On Normal ordering and Canonical transformations in Thermal Field Theory

We look at a real scalar field in thermal equilibrium in the context of the new normal ordering and field split defined by Evans and Steer. We show that the field split defines a natural canonical transformation, but that this transformation differs from others known in thermal field theory.Comment: 13 pages, LaTeX. (Revisions made to discussion and various small errors in equations corrected

Wick's Theorem for non-symmetric normal ordered products and contractions

We consider arbitrary splits of field operators into two parts, and use the corresponding definition of normal ordering introduced by Evans and Steer. In this case the normal ordered products and contractions have none of the special symmetry properties assumed in existing proofs of Wick's theorem. Despite this, we prove that Wick's theorem still holds in its usual form as long as the contraction is a c-number. Wick's theorem is thus shown to be much more general than existing derivations suggest, and we discuss possible simplifying applications of this result.Comment: 17 page

Gravitational Wave Bursts from Cosmic Superstrings with Y-junctions

Cosmic superstring loops generically contain strings of different tensions that meet at Y-junctions. These loops evolve non-periodically in time, and have cusps and kinks that interact with the junctions. We study the effect of junctions on the gravitational wave signal emanating from cosmic string cusps and kinks. We find that earlier results on the strength of individual bursts from cusps and kinks on strings without junctions remain largely unchanged, but junctions give rise to additional contributions to the gravitational wave signal coming from strings expanding at the speed of light at a junction and kinks passing through a junction.Comment: 20 pages, 5 figure

Monolithic Implementation of a Planar Gunn Diode and a pHEMT

No abstract available

Economies of Scale and Scope in Network Industries: Lessons for the UK water and sewerage sectors

Many studies of the water and sewerage industries place significant importance on the benefits of economies of scale and scope and how these relate to vertically integrated firms. We have re-examined the early literature on scale and scope economies and find that these studies do not implicitly preclude non-integrated firms from fully utilising assets for multi-product activities; they can still reap scope economies through trading in the open market. Further, we demonstrate difficulties in separating these two types of economies when assessing firm performance. Trade-offs between governance and production costs are a key issue in determining the value of vertically integrated firms that may undergo divestiture. We discuss the present policy debate regarding the optimal structure of the water and sewerage markets in England and Wales in the light of this, and recommend avenues of research that will help determine the optimal policy

Local energy policy and managing low carbon transition: the case of Leicester, UK

National and local energy policies are implemented within a complex energy landscape that makes any evaluation of their impacts far from straightforward. Drawing upon a case study of Leicester this paper argues that the ability of local authorities to deliver significant energy savings within this landscape is questionable, albeit with other additional benefits being realised (e.g. job creation, community engagement). It examines existing domestic energy demand and multiple deprivation data for Leicester and neighbouring cities and combines this with a qualitative description of the transition process. The paper identifies the need for a more systematic analysis of how national energy policy translates to the local level and concludes that it is problematic even for a leading, pro-active and innovative local authority to have a statistically meaningful energy policy. Even where energy policies are favourable, carbon reduction is less easy to realise than other – more local - co-benefits and that in the light of significant financial and co-ordination constraints more attention needs to be given to how local communities can be more effectively supported in their desire to meet (or exceed) national targets.We acknowledge the financial assistance of the EPSRC Flexnet award (EP/E0411X/1) and all of the Leicester based contributors to the project, as well as the very helpful comments of two anonymous referees; the usual disclaimers apply

Main-Sequence Effective Temperatures from a Revised Mass-Luminosity Relation Based on Accurate Properties

The mass-luminosity (M-L), mass-radius (M-R) and mass-effective temperature ($M-T_{eff}$) diagrams for a subset of galactic nearby main-sequence stars with masses and radii accurate to $\leq 3\%$ and luminosities accurate to $\leq 30\%$ (268 stars) has led to a putative discovery. Four distinct mass domains have been identified, which we have tentatively associated with low, intermediate, high, and very high mass main-sequence stars, but which nevertheless are clearly separated by three distinct break points at 1.05, 2.4, and 7$M_{\odot}$ within the mass range studied of $0.38-32M_{\odot}$. Further, a revised mass-luminosity relation (MLR) is found based on linear fits for each of the mass domains identified. The revised, mass-domain based MLRs, which are classical ($L \propto M^{\alpha}$), are shown to be preferable to a single linear, quadratic or cubic equation representing as an alternative MLR. Stellar radius evolution within the main-sequence for stars with $M>1M_{\odot}$ is clearly evident on the M-R diagram, but it is not the clear on the $M-T_{eff}$ diagram based on published temperatures. Effective temperatures can be calculated directly using the well-known Stephan-Boltzmann law by employing the accurately known values of M and R with the newly defined MLRs. With the calculated temperatures, stellar temperature evolution within the main-sequence for stars with $M>1M_{\odot}$ is clearly visible on the $M-T_{eff}$ diagram. Our study asserts that it is now possible to compute the effective temperature of a main-sequence star with an accuracy of $\sim 6\%$, as long as its observed radius error is adequately small (<1%) and its observed mass error is reasonably small (<6%).Comment: 57 pages, including 12 figures and 7 tables, accepted for publication in Astronomical Journa