Table of contents

The problem of defining and constructing representations of the canonical commutation relations can be systematically approached via the technique of algebraic quantization. In particular, when the phase space of the system is linear and finite dimensional, the 'vertical polarization' provides an unambiguous quantization. For infinite-dimensional field theory systems, where the Stone–von Neumann theorem fails to be valid, even the simplest representation, the Schrödinger functional picture has some non-trivial subtleties. In this letter we consider the quantization of a real free scalar field—where the Fock quantization is well understood—on an arbitrary background and show that the representation from the most natural application of the algebraic quantization approach is not, in general, unitarily equivalent to the corresponding Schrödinger–Fock quantization. We comment on the possible implications of this result for field quantization.

This paper provides an overview of stellar instabilities as sources of gravitational waves. The aim is to put recent work on secular and dynamical instabilities in compact stars in context, and to summarize the current thinking about the detectability of gravitational waves from various scenarios. As a new generation of kilometre length interferometric detectors is now coming online this is a highly topical theme. The review is motivated by two key questions for future gravitational-wave astronomy: are the gravitational waves from various instabilities detectable? If so, what can these gravitational-wave signals teach us about neutron star physics? Even though we may not have clear answers to these questions, recent studies of the dynamical bar-mode instability and the secular r-mode instability have provided new insights into many of the difficult issues involved in modelling unstable stars as gravitational-wave sources.

It has been shown in several recent papers that the six Doppler data streams obtained from a triangular LISA configuration can be combined by appropriately delaying the data streams for cancelling the laser frequency noise. Raw laser noise is several orders of magnitude above the other noises and thus it is essential to bring it down to the level of other noises such as shot, acceleration, etc. A rigorous and systematic formalism using the powerful techniques of computational commutative algebra was developed, which generates in principle all the data combinations cancelling the laser frequency noise. The relevant data combinations form a first module of syzygies.

In this paper, we use this formalism to advantage for optimizing the sensitivity of LISA by analysing the noise and signal covariance matrices. The signal covariance matrix is calculated for binaries whose frequency changes at most adiabatically and the signal is averaged over polarizations and directions. We then present the extremal SNR curves for all the data combinations in the module. They correspond to the eigenvectors of the noise and signal covariance matrices. A LISA 'network' SNR is also computed by combining the outputs of the eigenvectors. We show that substantial gains in sensitivity can be obtained by employing these strategies. The maximum SNR curve can yield an improvement up to 70% over the Michelson, mainly at high frequencies, while the improvement using the network SNR ranges from 40% to over 100%.

Finally, we describe a simple toy model, in which LISA rotates in a plane. In this analysis, we estimate the improvement in the LISA sensitivity, if one switches from one data combination to another as it rotates. Here the improvement in sensitivity, if one switches optimally over three cyclic data combinations of the eigenvector, is about 55% on average over the LISA bandwidth. The corresponding SNR improvement increases to 60%, if one maximizes over the module.

We construct actions for (p, 0)- and (p, 1)-supersymmetric, 1 ⩽ p ⩽ 4, two-dimensional gauge theories coupled to nonlinear sigma model matter with a Wess–Zumino term. We derive the scalar potential for a large class of these models. We then show that the Euclidean actions of the (2, 0)- and (4, 0)-supersymmetric models without Wess–Zumino terms are bounded by topological charges which involve the equivariant extensions of the Kähler forms of the sigma model target spaces evaluated on the two-dimensional spacetime. We give similar bounds for Euclidean actions of appropriate gauge theories coupled to nonlinear sigma model matter in higher spacetime dimensions which now involve the equivariant extensions of the Kähler forms of the sigma model target spaces and the second Chern character of gauge fields. The BPS configurations are generalizations of Abelian and non-Abelian vortices.

It is well known that the building blocks for state sum models of quantum gravity are given by 6j and 10j symbols. In this work, we study the asymptotics of these symbols by using their expressions as group integrals. We carefully describe the measure involved in terms of invariant variables and develop new technics in order to study their asymptotics. Using these technics, we compute the asymptotics of the various Euclidean and Lorentzian 6j symbols. Finally, we compute the asymptotic expansion of the 10j symbol which is shown to be non-oscillating, in agreement with a recent result of Baez et al. We discuss the physical origin of this behaviour and a way to modify the Barrett–Crane model in order to cure this disease.

The Einstein–Infeld–Hoffmann (EIH) equations of motion for two point particles or spherically symmetric bodies are shown to be the unique 1PN extension of the Newtonian equations of motion which (i) are dimensionally correct and symmetric under interchange of the particles, (ii) are Poincaré invariant, (iii) agree with the geodesics of Schwarzschild (in harmonic coordinates) in the test particle limit and (iv) are the Euler–Lagrange equations of some Lagrangian which extends the Newtonian Lagrangian.

The capture of a straight, infinitely long cosmic string by a rotating black hole with rotation parameter a is considered. We assume that a string is moving with velocity v and that initially the string is parallel to the axis of rotation of the black hole and has the impact parameter b. The string can be either scattered or captured by the black hole. We demonstrate that there exists a critical value of the impact parameter b_c(v, a) which separates these two regimes. Using numerical simulations we obtain the critical impact parameter curve for different values of the rotation parameter a. We show that for the prograde motion of the string this curve lies below the curve for the retrograde motion. Moreover, for ultrarelativistic strings moving in the prograde direction and nearly extremal black holes the critical impact parameter curve is found to be a multiply valued function of v. We obtain real time profiles of the scattered strings in the regime close to the critical. We also study critical scattering and capture of strings by the rotating black hole in the relativistic and ultrarelativistic regimes and especially such relativistic effects as coil formation and wrapping effect.

