On the stability of thick brane worlds non-minimally coupled to gravity

We analyze a class of 5D models where a 3 brane is generated by a bulk scalar field non minimally coupled to gravity. We show that perturbative stability of such branes is normally guaranteed although non minimal couplings are not innocuous in general. After the physical states are identified the linearized equations for propagating modes are evaluated into a Schroedinger form and supersymmetric quantum mechanics provides the absence of tachyons. The spectrum contains a tower of spin 2 and spin 0 fields with continuous masses starting from zero ones. For regular geometries the scalar spectrum contains a state with zero mass which is always non normalizable. The propagating massive scalar states are repelled off the brane due to a centrifugal potential.Comment: 15 page

New Two-Dimensional Quantum Models Partially Solvable by Supersymmetrical Approach

New solutions for second-order intertwining relations in two-dimensional SUSY QM are found via the repeated use of the first order supersymmetrical transformations with intermediate constant unitary rotation. Potentials obtained by this method - two-dimensional generalized P\"oschl-Teller potentials - appear to be shape-invariant. The recently proposed method of $SUSY-$separation of variables is implemented to obtain a part of their spectra, including the ground state. Explicit expressions for energy eigenvalues and corresponding normalizable eigenfunctions are given in analytic form. Intertwining relations of higher orders are discussed.Comment: 21 pages. Some typos corrected; imrovements added in Subsect.4.2; some references adde

Dimensional structural constants from chiral and conformal bosonization of QCD

We derive the dimensional non-perturbative part of the QCD effective action for scalar and pseudoscalar meson fields by means of chiral and conformal bosonization. The related structural coupling constants L_5 and L_8 of the chiral lagrangian are estimated using general relations which are valid in a variety of chiral bosonization models without explicit reference to model parameters. The asymptotics for large scalar fields in QCD is elaborated, and model-independent constraints on dimensional coupling constants of the effective meson lagrangian are evaluated. We determine also the interaction between scalar quarkonium and the gluon density and obtain the scalar glueball-quarkonium potential.Comment: 21 pages, LaTe

Higher Order Matrix SUSY Transformations in Two-Dimensional Quantum Mechanics

The iteration procedure of supersymmetric transformations for the two-dimensional Schroedinger operator is implemented by means of the matrix form of factorization in terms of matrix 2x2 supercharges. Two different types of iterations are investigated in detail. The particular case of diagonal initial Hamiltonian is considered, and the existence of solutions is demonstrated. Explicit examples illustrate the construction.Comment: 15

Remarks on the general solution for the flat Friedman universe with exponential scalar-field potential and dust

We show that the simple extension of the method of obtaining the general exact solution for the cosmological model with the exponential scalar-field potential to the case when the dust is present fails and we discuss the reasons of this puzzling phenomenon.Comment: 11 page

Lorentz Symmetry Breaking in Abelian Vector-Field Models with Wess-Zumino Interaction

We consider the abelian vector-field models in the presence of the Wess-Zumino interaction with the pseudoscalar matter. The occurence of the dynamic breaking of Lorentz symmetry at classical and one-loop level is described for massless and massive vector fields. This phenomenon appears to be the non-perturbative counterpart of the perturbative renormalizability and/or unitarity breaking in the chiral gauge theories.Comment: 11 pages,LaTeX, Preprint DFUB/94 - 1

Phantom universe from CPT symmetric QFT

Inspired by the generalization of quantum theory for the case of non-Hermitian Hamiltonians with CPT symmetry, we construct a simple classical cosmological scalar field based model describing a smooth transition from ordinary dark energy to the phantom one

Supersymmetrical Separation of Variables for Scarf II Model: Partial Solvability

Recently, a new quantum model - two-dimensional generalization of the Scarf II - was completely solved analytically by SUSY method for the integer values of parameter. Now, the same integrable model, but with arbitrary values of parameter, will be studied by means of supersymmetrical intertwining relations. The Hamiltonian does not allow the conventional separation of variables, but the supercharge operator does allow, leading to the partial solvability of the model. This approach, which can be called as the first variant of SUSY-separation, together with shape invariance of the model, provides analytical calculation of the part of spectrum and corresponding wave functions (quasi-exact-solvability). The model is shown to obey two different variants of shape invariance which can be combined effectively in construction of energy levels and wave functions.Comment: 6 p.p., accepted for publication in EP

Dynamical Lorentz simmetry breaking from 3+1 Axion-Wess-Zumino model

We study the renormalizable abelian vector-field models in the presence of the Wess-Zumino interaction with the pseudoscalar matter. The renormalizability is achieved by supplementing the standard kinetic term of vector fields with higher derivatives. The appearance of fourth power of momentum in the vector-field propagator leads to the super-renormalizable theory in which the $\beta$-function, the vector-field renormalization constant and the anomalous mass dimension are calculated exactly. It is shown that this model has the infrared stable fixed point and its low-energy limit is non-trivial. The modified effective potential for the pseudoscalar matter leads to the possible occurrence of dynamical breaking of the Lorentz symmetry. This phenomenon is related to the modification of Electrodynamics by means of the Chern-Simons (CS) interaction polarized along a constant CS vector. Its presence makes the vacuum optically active that has been recently estimated from astrophysical data. We examine two possibilities for the CS vector to be time-like or space-like, under the assumption that it originates from v.e.v. of some pseudoscalar matter and show that only the latter one is consistent in the framework of the AWZ model, because a time-like CS vector makes the vacuum unstable under pairs creation of tachyonic photon modes with the finite vacuum decay rate.Comment: 33 pages, no Figures, Plain TeX, submitted to Phys. Rev.

Contribution of higher meson resonances to the electromagnetic π\pi-meson mass difference

Modifications of the DGMLY relation for calculation of electromagnetic $\pi$-meson mass difference based on the Chiral Symmetry Restoration phenomenon at high energies as well as the Operator Product Expansion of quark densities for vector ($\rho$) and axial-vector ($a_1$) meson fields difference are proposed. In the calculations higher meson resonances in vector and axial-vector channels are taken into account. It is shown that the inclusion of the first $\rho$ and $a_1$ radial excitations improves the results for electromagnetic $\pi$-meson mass difference as compared with the previous ones. Estimations on the electromagnetic $\rho$ and $a_1$-meson decay constants and the constant $L_{10}$ of effective chiral Lagrangian are obtained from the generalized Weinberg sum rules.Comment: Latex2e, 10 pages, submitted to Yad. Phy