arXiv:1103.6080

Coherent states in real parameterization up to SU(5) and classical dynamics of spin systems

Khikmat Kh. Muminov, Yousef Yousefi

Published Mar 31, 2011• 1 citation

Abstract

In this paper, we develop the formulation of the spin coherent state in real parameterization up to SU(5). The path integral in this representation of coherent state and its classical consequence are investigated. Using the resolution of unity of the coherent state, we derive a path integral expression for transition amplitude and in the classical limit we derive the classical equation of motion.

DOI: 10.48550/arxiv.1103.6080

Related papers

Path integral in the representation of SU(2) coherent state and classical dynamics in a generalized phase space

Hiroshi Kuratsuji, T. Suzuki

Path integral in the representation of coherent state for the simplest semisimple Lie group SU(2) and its classical consequences are investigated. Using the completeness relation of the coherent state, we derive a path integral expression for the transition amplitude which connects a pair of SU(2) coherent states. In the classical limit we arrive at a canonical equation of motion in a ’’curved phase space’’ (two-dimensional sphere) which reproduces the ordinary Euler’s equation of a rigid body when applied to a rotator.

Journal of Mathematical PhysicsMar 1, 1980127 citations

Path integral formalism for SUq(2) coherent states

Renshan Gong

A path integral formulation in the representation of coherent states for the quantum group SU q (2) is introduced. An expression for the transition amplitude connecting two SU q (2) coherent states is constructed, and the corresponding canonical equations of motion are also derived.

Journal of Physics A Mathematical and GeneralOct 7, 19926 citations

Coherent states in complex variables and classical dynamics

Yousef Yousefi, Х. Х. Муминов

It was studied coherent states in complex variables in SU(2), SU(3), SU(4) groups and in general in SU(n) group. Using the completeness relation of the coherent state, we obtain a path integral expression for transition amplitude which connects a pair of SU(n) coherent states. In the classical limit, a canonical equation of motion is obtained.

arXiv:1105.0070Apr 30, 20110 citations

Path integral for new coherent states of Lie superalgebra osp(1/2, R)

Xin Chen, Le‐Man Kuang

A path integral formulation in the representation of new coherent states for the Lie superalgebra osp(l/2, R) is introduced. By the use of the completeness relation of the new coherent states, a path integral expression for the transition amplitude between two osp(l/2, R) new coherent states for a Hamiltonian which is linear in the generators of the superalgebra are obtained. In the classical limit the equations of motion for the system are derived.

Journal of Physics A Mathematical and GeneralSep 21, 19944 citations

Path integral formalism for Osp(1/2, R) coherent states

H. A. Schmitt, A. Mufti

A path integral formulation in the representation of coherent states for the non-compact supergroup Osp(1/2, R) is introduced. An expression for the transition amplitude connecting two Osp(1/2, R) coherent states is constructed, and the corresponding canonical equations of motion derived. A set of generalized Poisson brackets is introduced and interpreted.

Journal of Physics A Mathematical and GeneralAug 7, 19917 citations

Path integral formalism for Osp(1 mod 2) coherent states

Xiaoming Liu, Shun-Jin Wang

A path-integral formulation in the representation of coherent states for the supergroup Osp(1 mod 2) is introduced. An expression for the transition amplitude connecting two Osp(1 mod 2) coherent states is constructed and the corresponding canonical equations of motion derived. A set of generalized Poisson brackets is introduced.

Journal of Physics A Mathematical and GeneralSep 21, 19941 citation