The pricing journey – The evolution of approach and execution as organisational pricing capability develops

This is an author version of an article which has been published in its definitive form as a Margin2 / Brunel Pricing Forum white paper and has been posted by permission of the Brunel Pricing Forum for personal use, not for redistribution. The article was published online by Margin2 and the original version can be accessed at the link below.An organisation’s approach to Pricing can be seen as a competency in the sense that it is a combination of skills, behaviours and the application of knowledge. As the efficiency and effectiveness of pricing decisions improve, then a range of indicators highlight a more thorough, considered and generally more successful approach. Fewer mistakes are made, results are more visibility linked to previous actions, and implementation becomes quicker and more comprehensive

Two-loop Renormalization Group Equations in the Standard Model

Two-loop renormalization group equations in the standard model are re-calculated. A new coefficient is found in the beta-function of the quartic coupling and a class of gauge invariants are found to be absent in the beta-functions of hadronic Yukawa couplings. The two-loop beta-function of the Higgs mass parameter is presented in complete form.Comment: 4 pages, RevTe

Comment on "Absence of Compressible Edge Channel Rings in Quantum Antidots"

In a recent article, Karakurt et al. [I. Karakurt et al., Phys. Rev. Lett. 89, 226803 (2002)] reported the absence of compressible regions around antidots in the quantum Hall regime. We wish to point out a significant flaw in their analysis, which invalidates their claim.Comment: 1 page 1 figure, to be published in Phys. Rev. Let

Detection of negative energy: 4-dimensional examples

We study the response of switched particle detectors to static negative energy densities and negative energy fluxes. It is demonstrated how the switching leads to excitation even in the vacuum and how negative energy can lead to a suppression of this excitation. We obtain quantum inequalities on the detection similar to those obtained for the energy density by Ford and co-workers and in an `operational' context by Helfer. We revisit the question `Is there a quantum equivalence principle?' in terms of our model. Finally, we briefly address the issue of negative energy and the second law of thermodynamics.Comment: 10 pages, 7 figure

Relativistic Elastic Differential Cross Sections for Equal Mass Nuclei

The effects of relativistic kinematics are studied for nuclear collisions of equal mass nuclei. It is found that the relativistic and non-relativistic elastic scattering amplitudes are nearly indistinguishable, and, hence, the relativistic and non-relativistic differential cross sections become indistinguishable. These results are explained by analyzing the Lippmann-Schwinger equation with the first order optical potential that was employed in the calculatio

Weak energy condition violation and superluminal travel

Recent solutions to the Einstein Field Equations involving negative energy densities, i.e., matter violating the weak-energy-condition, have been obtained, namely traversable wormholes, the Alcubierre warp drive and the Krasnikov tube. These solutions are related to superluminal travel, although locally the speed of light is not surpassed. It is difficult to define faster-than-light travel in generic space-times, and one can construct metrics which apparently allow superluminal travel, but are in fact flat Minkowski space-times. Therefore, to avoid these difficulties it is important to provide an appropriate definition of superluminal travel.Comment: 15 pages, 3 figures, LaTeX2e, Springer style files -included. Contribution to the Proceedings of the Spanish Relativity Meeting-2001 (Madrid, September 2001

Quantum Field Theory Constrains Traversable Wormhole Geometries

Recently a bound on negative energy densities in four-dimensional Minkowski spacetime was derived for a minimally coupled, quantized, massless, scalar field in an arbitrary quantum state. The bound has the form of an uncertainty principle-type constraint on the magnitude and duration of the negative energy density seen by a timelike geodesic observer. When spacetime is curved and/or has boundaries, we argue that the bound should hold in regions small compared to the minimum local characteristic radius of curvature or the distance to any boundaries, since spacetime can be considered approximately Minkowski on these scales. We apply the bound to the stress-energy of static traversable wormhole spacetimes. Our analysis implies that either the wormhole must be only a little larger than Planck size or that there is a large discrepancy in the length scales which characterize the wormhole. In the latter case, the negative energy must typically be concentrated in a thin band many orders of magnitude smaller than the throat size. These results would seem to make the existence of macroscopic traversable wormholes very improbable.Comment: 26 pages, plain LaTe

Multi-scale Renormalisation Group Improvement of the Effective Potential

Using the renormalisation group and a conjecture concerning the perturbation series for the effective potential, the leading logarithms in the effective potential are exactly summed for $O(N)$ scalar and Yukawa theories.Comment: 19 pages, DIAS STP 94-09. Expanded to check large N limit, typo's corrected, to appear in Phys Rev

Stochastic Spacetime and Brownian Motion of Test Particles

The operational meaning of spacetime fluctuations is discussed. Classical spacetime geometry can be viewed as encoding the relations between the motions of test particles in the geometry. By analogy, quantum fluctuations of spacetime geometry can be interpreted in terms of the fluctuations of these motions. Thus one can give meaning to spacetime fluctuations in terms of observables which describe the Brownian motion of test particles. We will first discuss some electromagnetic analogies, where quantum fluctuations of the electromagnetic field induce Brownian motion of test particles. We next discuss several explicit examples of Brownian motion caused by a fluctuating gravitational field. These examples include lightcone fluctuations, variations in the flight times of photons through the fluctuating geometry, and fluctuations in the expansion parameter given by a Langevin version of the Raychaudhuri equation. The fluctuations in this parameter lead to variations in the luminosity of sources. Other phenomena which can be linked to spacetime fluctuations are spectral line broadening and angular blurring of distant sources.Comment: 15 pages, 3 figures. Talk given at the 9th Peyresq workshop, June 200

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