Topological Aspects of the Non-adiabatic Berry Phase

The topology of the non-adiabatic parameter space bundle is discussed for evolution of exact cyclic state vectors in Berry's original example of split angular momentum eigenstates. It turns out that the change in topology occurs at a critical frequency. The first Chern number that classifies these bundles is proportional to angular momentum. The non-adiabatic principal bundle over the parameter space is not well-defined at the critical frequency.Comment: 14 pages, Dep. of Physics, Uni. of Texas at Austin, Austin, Texas 78712, to appear in J. Physics

Symmetry Representations in the Rigged Hilbert Space Formulation of Quantum Mechanics

We discuss some basic properties of Lie group representations in rigged Hilbert spaces. In particular, we show that a differentiable representation in a rigged Hilbert space may be obtained as the projective limit of a family of continuous representations in a nested scale of Hilbert spaces. We also construct a couple of examples illustrative of the key features of group representations in rigged Hilbert spaces. Finally, we establish a simple criterion for the integrability of an operator Lie algebra in a rigged Hilbert space

Factorization Structure of Gauge Theory Amplitudes and Application to Hard Scattering Processes at the LHC

Previous work on electroweak radiative corrections to high energy scattering using soft-collinear effective theory (SCET) has been extended to include external transverse and longitudinal gauge bosons and Higgs bosons. This allows one to compute radiative corrections to all parton-level hard scattering amplitudes in the standard model to NLL order, including QCD and electroweak radiative corrections, mass effects, and Higgs exchange corrections, if the high-scale matching, which is suppressed by two orders in the log counting, and contains no large logs, is known. The factorization structure of the effective theory places strong constraints on the form of gauge theory amplitudes at high energy for massless and massive gauge theories, which are discussed in detail in the paper. The radiative corrections can be written as the sum of process-independent one-particle collinear functions, and a universal soft function. We give plots for the radiative corrections to q qbar -> W_T W_T, Z_T Z_T, W_L W_L, and Z_L H, and gg -> W_T W_T to illustrate our results. The purely electroweak corrections are large, ranging from 12% at 500 GeV to 37% at 2 TeV for transverse W pair production, and increasing rapidly with energy. The estimated theoretical uncertainty to the partonic (hard) cross-section in most cases is below one percent, smaller than uncertainties in the parton distribution functions (PDFs). We discuss the relation between SCET and other factorization methods, and derive the Magnea-Sterman equations for the Sudakov form factor using SCET, for massless and massive gauge theories, and for light and heavy external particles.Comment: 44 pages, 30 figures. Refs added, typos fixed. ZL ZL plots removed because of a possible subtlet

Schwinger, Pegg and Barnett and a relationship between angular and Cartesian quantum descriptions

From a development of an original idea due to Schwinger, it is shown that it is possible to recover, from the quantum description of a degree of freedom characterized by a finite number of states (\QTR{it}{i.e}., without classical counterpart) the usual canonical variables of position/momentum \QTR{it}{and} angle/angular momentum, relating, maybe surprisingly, the first as a limit of the later.Comment: 7 pages, revised version, to appear on J. Phys. A: Math and Ge

Time Asymmetric Quantum Physics

Mathematical and phenomenological arguments in favor of asymmetric time evolution of micro-physical states are presented.Comment: Tex file with 2 figure

Basis States for Relativistic, Dynamically-Entangled Particles

In several recent papers on entanglement in relativistic quantum systems and relativistic Bell's inequalities, relativistic Bell-type two-particle states have been constructed in analogy to non-relativistic states. These constructions do not have the form suggested by relativistic invariance of the dynamics. Two relativistic formulations of Bell-type states are shown for massive particles, one using the standard Wigner spin basis and one using the helicity basis. The construction hinges on the use of Clebsch-Gordan coefficients of the Poincar\'e group to reduce the direct product of two unitary irreducible representations (UIRs) into a direct sum of UIRs.Comment: 19 pages, three tables, revte

Choice of baseline affects historical population trends in hunted mammals of North America

Establishing historical baselines of species' populations is important for contextualising present-day population trends, identifying significant anthropogenic threats, and preventing a cultural phenomenon known as ‘shifting baseline syndrome’. However, our knowledge of historical baselines is limited by a lack of direct observation data on species abundance pre-1970. We present historical data of species-specific fur harvests from the Canadian government and Hudson's Bay Company as a proxy for estimating species abundance over multiple centuries. Using stochastic stock reduction analysis originally developed for marine species, we model historical population trends for eight mammals, and assess population trends based on two different baseline years: 1850 and 1970. Results show that population declines are significantly greater when using an 1850 baseline, as opposed to a 1970 baseline, and for four species, the population trend shifted from a population increase to a decrease. Overall, the median population change of the eight species changed from a 15% decline for 1850, to a 4% increase for 1970. This study shows the utility of harvest data for deriving population baselines for hunted terrestrial mammals which can be used in addition to other historical data such as local ecological knowledge. Results highlight the need for developing historically relevant population baselines in order to track abundances over time in threatened species and common species alike, to better inform species conservation programs, wildlife management plans and biodiversity indicators

Poincare Semigroup Symmetry as an Emergent Property of Unstable Systems

The notion that elementary systems correspond to irreducible representations of the Poincare group is the starting point for this paper, which then goes on to discuss how a semigroup for the time evolution of unstable states and resonances could emerge from the underlying Poincare symmetry. Important tools in this analysis are the Clebsch-Gordan coefficients for the Poincare group.Comment: 17 pages, 1 figur

Maximally Causal Quantum Mechanics

We present a new causal quantum mechanics in one and two dimensions developed recently at TIFR by this author and V. Singh. In this theory both position and momentum for a system point have Hamiltonian evolution in such a way that the ensemble of system points leads to position and momentum probability densities agreeing exactly with ordinary quantum mechanics.Comment: 7 pages,latex,no figures,to appear in Praman

Consciousness and the Wigner's friend problem

It is generally agreed that decoherence theory is, if not a complete answer, at least a great step forward towards a solution of the quantum measurement problem. It is shown here however that in the cases in which a sentient being is explicitly assumed to take cognizance of the outcome the reasons we have for judging this way are not totally consistent, so that the question has to be considered anew. It is pointed out that the way the Broglie-Bohm model solves the riddle suggests a possible clue, consisting in assuming that even very simple systems may have some sort of a proto-consciousness, but that their ``internal states of consciousness'' are not predictive. It is, next, easily shown that if we imagine the systems get larger, in virtue of decoherence their internal states of consciousness progressively gain in predictive value. So that, for macro-systems, they may be identified (in practice) with the predictive states of consciousness on which we ground our observational predictions. The possibilities of carrying over this idea to standard quantum mechanics are then investigated. Conditions of conceptual consistency are considered and found rather strict, and, finally, two solutions emerge, differing conceptually very much from one another but in both of which the, possibly non-predictive, generalized internal states of consciousness play a crucial role