The Representation of Single Particle Operators in Two-Particle Form

Saul T. Epstein

Ren Zheng-xu

The expansion of single- particle transition operator( defined as the product of creation and annihilation operator,namely a+iajin single- particle state is obtained through the form of single- operator in occupation particle number representation,and the commutation relations for transition operator and creation( annihilation) operator are also given,then based on these conclusions,the form of general two- and n- particle operators in occupation particle number representation can be derived succinctly without distinguishing the statistical property of identical particle system.

Melih Kızılkaya

BRITTON, STEPHEN K, Sergey A. Frolov

The process of using the free field representation to construct form factors of two dimensional integrable models is very promising. In this thesis, this procedure is analysed and adapted for application to the chiral Gross-Neveu model. The vertex operators and Zamolodchikov-Faddeev algebra for the particles are presented, with a similar structure producing a representation of the local operators of the theory. Using these techniques, the form factors of the model are then constructed as traces over the space of Zamolodchikov-Faddeev operators, and given in terms of an integral representation. In particular, the two-particle form factors of the current operator are found, and shown to agree with previous results in the literature.

Jørgen Rammer

Tran Trong Gien

Recently, Lippmann showed that a time operator might exist in quantum theory and that its explicit form is i ∂/∂E in the energy representation. In this paper, we wish to stress that i ∂/∂E actually represents only the time which the particle used to move from the scattering center to a certain point at the outside. (Later on, we shall call this time the "time of motion.") We also show that, although it is possible to define an operator for the "time of motion" of the particle in the energy representation, it is necessary to introduce a new conjugate representation of the energy representation, the "time representation," to overcome difficulties which may arise in the evaluation of the mean time of motion [Formula: see text]. If the position representation is used for the calculation instead, we shall meet these difficulties. The reason is that time of motion T, position x, and energy E are not two-by-two compatible variables. Bearing in mind that i ∂/∂E only represents the time of motion of the particle, we can then deduce the explicit form of the delay time operator Q in terms of the scattering matrix S directly from the time of motion operator by simple reasoning. This form is Q = −i(∂S/∂E)·S† as was found previously. Some interesting features of the delay time operator will also be sketched at the end of the paper.