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The averaged null energy condition for general quantum field theories in two dimensions

Rainer Verch

Abstract

It is shown that the averaged null energy condition is fulfilled for a dense, translationally invariant set of vector states in any local quantum field theory in two-dimensional Minkowski spacetime whenever the theory has a mass gap and possesses an energy-momentum tensor. The latter is assumed to be a Wightman field which is local relative to the observables, generates locally the translations, is divergence-free, and energetically bounded. Thus the averaged null energy condition can be deduced from completely generic, standard assumptions for general quantum field theory in two-dimensional flat spacetime.

The averaged null energy condition for general quantum field theories in two dimensions

Abstract

It is shown that the averaged null energy condition is fulfilled for a dense, translationally invariant set of vector states in any local quantum field theory in two-dimensional Minkowski spacetime whenever the theory has a mass gap and possesses an energy-momentum tensor. The latter is assumed to be a Wightman field which is local relative to the observables, generates locally the translations, is divergence-free, and energetically bounded. Thus the averaged null energy condition can be deduced from completely generic, standard assumptions for general quantum field theory in two-dimensional flat spacetime.

Paper Structure

This paper contains 7 sections, 7 theorems, 43 equations.

Table of Contents

  1. Introduction
  2. ANEC in quantum field theory on two-dimensional Minkowski spacetime
  3. Assumptions
  4. Comments and some implications
  5. Main result
  6. A result for lightlike half-lines
  7. Concluding remarks

Key Result

Proposition 2.1

BorDri One has weak asymptotic lightlike clustering: For any lightlike $k \in {\mathbb R}^2\backslash\{0\}$ and any pair of vectors $\psi,\psi' \in {\cal H}$, it holds that

Theorems & Definitions (10)

  • Proposition 2.1
  • Lemma 2.2
  • proof
  • Proposition 2.3
  • Lemma 2.4
  • Theorem 2.5
  • Corollary 2.6
  • proof
  • Proposition 3.1
  • proof