7,264 research outputs found
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
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