This article is cited in 2 papers

Quantum field theory with non-Fock asymptotic fields: the existence of the $S$-matrix

O. I. Zavialov, A. M. Malokostov

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: We construct a family of relativistic-invariant generating functionals of the form
$$F(f^*,g)=\exp\left\{\gamma\int\frac{d\mathbf k}{\omega(\mathbf k)}f^*(\mathbf k)g(\mathbf k)\right\}$$
for the non-Fock representations of the CCR. We analyze the first order in the coupling constant of the model theory. In this theory, the asymptotic in field coincides with the field $\varphi(x)$ corresponding to such a functional. We prove that in the first order, the in and out fields are unitarily equivalent and the scattering matrix consequently exists. Moreover, the kinematics of the “non-Fock quantum field theory” is much richer than the standard kinematics: in this case, the $S$-matrix does not coincide with the chronologically ordered exponent of the interaction Lagrangian.

Received: 25.01.1999

DOI: 10.4213/tmf796

 English version: Theoretical and Mathematical Physics, 1999, 121:1, 1281–1293

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