Zhang Peng-Fei

A new kind of special function and its application

By virtue of the operator Hermite polynomial method and the technique of integration within the ordered product of operators we derive a new kind of special function, which is closely related to one- and two-variable Hermite polynomials. Its application in deriving the normalization for some quantum optical states is presented.

Feynman propagator for an arbitrary half-integral spin

Based on the solution to Bargmann-Wigner equation for a particle with arbitrary half-integral spin, a direct derivation of the projection operator and propagator for a particle with arbitrary half-integral spin is worked out. The projection operator constructed by Behrends and Fronsdal is re-deduced and confirmed and simplified, the general commutation rules and Feynman propagator with additional non-covariant terms for a free particle with arbitrary half-integral spin are derived, and explicit expressions for the propagators for spins 3/2, 5/2 and 7/2 are provided.

Generating function of product of bivariate Hermite polynomials and their applications in studying quantum optical states

By virtue of the operator-Hermite-polynomial method, we derive some new generating function formulas of the product of two bivariate Hermite polynomials. Their applications in studying quantum optical states are presented.

Projection Operator and Feynman Propagator for a Free MassiVe Particle of Arbitrary Spin

Based on the solution to the Bargmann–Wigner equations, a direct derivation of the projection operator and Feynman propagator for a free massive particle of arbitrary spin is worked out. The projection operator constructed by Behrends and Fronsdal is re-deduced and confirmed, and simplified in the case of half-integral spin, the general commutation rules and Feynman propagator with additional non-covariant terms for a free massive particle with any spin are derived, and explicit expressions for the propagators for spins 3/2, 2, 5/2, 3, 7/2, and 4 are provided.

A theorem for quantum operator correspondence to the solution of the Helmholtz equation

We propose a theorem for the quantum operator that corresponds to the solution of the Helmholtz equation, i.e., ∫∫∫V(x1,x2,x3)|x1,x2,x3x1,x2,x3|d3x = V(X1,X2,X3) = e−λ2/4:V(X1,X2,X3):, where V(x1,x2,x3) is the solution to the Helmholtz equation 2V + λ2V = 0, the symbol: : denotes normal ordering, and X1,X2,X3 are three-dimensional coordinate operators. This helps to derive the normally ordered expansion of Diracs radius operator functions. We also discuss the normally ordered expansion of Bessel operator functions.

Relativistic Spin Operators

A systematic theory on the appropriate spin operators for the relativistic states is developed. For a massive relativistic particle with arbitrary nonzero spin, the spin operator should be replaced with the relativistic one, which is called in this paper as moving spin. Further the concept of moving spin is discussed in the quantum field theory. A new operator, field quanta spin is defined and in terms of the generators of Poincare group the moving spin of field system is constructed. It is shown that, in virtue of the two operators, problems in quantum field concerned spin can be neatly settled.