Abstract
It is proposed that field theories quantized in a curved space-time manifold can be conveniently regularized and renormalized with the aid of Pauli--Villars regulator fields. The method avoids the conceptual difficulties of covariant point-separation approaches, by always starting from a manifestly generally covariant action, and the technical limitations of the dimensional regularization approach, which requires solution of the theory in arbitrary dimension in order to go beyond a weak-field expansion. An action is constructed which renormalizes the weak-field perturbation theory of a massive scalar field in two space-time dimensions, it is shown that the trace anomaly previously found in dimensional regularization and some point-separation calculations also arises in perturbation theory when the theory is Pauli--Villars regulated. We then study a specific solvable two-dimensional model of a massive scalar field in a Robertson--Walker asymptotically flat universe. It is shown that the action previously considered leads, in this model, to a well-defined finite expectation value for the stress-energy tensor. The particle production ( for t..-->..+infinity) is computed explicitly. Finally, the validity of weak-field perturbation theory (in the appropriate range of parameters) is checked directly in the solvable model, and the trace anomaly computed in the asymptoticmore » regions t..-->.. +- infinity independently of any weak-field approximation. The extension of our model to higher dimensions and the renormalization of interacting (scalar) field theories are briefly discussed.« less
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