Recursive renormalization of the singlet one-pion-exchange plus point-like interactions

The subtracted kernel approach is shown to be a powerful method to be implemented recursively in scattering equations with regular plus point-like interactions. The advantages of the method allows one to recursively renormalize the potentials, with higher derivatives of the Dirac-delta, improving previous results. The applicability of the method is verified in the calculation of the 1 So nucleon-nucleon phase-shifts, when considering a potential with one-pion-exchange plus a contact interaction and its derivatives. The S-1(0) renormalization parameters are fitted to the data. The method can in principle be extended to any derivative order of the contact interaction, to higher partial waves and to coupled channels. (c) 2005 Elsevier B.V. All rights reserved.

Theory of small aspect ratio waves in deep water

In the limit of small values of the aspect ratio parameter (or wave steepness) which measures the amplitude of a surface wave in units of its wave-length, a model equation is derived from the Euler system in infinite depth (deep water) without potential flow assumption. The resulting equation is shown to sustain periodic waves which on the one side tend to the proper linear limit at small amplitudes, on the other side possess a threshold amplitude where wave crest peaking is achieved. An explicit expression of the crest angle at wave breaking is found in terms of the wave velocity. By numerical simulations, stable soliton-like solutions (experiencing elastic interactions) propagate in a given velocities range on the edge of which they tend to the peakon solution. (c) 2005 Elsevier B.V. All rights reserved.

Momentum-space non-hydrogenic wavefunction of quantum defect theory

We derive a closed-form analytic expression in momentum space for the asymptotic non-hydrogenic wavefunction of the quantum defect theory (QDT) due to Seaton and compare it with a widely used QDT-approximate wavefunction for the Rydberg states Li-3(2s), Mg-24(6s) and Rb-37(5s).

Quadratic gravity in (2+1)D with a topological Chern-Simons term

Three-dimensional quadratic gravity, unlike general relativity in (2+1)D, is dynamically nontrivial and has a well behaved nonrelativistic potential. Here we analyse the changes that occur when a topological Chem-Simons term is added to this theory. It is found that the harmless massive scalar mode of the latter gives rise to a troublesome massive spin-0 ghost, while the massive spin-2 ghost is replaced by two massive physical particles both of spin 2. We also found that light deflection does not have the 'wrong sign' such as in the framework of three-dimensional quadratic gravity.

Propagator, tree-level unitarity and effective nonrelativistic potential for higher-derivative gravity theories in D dimensions

A prescription for computing the propagator for D-dimensional higher-derivative gravity theories, based on the Barnes-Rivers operators, is presented. A systematic study of the tree-level unitarity of these theories is developed and the agreement of their linearized versions with Newton's law is investigated by computing the corresponding effective nonrelativistic potential. Three-dimensional quadratic gravity with a gravitational Chern-Simons term is also analyzed. A discussion on the issue of light bending within the framework of both D-dimensional quadratic gravity and three-dimensional quadratic gravity with a Chern-Simons term is provided as well. (C) 2002 American Institute of Physics.

N=2 sigma models for Ramond-Ramond backgrounds

Using the U(4) hybrid formalism, manifestly N = (2,2) worldsheet supersymmetric sigma models are constructed for the type-IIB superstring in Ramond-Ramond backgrounds. The Kahler potential in these N = 2 sigma models depends on four chiral and antichiral bosonic superfields and two chiral and antichiral fermionic superfields. When the Kahler potential is quadratic, the model is a free conformal field theory which describes a flat ten-dimensional target space with Ramond-Ramond flux and non-constant dilaton. For more general Kahler potentials, the model describes curved target spaces with Ramond-Ramond flux that are not plane-wave backgrounds. Ricci-flatness of the Kahler metric implies the on-shell conditions for the background up to the usual four-loop conformal anomaly.

The Fermi pseudo-potential in one dimension

Wu and Yu recently examined point interactions in one dimension in the form of the Fermi pseudo-potential. on the other hand there are point interactions in the form of self-adjoint extensions (SAEs) of the kinetic energy operator. We examine the relationship between the point interactions in these two forms in the one-channel and two-channel cases. In the one-channel case the pseudo-potential leads to the standard three-parameter family of SAEs. In the two-channel case the pseudo-potential furnishes a ten-parameter family of SAEs.

