Topological Background Fields as Quantum Degrees of Freedom of Compactified Strings

It is shown that background fields of a topological character usually introduced as such in compactified string theories correspond to quantum degrees of freedom which parametrise the freedom in choosing a representation of the zero mode quantum algebra in the presence of non-trivial topology. One consequence would appear to be that the values of such quantum degrees of freedom, in other words of the associated topological background fields, cannot be determined by the nonperturbative string dynamics.Comment: 1+10 pages, no figure

Topologically Massive Gauge Theories and their Dual Factorised Gauge Invariant Formulation

There exists a well-known duality between the Maxwell-Chern-Simons theory and the self-dual massive model in 2+1 dimensions. This dual description has been extended to topologically massive gauge theories (TMGT) in any dimension. This Letter introduces an unconventional approach to the construction of this type of duality through a reparametrisation of the master theory action. The dual action thereby obtained preserves the same gauge symmetry structure as the original theory. Furthermore, the dual action is factorised into a propagating sector of massive gauge invariant variables and a sector with gauge variant variables defining a pure topological field theory. Combining results obtained within the Lagrangian and Hamiltonian formulations, a new completed structure for a gauge invariant dual factorisation of TMGT is thus achieved.Comment: 1+7 pages, no figure

Gauge Invariant Factorisation and Canonical Quantisation of Topologically Massive Gauge Theories in Any Dimension

Abelian topologically massive gauge theories (TMGT) provide a topological mechanism to generate mass for a bosonic p-tensor field in any spacetime dimension. These theories include the 2+1 dimensional Maxwell-Chern-Simons and 3+1 dimensional Cremmer-Scherk actions as particular cases. Within the Hamiltonian formulation, the embedded topological field theory (TFT) sector related to the topological mass term is not manifest in the original phase space. However through an appropriate canonical transformation, a gauge invariant factorisation of phase space into two orthogonal sectors is feasible. The first of these sectors includes canonically conjugate gauge invariant variables with free massive excitations. The second sector, which decouples from the total Hamiltonian, is equivalent to the phase space description of the associated non dynamical pure TFT. Within canonical quantisation, a likewise factorisation of quantum states thus arises for the full spectrum of TMGT in any dimension. This new factorisation scheme also enables a definition of the usual projection from TMGT onto topological quantum field theories in a most natural and transparent way. None of these results rely on any gauge fixing procedure whatsoever.Comment: 1+25 pages, no figure

Topology Classes of Flat U(1) Bundles and Diffeomorphic Covariant Representations of the Heisenberg Algebra

The general construction of self-adjoint configuration space representations of the Heisenberg algebra over an arbitrary manifold is considered. All such inequivalent representations are parametrised in terms of the topology classes of flat U(1) bundles over the configuration space manifold. In the case of Riemannian manifolds, these representations are also manifestly diffeomorphic covariant. The general discussion, illustrated by some simple examples in non relativistic quantum mechanics, is of particular relevance to systems whose configuration space is parametrised by curvilinear coordinates or is not simply connected, which thus include for instance the modular spaces of theories of non abelian gauge fields and gravity.Comment: 22 pages, no figures, plain LaTeX file; changes only in details of affiliation and financial suppor

Improved Determination of the Mass of the 1−+1^{-+} Light Hybrid Meson From QCD Sum Rules

We calculate the next-to-leading order (NLO) $\alpha_s$-corrections to the contributions of the condensates $$ and $^2$ in the current-current correlator of the hybrid current g\barq(x)\gamma_{\nu}iF_{\mu\nu}^aT^aq(x) using the external field method in Feynman gauge. After incorporating these NLO contributions into the Laplace sum-rules, the mass of the $J^{PC}$=$1^{-+}$ light hybrid meson is recalculated using the QCD sum rule approach. We find that the sum rules exhibit enhanced stability when the NLO $\alpha_s$-corrections are included in the sum rule analysis, resulting in a $1^{-+}$ light hybrid meson mass of approximately 1.6 GeV.Comment: revtex4, 10 pages, 7 eps figures embedded in manuscrip

Nonlinear Dynamics of Structures with Material Degradation

Structures usually experience deterioration during their working life. Oxidation, corrosion, UV exposure, and thermo-mechanical fatigue are some of the most well-known mechanisms that cause degradation. The phenomenon gradually changes structural properties and dynamic behaviour over their lifetime, and can be more problematic and challenging in the presence of nonlinearity. In this paper, we study how the dynamic behaviour of a nonlinear system changes as the thermal environment causes certain parameters to vary. To this end, a nonlinear lumped mass modal model is considered and defined under harmonic external force. Temperature dependent material functions, formulated from empirical test data, are added into the model. Using these functions, bifurcation parameters are defined and the corresponding nonlinear responses are observed by numerical continuation. A comparison between the results gives a preliminary insight into how temperature induced properties affects the dynamic response and highlights changes in stability conditions of the structure

Coherent State Approach to Quantum Clocks

The ``problem of time'' has been a pressing issue in quantum gravity for some time. To help understand this problem, Rovelli proposed a model of a two harmonic oscillators system where one of the oscillators can be thought of as a ``clock'' for the other oscillator thus giving a natural time reference frame for the system. Recently, the author has constructed an explicit form for the coherent states on the reduced phase space of this system in terms of Klauder's projection operator approach. In this paper, by using coherent state representations and other tools from coherent state quantization, I investigate the construction of gauge invariant operators on this reduced phase space, and the ability to use a quantum oscillator as a ``clock.''Comment: 13 pages, Late

The electromagnetic effects in isospin symmetry breakings of q{\bar q} systems

The isospin symmetry breakings of q{\bar q} are investigated in the QCD sum rule method. The electromagnetic effects are evaluated following the procedure requiring that the electromagnetic effects for charged meson be gauge invariant. We find that the electromagnetic effects are also dominant in the isospin violations of rho meson, which have been shown to be the case in the mass splittings of pions. The numerical results for the difference of pion decay constants and the masses of rho mesons are presented, which are consistent with the data.Comment: To appear in Phys. Rev. D (1997

Coherent State Approach to Time Reparameterization Invariant Systems

For many years coherent states have been a useful tool for understanding fundamental questions in quantum mechanics. Recently, there has been work on developing a consistent way of including constraints into the phase space path integral that naturally arises in coherent state quantization. This new approach has many advantages over other approaches, including the lack of any Gribov problems, the independence of gauge fixing, and the ability to handle second-class constraints without any ambiguous determinants. In this paper, I use this new approach to study some examples of time reparameterization invariant systems, which are of special interest in the field of quantum gravity