satisfy an infinite succession of stated conditions.
Book
Special Functions and the Theory of Group Representations
TL;DR: In this paper, a standard scheme for a relation between special functions and group representation theory is the following: certain classes of special functions are interpreted as matrix elements of irreducible representations of a certain Lie group, and then properties of special function are related to (and derived from) simple well-known facts of representation theory.
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