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

Leap of Death

‘Leap of Death’ is collaborative, multi-media project by composer Robert Stillman, artist Anna Fewster, and bookbinder Sarah Bryant. It seeks to interpret archival material for the ‘lost’ 1929 F.W. Murnau film ‘4 Devils’. The main output of the project is a limited edition of 50 bookwork/LP’s that use letterpress text, trace-monotype print images, and recorded music to construct an abstract, non-linear ‘impression’ of the film’s narrative. The project also included a ‘live’ version of this work using projections of the bookwork text and imagery, and performance of the music by the ensemble The Archaic Future Players. The wider research questions for this project include: • Can archival research be carried out and disseminated as contemporary artistic/creative work? What is distinctive about such an approach (compared, for example, to scholarly research). • How can creative content (i.e. narrative) in one form, like film, be translated into, or indeed extended by, other forms like still image, text, and music? • How can ‘traditional’ media like slideshows, live/recorded music, or books present narrative structure in an ‘open’ (i.e. non-linear way?) • How can a digital format (i.e. web) most effectively represent physical media (i.e. an artist’s bookwork)

Quantum energy inequalities and local covariance II: Categorical formulation

We formulate Quantum Energy Inequalities (QEIs) in the framework of locally covariant quantum field theory developed by Brunetti, Fredenhagen and Verch, which is based on notions taken from category theory. This leads to a new viewpoint on the QEIs, and also to the identification of a new structural property of locally covariant quantum field theory, which we call Local Physical Equivalence. Covariant formulations of the numerical range and spectrum of locally covariant fields are given and investigated, and a new algebra of fields is identified, in which fields are treated independently of their realisation on particular spacetimes and manifestly covariant versions of the functional calculus may be formulated.Comment: 27 pages, LaTeX. Further discussion added. Version to appear in General Relativity and Gravitatio

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

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

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

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

Quantum inequalities in two dimensional curved spacetimes

We generalize a result of Vollick constraining the possible behaviors of the renormalized expected stress-energy tensor of a free massless scalar field in two dimensional spacetimes that are globally conformal to Minkowski spacetime. Vollick derived a lower bound for the energy density measured by a static observer in a static spacetime, averaged with respect to the observers proper time by integrating against a smearing function. Here we extend the result to arbitrary curves in non-static spacetimes. The proof, like Vollick's proof, is based on conformal transformations and the use of our earlier optimal bound in flat Minkowski spacetime. The existence of such a quantum inequality was previously established by Fewster.Comment: revtex 4, 5 pages, no figures, submitted to Phys. Rev. D. Minor correction

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

Probability distributions of smeared quantum stress tensors

We obtain in closed form the probability distribution for individual measurements of the stress-energy tensor of two-dimensional conformal field theory in the vacuum state, smeared in time against a Gaussian test function. The result is a shifted Gamma distribution with the shift given by the previously known optimal quantum inequality bound. For small values of the central charge it is overwhelmingly likely that individual measurements of the sampled energy density in the vacuum give negative results. For the case of a single massless scalar field, the probability of finding a negative value is 84%. We also report on computations for four-dimensional massless scalar fields showing that the probability distribution of the smeared square field is also a shifted Gamma distribution, but that the distribution of the energy density is not.Comment: 9 pages, 1 figure. Minor edits implemente