Stated succinctly, the original version of the Campbell–Magaard theorem says that it is always possible to locally embed any solution of four-dimensional general relativity in a five-dimensional Ricci-flat manifold. We discuss the proof of this theorem (and its variants) in n dimensions, and its application to current theories that postulate that our universe is a four-dimensional hypersurface Σ₀ within a five-dimensional manifold, such as space–time–matter (STM) theory and the Randall and Sundrum (RS) braneworld scenario. In particular, we determine whether or not arbitrary spacetimes may be embedded in such theories, and demonstrate how these seemingly disparate models are interconnected. Special attention is given to the motion of test observers in five dimensions, and the circumstances under which they are confined to Σ₀. For each five-dimensional scenario considered, the requirement that observers be confined to the embedded spacetime places restrictions on the 4-geometry. For example, we find that observers in the thin braneworld scenario can be localized around the brane if its total stress–energy tensor obeys the five-dimensional strong energy condition. As a concrete example of some of our technical results, we discuss a ₂ symmetric embedding of the standard radiation-dominated cosmology in a five-dimensional vacuum.

The stationary phase technique is used to calculate asymptotic formulae for SO(4) relativistic spin networks. For the tetrahedral spin network this gives the square of the Ponzano–Regge asymptotic formula for the SU(2) 6j-symbol. For the 4-simplex (10j-symbol) the asymptotic formula is compared with numerical calculations of the spin network evaluation. Finally, we discuss the asymptotics of the SO(3, 1) 10j-symbol.

We look for necessary isotropization conditions of Bianchi class A models with curvature in the presence of a massive and minimally coupled scalar field when a function ℓ of the scalar field tends to a constant, diverges monotonically or with sufficiently small oscillations. Isotropization leads the metric functions to tend to a power or exponential law of the proper time t and the potential, respectively, to vanish as t⁻² or to a constant. Moreover, isotropization always requires late-time accelerated expansion and flatness of the universe.

Regularization of quantum field theories introduces a mass scale which breaks axial rotational and scaling invariances. We demonstrate from first principles that axial torsion and torsion trace modes have non-transverse vacuum polarization tensors, and become massive as a result. The underlying reasons are similar to those responsible for the Adler–Bell–Jackiw (ABJ) and scaling anomalies. Since these are the only torsion components that can couple minimally to spin-½ particles, the anomalous generation of masses for these modes, naturally of the order of the regulator scale, may help to explain why torsion and its associated effects, including CPT violation in chiral gravity, have so far escaped detection. As a simpler manifestation of the reasons underpinning the ABJ anomaly than triangle diagrams, the vacuum polarization demonstration is also pedagogically useful. In addition, it is shown that the teleparallel limit of a Weyl fermion theory coupled only to the left-handed spin connection leads to a counter term which is the Samuel–Jacobson–Smolin action of chiral gravity in four dimensions.

In this paper a new generalized Einstein gravitational theory with four physical vacuum potentials and the Weyl connection is proposed. In the examined case of dust-like matter, differential equations of the second order for the vacuum potentials consistent with the proposed gravitational equations are obtained. A nonsingular cosmological solution for the homogeneous and isotropic physical vacuum and a vacuum cosmological influence on particles are found. Astronomical applications of this solution are discussed.

Dilaton black-hole solutions which are neither asymptotically flat nor (anti-) de Sitter but reduce to asymptotically flat solutions in some special limits have been known for a Liouville-type dilatonic potential. It is shown how, by solving a pair of coupled differential equations, infinitesimally small angular momentum can be added to these static solutions to produce rotating black-hole solutions.

The discrepancy between previous results of the author and of Manko and collaborators is discussed. Further work which should help settle the disagreement is proposed.

On page 4250, equation (6) should read

On page 4250, the text immediately following equation (7) should begin as follows.

When the velocity vector field u^μ for the perfect fluid is spacelike or timelike, one has equation (6a), and when u^μ is null, one has equation (6a), respectively, for the conservation of the energy-momentum tensor T_μν.

In section 3.1, the statement that `one expects that the time-step constraint' given in equation (3.4) `will ensure stability' is ambiguous. This is the correct constraint for the MacCormack predictor-corrector scheme described in [13] as applied either to the paper's model problem or the 1+1 scalar wave equation. However, as applied to these scenarios, the slightly different scheme described in section 3.2 has a time-step constraint of 0.5. Although not as common, this scheme is in consistent conservation form (see R J LeVeque 1992 Numerical Methods for Conservation Laws 2nd edn (Basel: Birkhauser)) as applied to a conservation law like the 1+1 scalar wave equation. Moreover, it is also a simple predictor-corrector scheme; and, compared with the MacCormack scheme for the paper's model problem, it has better local stability properties at the coordinate origin. These considerations do not pertain to the described outer boundary conditions, the paper's main focus.

Also, I regret that I neglected to acknowledge many helpful discussions with M Kossowski.