Coherent States of the SU(N) groups

Abstract

Coherent states $(CS)$ of the $SU(N)$ groups are constructed explicitly and their properties are investigated. They represent a nontrivial generalization of the spining $CS$ of the $SU(2)$ group. The $CS$ are parametrized by the points of the coset space, which is, in that particular case, the projective space $C{P}^{N-1}$ and plays the role of the phase space of a corresponding classical mechanics. The $CS$ possess of a minimum uncertainty, they minimize an invariant dispersion of the quadratic Casimir operator. The classical limit is ivestigated in terms of symbols of operators. The role of the Planck constant playes $h=P^{-1}$, where $P$ is the signature of the representation. The classical limit of the so called star commutator generates the Poisson bracket in the $C{P}^{N-1}$ phase space. The logarithm of the modulus of the $CS$ overlapping, being interpreted as a symmetric in the space, gives the Fubini-Study metric in $C{P}^{N-1}$. The $CS$ constructed are useful for the quasi-classical analysis of the quantum equations of the $SU(N)$ gauge symmetric theories.

19pg, IFUSP/P-974 March/1992

Cited by in corpus (18)

• Renyi-Wehrl entropies as measures of localization in phase space
• Random walks of partons in SU(N_c) and classical representations of color charges in QCD at small x
• Coherent States For SU(3)
• Wehrl entropy, Lieb conjecture and entanglement monotones
• Classical spin dynamics based on SU($N$) coherent states
• Fuzzy Line Bundles, the Chern Character and Topological Charges over the Fuzzy Sphere
• SU(N) Coherent States
• Qubit phase-space: SU(n) coherent state P-representations
• Mean dynamical entropy of quantum system tends to infinity in the semiclassical limit
• Coherent State Quantization of SU(N) Non-Abelian Chern-Simons Particles
• SU(N) Coherent States and Irreducible Schwinger Bosons
• The classical limit and spontaneous symmetry breaking in algebraic quantum theory
• Spin 1 condensates at thermal equilibrium : a $SU(3)$ coherent state approach
• Coherent States of $SU(l,1)$ groups
• Letting the tiger out of its cage: bosonic coding without concatenation
• Analytic representations based on su(3) coherent states and Robertson intelligent states
• Quantum error correction beyond $SU(2)$: spin, bosonic, and permutation-invariant codes from convex geometry
• Spin amplitude wave due to dipole-quadrupole hybridization in spin-1 pyrochlore magnets