Quantum particle on hyperboloid

We present quantization of particle dynamics on one-sheet hyperboloid embedded in three dimensional Minkowski space. Taking account of all global symmetries enables unique quantization. Making use of topology of canonical variables not only simplifies calculations but also gives proper framework for analysis.Comment: 7 pages, no figures, revtex

Semiclassical Time Evolution and Trace Formula for Relativistic Spin-1/2 Particles

We investigate the Dirac equation in the semiclassical limit \hbar --> 0. A semiclassical propagator and a trace formula are derived and are shown to be determined by the classical orbits of a relativistic point particle. In addition, two phase factors enter, one of which can be calculated from the Thomas precession of a classical spin transported along the particle orbits. For the second factor we provide an interpretation in terms of dynamical and geometric phases.Comment: 8 pages, no figure

Quantum Particle-Trajectories and Geometric Phase

"Particle"-trajectories are defined as integrable $dx_\mu dp^\mu = 0$ paths in projective space. Quantum states evolving on such trajectories, open or closed, do not delocalise in $(x, p)$ projection, the phase associated with the trajectories being related to the geometric (Berry) phase and the Classical Mechanics action. High Energy Physics properties of states evolving on "particle"-trajectories are discussed.Comment: 4 page

Limitations on the superposition principle: superselection rules in non-relativistic quantum mechanics

The superposition principle is a very basic ingredient of quantum theory. What may come as a surprise to many students, and even to many practitioners of the quantum craft, is tha superposition has limitations imposed by certain requirements of the theory. The discussion of such limitations arising from the so-called superselection rules is the main purpose of this paper. Some of their principal consequences are also discussed. The univalence, mass and particle number superselection rules of non-relativistic quantum mechanics are also derived using rather simple methods.Comment: 22 pages, no figure

Equations of Motion of Spinning Relativistic Particle in External Fields

We consider the motion of a spinning relativistic particle in external electromagnetic and gravitational fields, to first order in the external field, but to an arbitrary order in spin. The correct account for the spin influence on the particle trajectory is obtained with the noncovariant description of spin. Concrete calculations are performed up to second order in spin included. A simple derivation is presented for the gravitational spin-orbit and spin-spin interactions of a relativistic particle. We discuss the gravimagnetic moment (GM), a specific spin effect in general relativity. It is demonstrated that for the Kerr black hole the gravimagnetic ratio, i.e., the coefficient at the GM, equals to unity (as well as for the charged Kerr hole the gyromagnetic ratio equals to two). The equations of motion obtained for relativistic spinning particle in external gravitational field differ essentially from the Papapetrou equations.Comment: 22 pages, latex, no figure

Equations of Motion of Spinning Relativistic Particle in Electromagnetic and Gravitational Fields

We consider the motion of a spinning relativistic particle in external electromagnetic and gravitational fields, to first order in the external field, but to an arbitrary order in spin. The noncovariant spin formalism is crucial for the correct description of the influence of the spin on the particle trajectory. We show that the true coordinate of a relativistic spinning particle is its naive, common coordinate \r. Concrete calculations are performed up to second order in spin included. A simple derivation is presented for the gravitational spin-orbit and spin-spin interactions of a relativistic particle. We discuss the gravimagnetic moment (GM), a specific spin effect in general relativity. It is shown that for the Kerr black hole the gravimagnetic ratio, i.e., the coefficient at the GM, equals unity (just as for the charged Kerr hole the gyromagnetic ratio equals two). The equations of motion obtained for relativistic spinning particle in external gravitational field differ essentially from the Papapetrou equations.Comment: 32 pages, latex, Plenary talk at the Fairbank Meeting on the Lense--Thirring Effect, Rome-Pescara, 29/6-4/7 199

Gravitation and inertia; a rearrangement of vacuum in gravity

We address the gravitation and inertia in the framework of 'general gauge principle', which accounts for 'gravitation gauge group' generated by hidden local internal symmetry implemented on the flat space. We connect this group to nonlinear realization of the Lie group of 'distortion' of local internal properties of six-dimensional flat space, which is assumed as a toy model underlying four-dimensional Minkowski space. The agreement between proposed gravitational theory and available observational verifications is satisfactory. We construct relativistic field theory of inertia and derive the relativistic law of inertia. This theory furnishes justification for introduction of the Principle of Equivalence. We address the rearrangement of vacuum state in gravity resulting from these ideas.Comment: 17 pages, no figures, revtex4, Accepted for publication in Astrophys. Space Sc