A new approach to superstring field theory

I review the construction of an action for open superstring field theory which does not suffer from the contact term problems of other approaches. I also discuss a possible generalization of this action for closed superstring field theory.

Potential symmetries and new solutions of a simplified model for reacting mixtures

In this paper, we investigate potential symmetries of a simplified model for reacting mixtures. We find new similarity reductions and wider class of solutions through this approach. Further, we explore an invertible mapping which linearizes the reacting mixture model.

Remarks on Duffin-Kemmer-Petiau theory and gauge invariance

Two problems relative to the electromagnetic coupling of Duffin-Kemmer-Petiau (DKP) theory are discussed: the presence of an anomalous term in the Hamiltonian form of the theory and the apparent difference between the interaction terms in DKP and Klein-Gordon (KG) Lagrangians. For this, we first discuss the behavior of DKP field and its physical components under gauge transformations. From this analysis, we can show that these problems simply do not exist if one correctly analyses the physical components of DKP field. (C) 2000 Elsevier B.V. B.V. All rights reserved.

The nucleon structure function and the quark effective potential

By considering a statistical model for the quark content of the nucleon, where the quark levels are generated by a Dirac equation with a harmonic scalar-plus-vector potential, we note that a good fit for the ratio between the structure functions of the neutron and proton, F-2(n)/F-2(p), can be obtained if different strengths are used for the effective confining potentials of the up and down quarks.

Dirac's hole theory versus quantum field theory

Dirac's hole theory and quantum field theory are usually considered equivalent to each other. The equivalence, however, does not necessarily hold, as we discuss in terms of models of a certain type. We further suggest that the equivalence may fail in more general models. This problem is closely related to the validity of the Pauli principle in intermediate states of perturbation theory.

Effective theory for trapped few-fermion systems

We apply the general principles of effective field theories to the construction of effective interactions suitable for few- and many-body calculations in a no-core shell model framework. We calculate the spectrum of systems with three and four two-component fermions in a harmonic trap. In the unitary limit, we find that three-particle results are within 10% of known semianalytical values even in small model spaces. The method is very general, and can be readily extended to other regimes, more particles, different species (e.g., protons and neutrons in nuclear physics), or more-component fermions (as well as bosons). As an illustration, we present calculations of the lowest-energy three-fermion states away from the unitary limit and find a possible inversion of parity in the ground state in the limit of trap size large compared to the scattering length. Furthermore, we investigate the lowest positive-parity states for four fermions, although we are limited by the dimensions we can currently handle in this case.

Noether and topological currents equivalence and soliton/particle correspondence in affine sl(2)((1)) Toda theory coupled to matter

A submodel of the so-called conformal affine Toda model coupled to the matter field (CATM) is defined such that its real Lagrangian has a positive-definite kinetic term for the Toda field and a usual kinetic term for the (Dirac) spinor field. After spontaneously broken the conformal symmetry by means of BRST analysis, we end up with an effective theory, the off-critical affine Toda model coupled to the matter (ATM). It is shown that the ATM model inherits the remarkable properties of the general CATM model such as the soliton solutions, the particle/soliton correspondence and the equivalence between the Noether and topological currents. The classical solitonic spectrum of the ATM model is also discussed. (C) 2001 Elsevier B.V. B.V. All rights reserved.

On the algebraic K theory of the massive D8 and M9-branes

In this paper we review some basic relations of algebraic K theory and we formulate them in the language of D-branes. Then we study the relation between the D8-branes wrapped on an orientable, compact manifold W in a massive Type IIA, supergravity background and the M9-branes wrapped on a compact manifold Z in a massive d = 11 supergravity background from the K-theoretic point of view. By interpreting the D8-brane charges as elements of K-0(C(W)) and the (inequivalent classes of) spaces of gauge fields on the M9-branes as the elements of K-0(C(Z) x ((k) over bar*) G) where G is a one-dimensional compact group, a connection between charges and gauge fields is argued to exists. This connection could be realized as a composition map between the corresponding algebraic K theory groups.