Gamow-Teller sum rule in relativistic nuclear models

Relativistic corrections are investigated to the Gamow-Teller(GT) sum rule with respect to the difference between the $\beta_-$ and $\beta_+$ transition strengths in nuclei. Since the sum rule requires the complete set of the nuclear states, the relativistic corrections come from the anti-nucleon degrees of freedom. In the relativistic mean field approximation, the total GT strengths carried by the nucleon sector is quenched by about 12% in nuclear matter, while by about 8% in finite nuclei, compared to the sum rule value. The coupling between the particle-hole states with the nucleon-antinucleon states is also discussed with the relativistic random phase approximation, where the divergence of the response function is renormalized with use of the counter terms in the Lagrangian. It is shown that the approximation to neglect the divergence, like the no-sea approximation extensively used so far, is unphysical, from the sum-rule point of view.Comment: 12 pages, Brief review for Mod. Phys. Lett. A, using ws-mpla.cl

Ultraviolet Behavior of the Gluon Propagator in the Maximal Abelian Gauge

The ultraviolet asymptotic behavior of the gluon propagator is evaluated in the maximal Abelian gauge in the SU(2) gauge theory on the basis of the renormalization-group improved perturbation theory at the one-loop level. Square-root singularities obtained in the Euclidean domain are attributed to artifacts of the one-loop approximation in the maximal Abelian gauge and the standard normalization condition for the propagator used in our study. It is argued that this gauge is essentially nonperturbative.Comment: 15 pages, 2 figure

The dilute A_L models and the integrable perturbations of unitary minimal CFTs

Recently, a set of thermodynamic Bethe ansatz equations is proposed by Dorey, Pocklington and Tateo for unitary minimal models perturbed by \phi_{1,2} or \phi_{2,1} operator. We examine their results in view of the lattice analogues, dilute A_L models at regime 1 and 2. Taking M_{5,6}+\phi_{1,2} and M_{3,4}+\phi_{2,1} as the simplest examples, we will explicitly show that the conjectured TBA equations can be recovered from the lattice model in a scaling limit.Comment: 14 pages, 2 figure

A survey of spinning test particle orbits in Kerr spacetime

We investigate the dynamics of the Papapetrou equations in Kerr spacetime. These equations provide a model for the motion of a relativistic spinning test particle orbiting a rotating (Kerr) black hole. We perform a thorough parameter space search for signs of chaotic dynamics by calculating the Lyapunov exponents for a large variety of initial conditions. We find that the Papapetrou equations admit many chaotic solutions, with the strongest chaos occurring in the case of eccentric orbits with pericenters close to the limit of stability against plunge into a maximally spinning Kerr black hole. Despite the presence of these chaotic solutions, we show that physically realistic solutions to the Papapetrou equations are not chaotic; in all cases, the chaotic solutions either do not correspond to realistic astrophysical systems, or involve a breakdown of the test-particle approximation leading to the Papapetrou equations (or both). As a result, the gravitational radiation from bodies spiraling into much more massive black holes (as detectable, for example, by LISA, the Laser Interferometer Space Antenna) should not exhibit any signs of chaos.Comment: Submitted to Phys. Rev. D. Follow-up to gr-qc/0210042. Figures are low-resolution in order to satisfy archive size constraints; a high-resolution version is available at http://www.michaelhartl.com/papers