arXiv subjects

Masao Matsumoto

Publications and source records attributed to Masao Matsumoto.

4 recordsLinked to original sources

arXiv2014

Restriction on types of coherent states due to gauge symmetry

From the viewpoint of the SU(2) coherent states (CS) and their path integrals (PI) labeled by a full set of Euler angles $(ϕ, θ, ψ)$ which we developed in the previous paper, we study the relations between gauge symmetries of Lagrangians and allowed quantum states; we investigate permissible types of fiducial vectors (FV) in the full quantum dynamics in terms of SU(2) coherent states for typical Lagrangians. We propose a general framework for a Lagrangian having a certain gauge symmetry with respect to one of the Euler angles $ψ$. We find that for the case fiducial vectors are so restricted that they belong to the eigenstates of ${\hat S}_3$ or to the orbits of them under the action of the SU(2); and the strength of a fictitious monopole, which appears in the Lagrangian, is a multiple of $\frac12$. In this case Dirac strings are permitted. Our formulations and results deepen those of the preceding work by Stone that has piloted us; we illustrate the relation between the two methods. The reasoning here does not work for a Lagrangian without the gauge symmetry. This suggests a new possibility about monopole charge quantization. Besides analogies to field theory and entanglements in quantum information (QI) are briefly mentioned.

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arXiv2012

SU(2) coherent state path integrals labeled by a full set of Euler angles: basic formulation

We develop a basic formulation of the spin (SU(2)) coherent state path integrals based not on the conventional highest or lowest weight vectors but on arbitrary fiducial vectors. The coherent states, being defined on a 3-sphere, are specified by a full set of Euler angles. They are generally considered as states without classical analogues. The overcompleteness relation holds for the states, by which we obtain the time evolution of general systems in terms of the path integral representation; the resultant Lagrangian in the action has a monopole-type term a la Balachandran etal. as well as some additional terms, both of which depend on fiuducial vectors in a simple way. The process of the discrete path integrals to the continuous ones is clarified. Complex variable forms of the states and path integrals are also obtained. During the course of all steps, we emphasize the analogies and correspondences to the general canonical coherent states and path integrals that we proposed some time ago. In this paper we concentrate on the basic formulation. The physical applications as well as criteria in choosing fiducial vectors for real Lagrangians, in relation to fictitious monopoles and geometric phases, will be treated in subsequent papers separately.

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arXiv1999

SU(2) coherent state path integrals based on arbitrary fiducial vectors and geometric phases

We develop the formulation of the spin(SU(2)) coherent state path integrals based on arbitrary fiducial vectors. The resultant action in the path integral expression extensively depends on the vector; It differs from the conventional one in that it has a generalized form having some additional terms. We also study, as physical applications, the geometric phases associated with the coherent state path integrals to find that new effects of the terms may appear in experiments. We see that the formalism gives a clear insight into geometric phases.

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arXiv1995

Geometric Phases, Coherent States and Resonant Hamiltonian

We study characteristic aspects of the geometric phase which is associated with the generalized coherent states. This is determined by special orbits in the parameter space defining the coherent state, which is obtained as a solution of the variational equation governed by a simple model Hamiltonian called the "resonant Hamiltonian". Three typical coherent states are considered: SU(2), SU(1,1) and Heisenberg-Weyl. A possible experimental detection of the phases is proposed in such a way that the geometric phases can be discriminated from the dynamical phase.

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