Correct path-integral formulation of quantum thermal field theory in coherent-state representation

The path-integral quantization of thermal scalar, vector and spinor fields is performed newly in the coherent-state representation. In doing this, we choose the thermal electrodynamics and $\phi ^4$ theory as examples. By this quantization, correct expressions of the partition functions and the generating functionals for the quantum thermal electrodynamics and $\phi ^4$ theory are obtained in the coherent-state representation. These expressions allow us to perform analytical calculations of the partition functions and generating functionals and therefore are useful in practical applications. Especially, the perturbative expansions of the generating functionals are derived specifically by virtue of the stationary-phase method. The generating functionals formulated in the position space are re-derived from the ones given in the coherent-state representation

Probing deeper into the risks of slips, trips and falls for an ageing rail passenger population: applying a systems approach

In this study, the authors report the findings from a study of the contributory factors leading to slips, trips and falls (STFs) amongst elderly passengers at train stations and how these are likely to change in the future over the medium to long term (the period 2035–2050). Their data draws on: stakeholder interviews with rail personnel and elderly passengers; a set of station observations carried out across the UK; and, a survey of the views of station managers. The findings point to a set of 22 contributory factors covering aspects of organisational, station environment and passenger (individual) influence on STFs. Amongst the factors which most concern station managers at the present and over the next few decades are: rushing behaviour on train platforms; the consumption of alcohol by passengers; aspects of station design (e.g. flooring); and, training for station staff as regard the risks of STFs. The authors summarise their findings in the form of a systems model which highlights priorities with regard to STFs in terms of all of the stakeholders taking part in the study. A final section discusses a set of issues which might form the basis for a future agenda for research and practice in this area

Integrable Open Spin Chain in Super Yang-Mills and the Plane-wave/SYM duality

We investigate the integrable structures in an N=2 superconfomal Sp(N) Yang-Mills theory with matter, which is dual to an open+closed string system. We restrict ourselves to the BMN operators that correspond to free string states. In the closed string sector, an integrable structure is inherited from its parent theory, N=4 SYM. For the open string sector, the planar one-loop mixing matrix for gauge invariant holomorphic operators is identified with the Hamiltonian of an integrable SU(3) open spin chain. Using the K-matrix formalism we identify the integrable open-chain boundary conditions that correspond to string boundary conditions. The solutions to the algebraic Bethe ansatz equations (ABAE) with a few impurities are shown to recover the anomalous dimensions that exactly match the spectrum of free open string in the plane-wave background. We also discuss the properties of the solutions of ABAE beyond the BMN regime.Comment: 18 pages, one eps figure, v3: typos corrected, clarifying footnotes added, treatment of complex roots revise

Glueball spectrum based on a rigorous three-dimensional relativistic equation for two-gluon bound states I: Derivation of the relativistic equation

A rigorous three-dimensional relativistic equation satisfied by two-gluon bound states is derived from the QCD with massive gluons. With the gluon fields and the quark fields being expanded in terms of the gluon multipole fields and the spherical Dirac spinors respectively, the equation is well established in the angular momentum representation and hence is much convenient for solving the problem of two-gluon glueball spectra. In particular, the interaction kernel in the equation is exactly derived and given a closed expression which includes all the interactions taking place in the two-gluon glueballs. The kernel contains only a few types of Green's functions and commutators. Therefore, it is not only easily calculated by the perturbation method, but also provides a suitable basis for nonperturbative investigations

Probability distribution of the index in gauge theory on 2d non-commutative geometry

We investigate the effects of non-commutative geometry on the topological aspects of gauge theory using a non-perturbative formulation based on the twisted reduced model. The configuration space is decomposed into topological sectors labeled by the index nu of the overlap Dirac operator satisfying the Ginsparg-Wilson relation. We study the probability distribution of nu by Monte Carlo simulation of the U(1) gauge theory on 2d non-commutative space with periodic boundary conditions. In general the distribution is asymmetric under nu -> -nu, reflecting the parity violation due to non-commutative geometry. In the continuum and infinite-volume limits, however, the distribution turns out to be dominated by the topologically trivial sector. This conclusion is consistent with the instanton calculus in the continuum theory. However, it is in striking contrast to the known results in the commutative case obtained from lattice simulation, where the distribution is Gaussian in a finite volume, but the width diverges in the infinite-volume limit. We also calculate the average action in each topological sector, and provide deeper understanding of the observed phenomenon.Comment: 16 pages,10 figures, version appeared in JHE

A non-perturbative study of 4d U(1) non-commutative gauge theory -- the fate of one-loop instability

Recent perturbative studies show that in 4d non-commutative spaces, the trivial (classically stable) vacuum of gauge theories becomes unstable at the quantum level, unless one introduces sufficiently many fermionic degrees of freedom. This is due to a negative IR-singular term in the one-loop effective potential, which appears as a result of the UV/IR mixing. We study such a system non-perturbatively in the case of pure U(1) gauge theory in four dimensions, where two directions are non-commutative. Monte Carlo simulations are performed after mapping the regularized theory onto a U(N) lattice gauge theory in d=2. At intermediate coupling strength, we find a phase in which open Wilson lines acquire non-zero vacuum expectation values, which implies the spontaneous breakdown of translational invariance. In this phase, various physical quantities obey clear scaling behaviors in the continuum limit with a fixed non-commutativity parameter $\theta$, which provides evidence for a possible continuum theory. The extent of the dynamically generated space in the non-commutative directions becomes finite in the above limit, and its dependence on $\theta$ is evaluated explicitly. We also study the dispersion relation. In the weak coupling symmetric phase, it involves a negative IR-singular term, which is responsible for the observed phase transition. In the broken phase, it reveals the existence of the Nambu-Goldstone mode associated with the spontaneous symmetry breaking.Comment: 29 pages, 23 figures, references adde

A Non-Perturbative Study of Gauge Theory on a Non-Commutative Plane

We perform a non-perturbative study of pure gauge theory in a two dimensional non-commutative (NC) space. On the lattice, it is equivalent to the twisted Eguchi-Kawai model, which we simulated at N ranging from 25 to 515. We observe a clear large-N scaling for the 1- and 2-point function of Wilson loops, as well as the 2-point function of Polyakov lines. The 2-point functions agree with a universal wave function renormalization. Based on a Morita equivalence, the large-N double scaling limit corresponds to the continuum limit of NC gauge theory, so the observed large-N scaling demonstrates the non-perturbative renormalizability of this NC field theory. The area law for the Wilson loops holds at small physical area as in commutative 2d planar gauge theory, but at large areas we find an oscillating behavior instead. In that regime the phase of the Wilson loop grows linearly with the area. This agrees with the Aharonov-Bohm effect in the presence of a constant magnetic field, identified with the inverse non-commutativity parameter.Comment: 18 pages, 6 figures, final version published in JHE

Interacting new generalized Chaplygin gas

We have presented a model in which the new generalized Chaplygin gas interacts with matter. We find that there exists a stable scaling solution at late times in the evolution of the universe. Moreover, the phantom crossing scenario is observed in this model.Comment: 16 pages, 6 figures, accepted for publication in Int. J. Theor. Phy