Ruan Tu-Nan

Some Applications of the Coherent State Formulation of the Wigner Operator

On the basis of the preceding paper we present some new applications of both the normal product form and the coherent state form of the Wigner operator, which involve deriving some new quantum operator formulas, giving the coherent state generalization of the Moyal theorem, evaluating some quantum operators which correspond to the given classical functions in the weyl manner and vice versa. Were it not for the Wigner operators coherent state formulation given by us the above-mentioned calculations would be hard to perform.

Coherent State Formulation of the Weyl Correspondence and the Wigner Function

We point out that there is a close connection between the Weyl correspondence and coherent state correspondence. By virtue of differential and integral method within normal ordered products we demonstrate that the essence of the Weyl correspondence is just coherent state correspondence in both boson and fermion cases. Furthermore, coherent state form and explicit operator form for the Wigner function are given. With these forms we can derive some important operator formulas from the Weyl correspondence. The Wigner functions zero-point value is also discussed.

Does the Creation Operator a+ Possess Eignvectors?

It is pointed out that the assertion that the eigenfunction of the creation operator a+ is identically zero is not rigorous. On the contrary, the eigenfunction of a+ may be discussed by using the contour integral representation of δ function, the property of which and the relation with the eigenstate of the annihilation operator are discussed. Its applications, especially the application in thoroughly studying the inverse operators properties, are presented. It is shown that the phase operator can also be represented by the inverse operator.

Search for exotic states in J / psi --> rho eta pi

It is an ideal place to search for exotic states through J/ψ hadronic decays. In this paper, we discuss theway to use the partial wave analysis (PWA) based on covariant helicity amplitude analysis to study the invariant massspectrum of r and to find the evidence of the existence of exotic states in this channel. The formula for PWA is alsogiven. It is the theoretical foundation of experimental physics analysis on exotic states searching in J/ hadronic decays.The t heoret ical formula can also be used in physics analysis of J / decays into a , φπ , K K , φ K K and K*(892)Kπ.

Covariant Helicity Amplitude Analysis for J/ψ → γPP*

Covariant helicity amplitude analysis for the process of J/ψ →γPP is discussed.Starting from the S- matrix elements of decay process,we deduce the formulae of helicity coupling amplitudes for two-body decay process. These formulae are used to analyze intermediate resonance states in the process of J/ψ decay to γππ,γKK,γηη＇ etc.

New Operator Identities Gained via Coherent State Formulation

By the properties of the coherent state and the technique of performing integrations within ordered products as in Ref. [1], we derive some new useful operator ordering identities. Their applications, especially in studying the Boglyubov transformations both in one and two dimensional cases, are presented. The explicit non-unitary operators which turn the coordinate or momentum eigen-state to the corresponding coherent state are also given. Moreover, by using the Schwinger angular momentum theory and the technique mentioned above we find the normal product form of the rotation operator, with which the coefficient of the rotation D-matrix can be easily obtained.

Relations Between Helicity Coupling Amplitude and L-S Coupling Amplitude*

Relations between helicity coupling amplitude and L-S coupling amplitude are discussed. The equivalence condition for these two kinematic analysis methods and the limitations of the L-S coupling amplitude are also studied in this paper.``

General Holomorphic Functional Integral and its Evolution to the Feynman Kernel

This paper is devoted to establishing the relation between the holomorphic form of the functional integral and its Feynman form, as well as presenting a new way to evaluate the Feynman transformation matrix element by using the coherent state. The Feynman kernel for the harmonic oscillator with two time-dependent sources is thus derived. Besides these, by the use of the normal product form of the Wigner operator derived in Ref.[1] and the Weyl correspondence, the general holomorphic form of the functional integral and its evolution to the Feynman kernel are discussed.

SU(3) Charged and hypercharged coheremt state and the color quantum number

We extend the coherent state which possesses definite Abel charge to the state possessing definite non-Abel charge, and construct SU(3) charged and hypercharged coherent states for both boson and fermion. In this way, the fractionally charged and hypercharged quark states can be obtained naturally. Moreover, this formulation also shows that in order to obtain integrally charged and hypercharged hadroh coherent state, one must introduce color quantum number and discuss the SU (6)⊕SUc(3) case.

State-Vector Space and Canonical Coherent States in Noncommutative Plane

The structure of the state-vector space of identical bosons in noncommutative spaces is investigated. To maintain Bose-Einstein statistics the commutation relations of phase space variables should simultaneously include coordinate-coordinate non-commutativity and momentum-momentum non-commutativity, which lead to noncommutative Fock space. By this we mean that creation and annihilation operators corresponding to different degrees of freedom of the bosons do not commute each other. The main character of the noncommutative Fock space is there are no ordinary number representations because of the non-commutativity between different number operators. However, eigenvectors of several pairs of commuting Hermitian operators are obtained which can also be served as bases in this Fock space. As a simple example, an explicit form of two-dimensional canonical coherent state in this noncommutative Fock space is constructed and its properties are discussed.The structure of the state-vector space of identical bosons in noncommutative spaces is investigated. To maintain Bose–Einstein statistics the commutation relations of phase space variables should simultaneously include coordinate-coordinate non-commutativity and momentum-momentum non-commutativity, which leads to a kind of deformed Heisenberg-Weyl algebra. Although there is no ordinary number representation in this state-vector space, several set of orthogonal and complete state-vectors can be derived which are common eigenvectors of corresponding pairs of commuting Hermitian operators. As a simple application of this state-vector space, an explicit form of two-dimensional canonical coherent state is constructed and its properties are discussed.