Threshold configurations in the presence of Lorentz violating dispersion relations

A general characterization of lower and upper threshold configurations for two particle reactions is determined under the assumptions that the single particle dispersion relations E(p) are rotationally invariant and monotonic in p, and that energy and momentum are conserved and additive for multiple particles. It is found that at a threshold the final particle momenta are always parallel and the initial momenta are always anti-parallel. The occurrence of new phenomena not occurring in a Lorentz invariant setting, such as upper thresholds and asymmetric pair production thresholds, is explained, and an illustrative example is given.Comment: 5 pages, 3 figure

Conservation Laws in Doubly Special Relativity

Motivated by various theoretical arguments that the Planck energy (Ep - 10^19 GeV) - should herald departures from Lorentz invariance, and the possibility of testing these expectations in the not too distant future, two so-called "Doubly Special Relativity" theories have been suggested -- the first by Amelino-Camelia (DSR1) and the second by Smolin and Magueijo (DSR2). These theories contain two fundamental scales -- the speed of light and an energy usually taken to be Ep. The symmetry group is still the Lorentz group, but in both cases acting nonlinearly on the energy-momentum sector. Accordingly, since energy and momentum are no longer additive quantities, finding their values for composite systems (and hence finding the correct conservation laws) is a nontrivial matter. Ultimately it is these possible deviations from simple linearly realized relativistic kinematics that provide the most promising observational signal for empirically testing these models. Various investigations have narrowed the conservation laws down to two possibilities per DSR theory. We derive unique exact results for the energy-momentum of composite systems in both DSR1 and DSR2, and indicate the general strategy for arbitrary nonlinear realizations of the Lorentz group.Comment: V2: Extensive revisions: merged with gr-qc/0205093, new author added, references added, discussion amplified. 4 pages, revtex4; V3: Revised in response to referee comments; no physics changes; version to appear in Physical Review

A realisation of Lorentz algebra in Lorentz violating theory

A Lorentz non-invariant higher derivative effective action in flat spacetime, characterised by a constant vector, can be made invariant under infinitesimal Lorentz transformations by restricting the allowed field configurations. These restricted fields are defined as functions of the background vector in such a way that background dependance of the dynamics of the physical system is no longer manifest. We show here that they also provide a field basis for the realisation of Lorentz algebra and allow the construction of a Poincar\'e invariant symplectic two form on the covariant phase space of the theory.Comment: text body edited, reference adde

Q methodology and rural research

Traditionally, rural scholarship has been limited in its methodological approach. This has begun to change in recent years as rural researchers have embraced a range of different methodological tools. The aim of this article is to contribute to greater methodological pluralism in rural sociology by introducing readers to a method of research that is rarely engaged in the field, that is, Q methodology. The article describes the defining features of the approach as well as providing examples of its application to argue that it is a method that offers particular opportunities and synergies for rural social science research

Loop-Generated Bounds on Changes to the Graviton Dispersion Relation

We identify the effective theory appropriate to the propagation of massless bulk fields in brane-world scenarios, to show that the dominant low-energy effect of asymmetric warping in the bulk is to modify the dispersion relation of the effective 4-dimensional modes. We show how such changes to the graviton dispersion relation may be bounded through the effects they imply, through loops, for the propagation of standard model particles. We compute these bounds and show that they provide, in some cases, the strongest constraints on nonstandard gravitational dispersions. The bounds obtained in this way are the strongest for the fewest extra dimensions and when the extra-dimensional Planck mass is the smallest. Although the best bounds come for warped 5-D scenarios, for which the 5D Planck Mass is O(TeV), even in 4 dimensions the graviton loop can lead to a bound on the graviton speed which is comparable with other constraints.Comment: 18 pages, LaTeX, 4 figures, uses revte

Lorentz breaking Effective Field Theory and observational tests

Analogue models of gravity have provided an experimentally realizable test field for our ideas on quantum field theory in curved spacetimes but they have also inspired the investigation of possible departures from exact Lorentz invariance at microscopic scales. In this role they have joined, and sometime anticipated, several quantum gravity models characterized by Lorentz breaking phenomenology. A crucial difference between these speculations and other ones associated to quantum gravity scenarios, is the possibility to carry out observational and experimental tests which have nowadays led to a broad range of constraints on departures from Lorentz invariance. We shall review here the effective field theory approach to Lorentz breaking in the matter sector, present the constraints provided by the available observations and finally discuss the implications of the persisting uncertainty on the composition of the ultra high energy cosmic rays for the constraints on the higher order, analogue gravity inspired, Lorentz violations.Comment: 47 pages, 4 figures. Lecture Notes for the IX SIGRAV School on "Analogue Gravity", Como (Italy), May 2011. V.3. Typo corrected, references adde

The STAR Time Projection Chamber: A Unique Tool for Studying High Multiplicity Events at RHIC

The STAR Time Projection Chamber (TPC) is used to record collisions at the Relativistic Heavy Ion Collider (RHIC). The TPC is the central element in a suite of detectors that surrounds the interaction vertex. The TPC provides complete coverage around the beam-line, and provides complete tracking for charged particles within +- 1.8 units of pseudo-rapidity of the center-of-mass frame. Charged particles with momenta greater than 100 MeV/c are recorded. Multiplicities in excess of 3,000 tracks per event are routinely reconstructed in the software. The TPC measures 4 m in diameter by 4.2 m long, making it the largest TPC in the world.Comment: 28 pages, 11 figure

Three-Dimensional Gravity with Conformal Scalar and Asymptotic Virasoro Algebra

Strominger has derived the Bekenstein-Hawking entropy of the BTZ black hole using asymptotic Virasoro algebra. We apply Strominger's method to a black hole solution found by Martinez and Zanelli (MZ). This is a solution of three-dimensional gravity with a conformal scalar field. The solution is not $AdS_3$, but it is asymptotically $AdS_3$; therefore, it has the asymptotic Virasoro algebra. We compute the central charge for the theory and compares Cardy's formula with the Bekenstein-Hawking entropy. It turns out that the functional form does agree, but the overall numerical coefficient does not. This is because this approach gives the "maximum possible entropy" for the numerical coefficient.Comment: 26 pages, LaTeX; v2: minor correction