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

@article{Verch2000TheAN,
  title={The averaged null energy condition for general quantum field theories in two dimensions},
  author={Rainer Verch},
  journal={Journal of Mathematical Physics},
  year={2000},
  volume={41},
  pages={206-217}
}
  • R. Verch
  • Published 29 April 1999
  • Physics, Mathematics
  • Journal of Mathematical Physics
It is shown that in any local quantum field theory in two-dimensional Minkowski space–time possessing a mass gap and an energy-momentum tensor, the averaged null energy condition is fulfilled for the set of those vector states which correspond to energetically strongly damped, local excitations of the vacuum. This set of physical vector states is translation invariant and dense. The energy-momentum tensor of the theory is assumed to be a Wightman field which is local relative to the observables… 

Figures from this paper

Quantum energy inequalities in two-dimensional conformal field theory
Quantum energy inequalities (QEIs) are state-independent lower bounds on weighted averages of the stress-energy tensor, and have been established for several free quantum field models. We present
Lectures on quantum energy inequalities
Quantum field theory violates all the classical energy conditions of general relativity. Nonetheless, it turns out that quantum field theories satisfy remnants of the classical energy conditions,
Averaged null energy condition from causality
A bstractUnitary, Lorentz-invariant quantum field theories in flat spacetime obey mi-crocausality: commutators vanish at spacelike separation. For interacting theories in more than two dimensions, we
A Quantum Weak Energy Inequality¶for Dirac Fields in Curved Spacetime
Abstract: Quantum fields are well known to violate the weak energy condition of general relativity: the renormalised energy density at any given point is unbounded from below as a function of the
Averaged null energy condition in spacetimes with boundaries
The averaged null energy condition (ANEC) requires that the average along a complete null geodesic of the projection of the stress-energy tensor onto the geodesic tangent vector can never be
Lower Bound on the Energy Density in Classical and Quantum Field Theories.
TLDR
A novel method for deriving energy conditions in stable field theories is described, and some extensions to higher dimensions are briefly discussed.
Quantum Energy Inequalities
Quantum Energy Inequalities (QEIs) are lower bounds on local averages of energy densities and related quantities in quantum field theory (QFT). They replace the classical energy conditions of
Proof of the Quantum Null Energy Condition
We prove the quantum null energy condition (QNEC), a lower bound on the stress tensor in terms of the second variation in a null direction of the entropy of a region. The QNEC arose previously as a
Quantum null energy condition and its (non)saturation in 2d CFTs
We consider the Quantum Null Energy Condition (QNEC) for holographic conformal field theories in two spacetime dimensions (CFT_22). We show that QNEC saturates for all states dual to vacuum solutions
Ju l 2 01 7 A Lower Bound on the Energy Density in Classical and Quantum Field Theories
A novel method for deriving energy conditions in stable field theories is described. In a local classical theory with one spatial dimension, a local energy condition always exists. For a relativistic
...
1
2
3
...

References

SHOWING 1-10 OF 29 REFERENCES
Averaged null energy condition and difference inequalities in quantum field theory.
  • Yurtsever
  • Physics, Medicine
    Physical review. D, Particles and fields
  • 1995
TLDR
A proof of the difference inequality for a minimally coupled massless scalar field in an arbitrary (globally hyperbolic) two-dimensional spacetime is given, using the same techniques as those used to prove the ANEC in an earlier paper with Wald.
Averaged energy conditions for free scalar fields in flat spacetime.
  • Klinkhammer
  • Physics, Medicine
    Physical review. D, Particles and fields
  • 1991
TLDR
This paper shows that a quantized, free scalar field in Minkowski spacetime has the following properties: The weak energy condition is satisfied for a wide class of states when averaged along a complete null geodesic, but it can be violated when averaging along a nongeodesic curve.
General proof of the averaged null energy condition for a massless scalar field in two-dimensional curved spacetime.
  • Wald, Yurtsever
  • Physics, Medicine
    Physical review. D, Particles and fields
  • 1991
TLDR
The proof shows that the ANEC is a direct consequence of the general positivity condition which must hold for the two-point function of any state, and extends to establish the AN EC for the null geodesic generators of the horizon (provided that there exists a stationary Hadamard state of the field).
Remarks on the averaged null energy condition in quantum field theory.
  • Yurtsever
  • Physics, Medicine
    Physical review. D, Particles and fields
  • 1995
TLDR
If generalized ANEC is satisfied in static traversable wormhole spacetimes, then macroscopic wormholes are ruled out by quantum field theory and the non-negativity of total energy and for singularity theorems similar to the implications of ANEC are argued.
Does back reaction enforce the averaged null energy condition in semiclassical gravity?
  • Flanagan, Wald
  • Physics, Medicine
    Physical review. D, Particles and fields
  • 1996
TLDR
It is suggested that if traversable wormholes do exist as solutions to the semiclassical equations, they cannot be macroscopic but must be ``Planck scale'', in agreement with conclusions drawn by Ford and Roman from entirely independent arguments.
The microlocal spectrum condition and Wick polynomials of free fields on curved spacetimes
Quantum fields propagating on a curved spacetime are investigated in terms of microlocal analysis. We discuss a condition on the wave front set for the correspondingn-point distributions, called
Scale anomalies imply violation of the averaged null energy condition
Abstract It is important to know whether or not quantum field theory on a fixed but curved background spacetime satisfies the so-called “averaged null energy condition” (ANEC). This result has a
Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics
In this book, Robert Wald provides a pedagogical introduction to the formulation of quantum field theory in curved spacetime. He begins with a treatment of the ordinary one-dimensional quantum
Energy conditions and spacetime singularities
In this paper, a number of theorems are proven which collectively show that singularities will occur in spacetime under weaker energy conditions than the strong energy condition. In particular, the
The CPT-theorem in two-dimensional theories of local observables
Let ℳ be a von Neumann algebra with cyclic and separating vector Ω, and letU(a) be a continuous unitary representation ofR with positive generator and Ω as fixed point. If these unitaries induce for
...
1
2
3
...