Thermal field theory to all orders in gradient expansion

Peter Millington,Apostolos Pilaftsis

doi:10.1088/1742-6596/447/1/012071

Peter Millington, Apostolos Pilaftsis

Open Access

https://doi.org/10.1088/1742-6596/447/1/012071

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Abstract

We present a new perturbative formulation of non-equilibrium thermal field theory, based upon non-homogeneous free propagators and time-dependent vertices. The resulting time-dependent diagrammatic perturbation series are free of pinch singularities without the need for quasi-particle approximation or effective resummation of finite widths. After arriving at a physically meaningful definition of particle number densities, we derive master time evolution equations for statistical distribution functions, which are valid to all orders in perturbation theory and all orders in a gradient expansion. For a scalar model, we make a loopwise truncation of these evolution equations, whilst still capturing fast transient behaviour, which is found to be dominated by energy-violating processes, leading to non-Markovian evolution of memory effects.

Highlights

The description of out-of-equilibrium many-body field-theoretic systems is of increasing relevance in theoretical and experimental physics at the density frontier
Having a well-defined underlying perturbation theory that is free of pinch singularities, these time evolution equations may be truncated in a loopwise sense whilst retaining all orders of the time behaviour
We have obtained master time evolution equations for particle number densities that are valid to all orders in perturbation theory and to all orders in gradient expansion

Summary

Introduction

The description of out-of-equilibrium many-body field-theoretic systems is of increasing relevance in theoretical and experimental physics at the density frontier. In [1], the present authors introduce a new perturbative approach to non-equilibrium thermal quantum field theory and an alternative framework in which to derive master time evolution equations for macroscopic observables. Existing frameworks, based upon systems of Kadanoff–Baym equations [2], whilst retaining all orders in perturbation theory, often rely upon the truncation of a gradient expansion in time derivatives in order to obtain calculable expressions. Where the CTP indices a, b = 1, 2 and ηab = diag (1, −1) is an SO (1, 1) ‘metric.’ Inserting into (9) complete sets of eigenstates of the Heisenberg field operator, we derive a path-integral representation of the CTP generating functional, which depends on the pathordered CTP propagator i∆ab(x, y, tf ; ti), written as the 2 × 2 matrix i∆ab(x, y, tf ; ti) ≡. ∆0a,b−1(x, y) self-energy, are the resummed analogous to (11)

Non-homogeneous diagrammatics

MMtt 110000200

Conclusions