Explicit Coordinate Dependence Research Articles

Impurity-doped scalar fields in arbitrary dimensions

We investigate the presence of localized structures for relativistic scalar fields coupled to impurities in arbitrary spatial dimensions. Such systems present spatial inhomogeneity, realized through the inclusion of explicit coordinate dependence in the Lagrangian. It is shown that, in stark contrast to the impurity-free scenario, Derrick's argument does not present a strong hindrance to the existence of stable solutions in this case. Bogomol'nyi equations giving rise to global minima of the energy are found, and some of the ensuing BPS configurations are presented.

Supersymmetric inhomogeneous field theories in 1+1 dimensions

We study supersymmetric inhomogeneous field theories in 1+1 dimensions which have explicit coordinate dependence. Although translation symmetry is broken, part of supersymmetries can be maintained. In this paper, we consider the simplest inhomogeneous theories with one real scalar field, which possess an unbroken supersymmetry. The energy is bounded from below by the topological charge which is not necessarily nonnegative definite. The bound is saturated if the first-order Bogomolny equation is satisfied. Non-constant static supersymmetric solutions above the vacuum involve in general a zero mode although the system lacks translation invariance. We consider two inhomogeneous theories obtained by deforming supersymmetric sine-Gordon theory and ϕ6 theory. They are deformed either by overall inhomogeneous rescaling of the superpotential or by inhomogeneous deformation of the vacuum expectation value. We construct explicitly the most general supersymmetric solutions and obtain the BPS energy spectrum for arbitrary position-dependent deformations. Nature of the solutions and their energies depend only on the boundary values of the inhomogeneous functions. The vacuum of minimum energy is not necessarily a constant configuration. In some cases, we find a one-parameter family of degenerate solutions which include a non-vacuum constant solution as a special case.

Quasiaverages and Degenerate Quantum Equilibriums of Magnetic Systems with SU(3) Symmetry of the Exchange Interaction

We consider magnetic systems with the SU(3) symmetry of the exchange interaction. For degenerate equilibriums with broken magnetic and phase symmetries, we formulate classification equations for the order parameter using the concept of residual symmetry. Based on them, we obtain an explicit form of the equilibrium values of the order parameters of a spin nematic and an antiferromagnet in the general form. We clarify the existence conditions for six types of superfluid equilibriums for the order parameter describing the Bose pair condensate. We study inhomogeneous equilibriums and obtain the explicit coordinate dependence of the magnetic order parameters.

Gauge fields on noncommutative geometries with curvature

It was shown recently that the lagrangian of the Grosse-Wulkenhaar model can be written as lagrangian of the scalar field propagating in a curved noncommutative space. In this interpretation, renormalizability of the model is related to the interaction with the background curvature which introduces explicit coordinate dependence in the action. In this paper we construct the $U_1$ gauge field on the same noncommutative space: since covariant derivatives contain coordinates, the Yang-Mills action is again coordinate dependent. To obtain a two-dimensional model we reduce to a subspace, which results in splitting of the degrees of freedom into a gauge and a scalar. We define the gauge fixing and show the BRST invariance of the quantum action.

On T-duality and integrability for strings on AdS backgrounds

We discuss an interplay between T-duality and integrability for certain classical non-linear sigma models. In particular, we consider strings on the AdS5 ? S5 background and perform T-duality along the four isometry directions of AdS5 in the Poincar? patch. The T-dual of the AdS5 sigma model is again a sigma model on an AdS5 space. This classical T-duality relation was used in the recently uncovered connection between light-like Wilson loops and MHV gluon scattering amplitudes in the strong coupling limit of the AdS/CFT duality. We show that the explicit coordinate dependence along the T-duality directions of the associated Lax connection (flat current) can be eliminated by means of a field dependent gauge transformation. As a result, the gauge equivalent Lax connection can easily be T-dualized, i.e. written in terms of the dual set of isometric coordinates. The T-dual Lax connection can be used for the derivation of infinitely many conserved charges in the T-dual model. Our construction implies that local (Noether) charges of the original model are mapped to non-local charges of the T-dual model and vice versa.

Symmetry of the remanent-state flux distribution in superconducting thin strips: Probing the critical state

The critical-state in a thin strip of YBaCuO is studied by magneto-optical imaging. The distribution of magnetic flux density is shown to have a specific symmetry in the remanent state after a large applied field. The symmetry was predicted [PRL 82, 2947 (1999)] for any Jc(B), and is therefore suggested as a simple tool to verify the applicability of the critical-state model. At large temperatures we find deviations from this symmetry, which demonstrates departure from the critical-state behavior. The observed deviations can be attributed to an explicit coordinate dependence of $j_c$ since both a surface barrier, and flux creep would break the symmetry in a different way.

Generalizations of the goldstone and the coleman theorems

Generalization of the Goldstone theorem and of the Coleman theorems are formulated and proven within the framework of the Wightman field theory. The generalization of the Goldstone theorem is to a class of currents in which implicit and explicit co-ordinate dependence are mixed. We get that vacuum noninvariance entails the existence of certain masses in the energy-momentum spectrum which are not necessarily zero. The generalizations of the Coleman theorems are to local tensor fields and to several classes of fields in which implicit and explicit co-ordinate dependence are mixed. Several examples are examined in light of the new theorems.

Heisenberg representation in classical general relativity

The energy of the gravitational field (as of any other system) is not always the numerical value of the Hamiltonian (for example, not in a Hamilton-Jacobi formulation). We define a classical « Heisenberg representation » which excludes Hamilton-Jacobi-like canonical transformations. Ordinarily, within the Heisenberg representation, there remains only the possibility of time-independent canonical transformation among the dynamical variables. However, the freedom of co-ordinate transformations in general relativity allows many extra « canonical » transformations not found in conventional Lorentz covariant theory. This wider class of canonical formalisms possess all the properties usually associated with the Heisenberg picture in that in each formalism the measurable quantities,gμv(t), are obtained from knowledge of the canonical variables at the same time without any explicit co-ordinate dependence. Further, the Hamiltonian is a constant of motion. Only in Heisenberg frames is the Hamiltonian to be associated with the energy of the system. In spite of the additional freedom of canonical transformations (due to the freedom of co-ordinate change mentioned above), it is shown that the Hamiltonian is numerically the same for a fixed state of the gravitational field in any Heisenberg representation. The energy is then a uniquely definable quantity in the theory. In the process, it is established that two Heisenberg frames can differ by co-ordinate transformations that depend only on the canonical variables and not explicitly on the co-ordinates. These transformations must also preserve the property that at spatial infinity the metric become Lorentz so that the physical boundary conditions be unaltered.