Quantization in background scalar fields

Abstract

We consider (0+1) and (1+1) dimensional Yukawa theory in various scalar field backgrounds, which are solving classical equations of motion:φ cl = 0 or φ cl = 0, correspondingly. The (0+1)-dimensional theory we solve exactly. In (1+1)-dimensions we consider background fields of the form φ cl = E t and φ cl = E x, which are inspired by the constant electric field. Here E is a constant. We study the backreaction problem by various methods, including the dynamics of a coherent state. We also calculate loop corrections to the correlation functions in the theory using the Schwinger-Keldysh diagrammatic technique. * akhmedov@itep.ru †

Secularly growing loop corrections in scalar wave background

“…In this section we show that one-loop corrections to the fermion Keldysh propagator (figure 3) and to the vertexes do not possess secular growth. This supports the general observation that was made in [22].…”

“…since p, q, k 1 and c − q 1 take their values in the interval (0, +∞). Thus, the Keldysh propagator for fermions does not receive secularly growing corrections, which agrees with the observations made in [22]. Now, it is worth to make the following observation.…”

“…1. it is possible to interpret the one loop correction to the one point correlation function in terms of the effective action for scalars which was found in [22];…”

“…In this respect it would be nice to find a simple but nontrivial example of a nonequilibrium field theory, in which calculations and dynamics itself are more transparent than in complex gravitational and electromagnetic fields. In the papers [14,22] such an example was proposed. There the Yukawa theory in (1+1)-dimensional Minkowski spacetime,…”

“…1 Whereas the separate paper [22] considers the case of the strong scalar field backgrounds of the forms φ cl = m λ + Et and φ cl = m λ + Ex.…”