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Membrane geometry with auxiliary variables and quadratic constraints
Get PDFConsider a surface described by a Hamiltonian which depends only on the metric and extrinsic curvature induced on the surface. The metric and the curvature, along with the basis vectors which connect them to the embedding functions defining the surface, are introduced as auxiliary variables by adding appropriate constraints, all of them quadratic. The response of the Hamiltonian to a deformation in each of the variables is examined and the relationship between the multipliers implementing the constraints and the conserved stress tensor of the theory established
Dhá théacs dlí
Get PDFEdition of two legal texts from the late sixteenth and early seventeenth centuries from manuscripts in John Rylands University Library, Manchester, and the National Library of Irelan
Perturbation Theory and the Renormalization Group in Genetic Dynamics
Get PDFAlthough much progress has been made in recent years in the theory of GAs and GP, there is still a conspicuous lack of tools with which to derive systematic, approximate solutions to their dynamics. In this article we propose and study perturbation theory as a potential tool to fill this gap. We concentrate mainly on selection-mutation systems, showing different implementations of the perturbative framework, developing, for example, perturbative expansions for the eigenvalues and eigenvectors of the transition matrix. The main focus however, is on diagrammatic methods, taken from physics, where we show how approximations can be built up using a pictorial representation generated by a simple set of rules, and how the renormalization group can be used to systematically improve the perturbation theory
Pre-Big Bang Scenarios on Self-T-Dual Bouncing Branes
Get PDFWe consider a new class of 5-dimensional dilatonic actions which are invariant under T-duality transformations along three compact coordinates, provided that an appropriate potential is chosen. We show that the invariance remains when we add a boundary term corresponding to a moving 3-brane, and we study the effects of the T-duality symmetry on the brane cosmological equations. We find that T-duality transformations in the bulk induce scale factor duality on the brane, together with a change of sign of the pressure of the brane cosmological matter. However, in a remarkable analogy with the Pre-Big Bang scenario, the cosmological equations are unchanged. Finally, we propose a model where the dual phases are connected through a scattering of the brane induced by an effective potential. We show how this model can realise a smooth, non-singular transition between a pre-Big Bang superinflationary Universe and a post-Big Bang accelerating Universe
Spontaneous Edge Currents for the Dirac Equation in Two Space Dimensions
Get PDFSpontaneous edge currents are known to occur in systems of two space dimensions in a strong magnetic field. The latter creates chirality and determines the direction of the currents. Here we show that an analogous effect occurs in a field-free situation when time reversal symmetry is broken by the mass term of the Dirac equation in two space dimensions. On a half plane, one sees explicitly that the strength of the edge current is proportional to the difference between the chemical potentials at the edge and in the bulk, so that the effect is analogous to the Hall effect, but with an internal potential. The edge conductivity differs from the bulk (Hall) conductivity on the whole plane. This results from the dependence of the edge conductivity on the choice of a selfadjoint extension of the Dirac Hamiltonian. The invariance of the edge conductivity with respect to small perturbations is studied in this example by topological techniques
Two Order Parameters in Quantum XZ Spin Models with Gibbsian Ground States
Get PDFWe describe a family of quantum spin models which are generators of a discrete Markovian process. We show that that there exists an explicit expression for the ground state of such models and give a simple argument for the existence of two types of long-range order in such systems. Two special examples of these systems are analysed in detail
Exact Solution of Noncommutative U(1) Gauge Theory in 4-Dimensions
Get PDFNoncommutative U(1) gauge theory on the Moyal-Weyl space R^2 × R_θ^2 is regularized by approximating the noncommutative spatial slice R_θ^2 by a fuzzy sphere of matrix size L and radius R. Classically we observe that the field theory on the fuzzy space R^2 × S^2_L reduces to the field theory on the Moyal-Weyl plane R^2 × R_θ^2 in the flattening continuum planar limits R, L→∞ where the ratio θ^2 = (R^2)/(|L|^(2q)) is kept fixed with q > 3/2. The effective noncommutativity parameter is found to be given by (θ_eff)^2 ~ 2(θ^2)(L/2)^(2q-1) and thus it corresponds to a strongly noncommuting space. In the quantum theory it turns out that this prescription is also equivalent to a dimensional reduction of the model where the noncommutative U(1) gauge theory in 4 dimensions is shown to be equivalent in the large L limit to an ordinary O(M) non-linear sigma model in 2 dimensions where M~3L^2 The Moyal-Weyl model defined this way is also seen to be an ordinary renormalizable theory which can be solved exactly using the method of steepest descents. More precisely we find for a fixed renormalization scale μ and a fixed renormalized coupling constant g_r^2 an O(M)—symmetric mass, for the different components of the sigma field, which is non-zero for all values of g_r^2 and hence the O(M) symmetry is never broken in this solution. We obtain also an exact representation of the beta function of the theory which agrees with the known one-loop perturbative result
A numerical study of a confined Q anti-Q system in compact U(1) lattice gauge theory in 4D
Get PDFWe present a numerical study about the confining regime of compact U(1) lattice gauge theory in 4D. To address the problem, we exploit the duality properties of the theory. The main features of this method are presented, and its possible advantages and limits with respect to alternative techniques are briefly discussed. In Monte Carlo simulations, we focus our attention onto the case when a pair of static external charges is present. Some results are shown, concerning different observables which are of interest in order to understand the confinement mechanism, like the profile of the electric field induced by the static charges, and the ratios between Polyakov loop correlation functions at different distances