463 research outputs found
A Unique Continuation Result for Klein-Gordon Bisolutions on a 2-dimensional Cylinder
We prove a novel unique continuation result for weak bisolutions to the
massive Klein-Gordon equation on a 2-dimensional cylinder M. Namely, if such a
bisolution vanishes in a neighbourhood of a `sufficiently large' portion of a
2-dimensional surface lying parallel to the diagonal in the product manifold of
M with itself, then it is (globally) translationally invariant. The proof makes
use of methods drawn from Beurling's theory of interpolation. An application of
our result to quantum field theory on 2-dimensional cylinder spacetimes will
appear elsewhere.Comment: LaTeX2e, 9 page
An absolute quantum energy inequality for the Dirac field in curved spacetime
Quantum Weak Energy Inequalities (QWEIs) are results which limit the extent
to which the smeared renormalised energy density of a quantum field can be
negative. On globally hyperbolic spacetimes the massive quantum Dirac field is
known to obey a QWEI in terms of a reference state chosen arbitrarily from the
class of Hadamard states; however, there exist spacetimes of interest on which
state-dependent bounds cannot be evaluated. In this paper we prove the first
QWEI for the massive quantum Dirac field on four dimensional globally
hyperbolic spacetime in which the bound depends only on the local geometry;
such a QWEI is known as an absolute QWEI
A quantum weak energy inequality for the Dirac field in two-dimensional flat spacetime
Fewster and Mistry have given an explicit, non-optimal quantum weak energy
inequality that constrains the smeared energy density of Dirac fields in
Minkowski spacetime. Here, their argument is adapted to the case of flat,
two-dimensional spacetime. The non-optimal bound thereby obtained has the same
order of magnitude, in the limit of zero mass, as the optimal bound of Vollick.
In contrast with Vollick's bound, the bound presented here holds for all
(non-negative) values of the field mass.Comment: Version published in Classical and Quantum Gravity. 7 pages, 1 figur
Quantum inequalities for the free Rarita-Schwinger fields in flat spacetime
Using the methods developed by Fewster and colleagues, we derive a quantum
inequality for the free massive spin- Rarita-Schwinger fields in
the four dimensional Minkowski spacetime. Our quantum inequality bound for the
Rarita-Schwinger fields is weaker, by a factor of 2, than that for the
spin- Dirac fields. This fact along with other quantum inequalities
obtained by various other authors for the fields of integer spin (bosonic
fields) using similar methods lead us to conjecture that, in the flat
spacetime, separately for bosonic and fermionic fields, the quantum inequality
bound gets weaker as the the number of degrees of freedom of the field
increases. A plausible physical reason might be that the more the number of
field degrees of freedom, the more freedom one has to create negative energy,
therefore, the weaker the quantum inequality bound.Comment: Revtex, 11 pages, to appear in PR
Quantum interest in two dimensions
The quantum interest conjecture of Ford and Roman asserts that any
negative-energy pulse must necessarily be followed by an over-compensating
positive-energy one within a certain maximum time delay. Furthermore, the
minimum amount of over-compensation increases with the separation between the
pulses. In this paper, we first study the case of a negative-energy square
pulse followed by a positive-energy one for a minimally coupled, massless
scalar field in two-dimensional Minkowski space. We obtain explicit expressions
for the maximum time delay and the amount of over-compensation needed, using a
previously developed eigenvalue approach. These results are then used to give a
proof of the quantum interest conjecture for massless scalar fields in two
dimensions, valid for general energy distributions.Comment: 17 pages, 4 figures; final version to appear in PR
Quantum inequalities and `quantum interest' as eigenvalue problems
Quantum inequalities (QI's) provide lower bounds on the averaged energy
density of a quantum field. We show how the QI's for massless scalar fields in
even dimensional Minkowski space may be reformulated in terms of the positivity
of a certain self-adjoint operator - a generalised Schroedinger operator with
the energy density as the potential - and hence as an eigenvalue problem. We
use this idea to verify that the energy density produced by a moving mirror in
two dimensions is compatible with the QI's for a large class of mirror
trajectories. In addition, we apply this viewpoint to the `quantum interest
conjecture' of Ford and Roman, which asserts that the positive part of an
energy density always overcompensates for any negative components. For various
simple models in two and four dimensions we obtain the best possible bounds on
the `quantum interest rate' and on the maximum delay between a negative pulse
and a compensating positive pulse. Perhaps surprisingly, we find that - in four
dimensions - it is impossible for a positive delta-function pulse of any
magnitude to compensate for a negative delta-function pulse, no matter how
close together they occur.Comment: 18 pages, RevTeX. One new result added; typos fixed. To appear in
Phys. Rev.
