Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1999-12-05
Physics
High Energy Physics
High Energy Physics - Theory
14pages, some minor modification
Scientific paper
Based on the renormalisability of the SU(n) theory with massive gauge bosons, we start with the path integral of the generating functional for the renormalized Green functions and develop a method to construct the scattering matrix so that the unitarity is evident. By using as basical variables the renormalized field functions and defining the unperturbed Hamiltonian operator $H_0$ that, under the Lorentz condition, describes the free particles of the initial and final states in scattering processes, we form an operator description with which the renormalized Green functions can be expressed as the vacuum expectations of the time ordered products of the Heisenberg operators of the renormalized field functions, that satisfy the usual equal time commutation or anticommutation rules. From such an operator description we find a total Hamiltonian $\widetilde{H}$ that determine the time evolution of the Heisenberg operators of the renormalized field functions. The scattering matrix is nothing but the matrix of the operator $U(\infty, -\infty)$, which describes the time evolution from $-\infty$ to $\infty$ in the interaction picture specified by $\widetilde{H}$ and $H_0$, respect to a base formed by the physical eigen states of $H_0$. We also explain the asymptotic field viewpoint of constructing the scattering matrix within our operator description. Moreover, we find a formular to express the scattering matrix elements in terms of the truncated renormalized Green functions.
Xianhui Li
Yushu Zhong
Ze-sen Yang
Zhining Zhou
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