From dynamical scaling to local scale-invariance: a tutorial

Dynamical scaling arises naturally in various many-body systems far from equilibrium. After a short historical overview, the elements of possible extensions of dynamical scaling to a local scale-invariance will be introduced. Schr\"odinger-invariance, the most simple example of local scale-invariance, will be introduced as a dynamical symmetry in the Edwards-Wilkinson universality class of interface growth. The Lie algebra construction, its representations and the Bargman superselection rules will be combined with non-equilibrium Janssen-de Dominicis field-theory to produce explicit predictions for responses and correlators, which can be compared to the results of explicit model studies. At the next level, the study of non-stationary states requires to go over, from Schr\"odinger-invariance, to ageing-invariance. The ageing algebra admits new representations, which acts as dynamical symmetries on more general equations, and imply that each non-equilibrium scaling operator is characterised by two distinct, independent scaling dimensions. Tests of ageing-invariance are described, in the Glauber-Ising and spherical models of a phase-ordering ferromagnet and the Arcetri model of interface growth.Comment: 1+ 23 pages, 2 figures, final for

Rationale and design of BISTRO: a randomized controlled trial to determine whether bioimpedance spectroscopy guided fluid management maintains residual kidney function in incident haemodialysis patients

Background: Preserved residual kidney function (RKF) and normal fluid status are associated with better patient outcomes in incident haemodialysis patients. The objective of this trial is to determine whether using bioimpedance technology in prescribing the optimal post-dialysis weight can reduce the rate of decline of RKF and potentially improve patient outcomes. Methods/Design: 516 patients commencing haemodialysis, aged >18 with RKF of > 3 ml/min/1.73 m2 or a urine volume >500 ml per day or per the shorter inter-dialytic period will be consented and enrolled into a pragmatic, open label, randomized controlled trial. The intervention is incorporation of bioimpedance spectroscopy (BI) determination of normally hydrated weight to set a post-dialysis target weight that limits volume depletion, compared to current standard practice. Clinicians and participants will be blinded to BI measures in the control group and a standardized record capturing management of fluid status will be used in all participants. Primary outcome is preservation of residual kidney function assessed as time to anuria (≤100 ml/day or ≤200 ml urine volume in the short inter-dialytic period). A sample size of 516 was based upon a cumulative incidence of 30% anuria in the control group and 20% in the treatment group and 11% competing risks (death, transplantation) over 10 months, with up to 2 years follow-up. Secondary outcomes include rate of decline in small solute clearance, significant adverse events, hospitalization, loss of vascular access, cardiovascular events and interventions, dialysis efficacy and safety, dialysis-related symptoms and quality of life. Economic evaluation will be carried out to determine the cost-effectiveness of the intervention. Analyses will be adjusted for patient characteristics and dialysis unit practice patterns relevant to fluid management. Discussion: This trial will establish the added value of undertaking BI measures to support clinical management of fluid status and establish the relationship between fluid status and preservation of residual kidney function in incident haemodialysis patients. Trial registration: ISCCTN Number: 11342007, completed 26/04/2016; NIHR Portfolio number: CPMS31766; Sponsor: Keele University Keywords: Fluid status, Body composition, Residual kidney function, Haemodialysis, Bioimpedance, Fluid management, Health economic

Peritoneal dialysis prescription in children: bedside principles for optimal practice

There is no unique optimal peritoneal dialysis prescription for all children, although the goals of ultrafiltration and blood purification are universal. In turn, a better understanding of the physiology of the peritoneal membrane, as a dynamic dialysis membrane with an exchange surface area recruitment capacity and unique permeability characteristics, results in the transition from an empirical prescription process based on clinical experience alone to the potential for a personalized prescription with individually adapted fill volumes and dwell times. In all cases, the prescribed exchange fill volume should be scaled for body surface area (ml/m2), and volume enhancement should be conducted based on clinical tolerance and intraperitoneal pressure measurements (IPP; cmH2O). The exchange dwell times should be determined individually and adapted to the needs of the patient, with particular attention to phosphate clearance and ultrafiltration capacity. The evolution of residual kidney function and the availability of new, more physiologic, peritoneal dialysis fluids (PDFs) also influence the prescription process. An understanding of all of these principles is integral to the provision of clinically optimal PD