Endomorphisms and automorphisms of locally covariant quantum field theories
In the framework of locally covariant quantum field theory, a theory is
described as a functor from a category of spacetimes to a category of
*-algebras. It is proposed that the global gauge group of such a theory can be
identified as the group of automorphisms of the defining functor. Consequently,
multiplets of fields may be identified at the functorial level. It is shown
that locally covariant theories that obey standard assumptions in Minkowski
space, including energy compactness, have no proper endomorphisms (i.e., all
endomorphisms are automorphisms) and have a compact automorphism group.
Further, it is shown how the endomorphisms and automorphisms of a locally
covariant theory may, in principle, be classified in any single spacetime. As
an example, the endomorphisms and automorphisms of a system of finitely many
free scalar fields are completely classified.Comment: v2 45pp, expanded to include additional results; presentation
improved and an error corrected. To appear in Rev Math Phy
On the spin-statistics connection in curved spacetimes
The connection between spin and statistics is examined in the context of
locally covariant quantum field theory. A generalization is proposed in which
locally covariant theories are defined as functors from a category of framed
spacetimes to a category of -algebras. This allows for a more operational
description of theories with spin, and for the derivation of a more general
version of the spin-statistics connection in curved spacetimes than previously
available. The proof involves a "rigidity argument" that is also applied in the
standard setting of locally covariant quantum field theory to show how
properties such as Einstein causality can be transferred from Minkowski
spacetime to general curved spacetimes.Comment: 17pp. Contribution to the proceedings of the conference "Quantum
Mathematical Physics" (Regensburg, October 2014
On a Recent Construction of "Vacuum-like" Quantum Field States in Curved Spacetime
Afshordi, Aslanbeigi and Sorkin have recently proposed a construction of a
distinguished "S-J state" for scalar field theory in (bounded regions of)
general curved spacetimes. We establish rigorously that the proposal is
well-defined on globally hyperbolic spacetimes or spacetime regions that can be
embedded as relatively compact subsets of other globally hyperbolic spacetimes,
and also show that, whenever the proposal is well-defined, it yields a pure
quasifree state. However, by explicitly considering portions of ultrastatic
spacetimes, we show that the S-J state is not in general a Hadamard state. In
the specific case where the Cauchy surface is a round 3-sphere, we prove that
the representation induced by the S-J state is generally not unitarily
equivalent to that of a Hadamard state, and indeed that the representations
induced by S-J states on nested regions of the ultrastatic spacetime also fail
to be unitarily equivalent in general. The implications of these results are
discussed.Comment: 25pp, LaTeX. v2 References added, typos corrected. To appear in Class
Quantum Gravit
A general worldline quantum inequality
Worldline quantum inequalities provide lower bounds on weighted averages of
the renormalised energy density of a quantum field along the worldline of an
observer. In the context of real, linear scalar field theory on an arbitrary
globally hyperbolic spacetime, we establish a worldline quantum inequality on
the normal ordered energy density, valid for arbitrary smooth timelike
trajectories of the observer, arbitrary smooth compactly supported weight
functions and arbitrary Hadamard quantum states. Normal ordering is performed
relative to an arbitrary choice of Hadamard reference state. The inequality
obtained generalises a previous result derived for static trajectories in a
static spacetime. The underlying argument is straightforward and is made
rigorous using the techniques of microlocal analysis. In particular, an
important role is played by the characterisation of Hadamard states in terms of
the microlocal spectral condition. We also give a compact form of our result
for stationary trajectories in a stationary spacetime.Comment: 19pp, LaTeX2e. The statement of the main result is changed slightly.
Several typos fixed, references added. To appear in Class Quantum Gra
- …