Coherent states in complex variables SU(2S+1)/SU(2S)*U(1)and classical dynamics (original) (raw)
arXiv (Cornell University), 2011
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.
Coherent states in complex variables and classical dynamics
2011
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.
Coherent-state path integrals in the continuum: The SU(2) case
Annals of Physics, 2016
We define the time-continuous spin coherent-state path integral in a way that is free from inconsistencies. The proposed definition is used to reproduce known exact results. Such a formalism opens new possibilities for applying approximations with improved accuracy and can be proven useful in a great variety of problems where spin Hamiltonians are used.
Coherent states in real parameterization up to SU(5) and classicaldynamics of spin systems
2011
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.
Journal of Mathematical Physics, 2001
We define coherent states for SU(3) using six bosonic creation and annihilation operators. These coherent states are explicitly characterized by six complex numbers with constraints. For the completely symmetric representations (n, 0) and (0, m), only three of the bosonic operators are required. For mixed representations (n, m), all six operators are required. The coherent states provide a resolution of identity, satisfy the continuity property, and possess a variety of group theoretic properties. We introduce an explicit parameterization of the group SU(3) and the corresponding integration measure. Finally, we discuss the path integral formalism for a problem in which the Hamiltonian is a function of SU(3) operators at each site.
Path integral formulation of quantum mechanics is presented through the formalism of coherent state. Coherent states for bosons are also presented as an example for fields.
Coherent State Path Integrals without Resolutions of Unity
2000
From the very beginning, coherent state path integrals have always relied on a coherent state resolution of unity for their construction. By choosing an inadmissible fiducial vector, a set of ``coherent states'' spans the same space but loses its resolution of unity, and for that reason has been called a set of weak coherent states. Despite having no resolution of unity, it is nevertheless shown how the propagator in such a basis may admit a phase-space path integral representation in essentially the same form as if it had a resolution of unity. Our examples are toy models of similar situations that arise in current studies of quantum gravity.
D ec 2 00 0 Coherent States For SU ( 3 )
2004
We define coherent states for SU(3) using six bosonic creation and annihilation operators. These coherent states are explicitly characterized by six complex numbers with constraints. For the completely symmetric representations (n, 0) and (0, m), only three of the bosonic operators are required. For mixed representations (n,m), all six operators are required. The coherent states provide a resolution of identity, satisfy the continuity property, and possess a variety of group theoretic properties. We introduce an explicit parameterization of the group SU(3) and the corresponding integration measure. Finally, we discuss the path integral formalism for a problem in which the Hamiltonian is a function of SU(3) operators at each site. PACS: 02.20.-a
Analytic representations based on SU (1 , 1) coherent states and their applications
Journal of Physics A: Mathematical and General, 1996
We consider two analytic representations of the SU (1, 1) Lie group: the representation in the unit disc based on the SU (1, 1) Perelomov coherent states and the Barut-Girardello representation based on the eigenstates of the SU (1, 1) lowering generator. We show that these representations are related through a Laplace transform. A 'weak' resolution of the identity in terms of the Perelomov SU (1, 1) coherent states is presented which is valid even when the Bargmann index k is smaller than 1 2. Various applications of these results in the context of the two-photon realization of SU (1, 1) in quantum optics are also discussed.
Coherent States and Their Generalizations: A Mathematical Overview
Reviews in Mathematical Physics, 1995
We present a survey of the theory of coherent states (CS) and some of their generalizations, with emphasis on the mathematical structure, rather than on physical applications. Starting from the standard theory of CS over Lie groups, we develop a general formalism, in which CS are associated to group representations which are square integrable over a homogeneous space. A further step allows us to dispense with the group context altogether, and thus obtain the so-called reproducing triples and continuous frames introduced in some earlier work. We discuss in detail a number of concrete examples, namely semisimple Lie groups, the relativity groups and various types of wavelets. Finally we turn to some physical applications, centering on quantum measurement and the quantization/dequantization problem, that is, the transition from the classical to the quantum level and vice versa.