$h(1) \oplus su(2)$ vector algebra eigenstates with eigenvalues in the
matrix domain
- URL: http://arxiv.org/abs/2301.10747v1
- Date: Wed, 25 Jan 2023 18:10:01 GMT
- Title: $h(1) \oplus su(2)$ vector algebra eigenstates with eigenvalues in the
matrix domain
- Authors: Nibaldo-Edmundo Alvarez-Moraga
- Abstract summary: We find a subset of generalized vector coherent states in the matrix domain.
For a special choice of the matrix eigenvalue parameters we found the so-called vector coherent states with matrices associated to the Heisenberg-Weyl group.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: A new set of $ h(1) \oplus su(2)$ vector algebra eigenstates on the matrix
domain is obtained by defining them as eigenstates of a generalized
annihilation operator formed from a linear combination of the generators of
this algebra which eigenvalues are distributed as the elements of a square
complex normal matrix. A combined method is used to compute these eigenstates,
namely, the method of exponential operators and that of a system of first-order
linear differential equations. We compute these states for all possible
combination of generators and classify them in different categories according
to a generalized commutation relation as well as according to the value of a
characteristic parameter related to the $su(2)$ algebra eigenvalues. Proceeding
in this way, we found a subset of generalized vector coherent states in the
matrix domain which can be easily separated from the general set of
Schr\"odinger-Robertson minimum uncertainty intelligent states. In particular,
for a special choice of the matrix eigenvalue parameters we found the so-called
vector coherent states with matrices associated to the Heisenberg-Weyl group as
well as a generalized version of them, and also a direct connection with the
coherent state quantization of quaternions.
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