Covariant gravity with Lagrange multiplier constraint

We review on the models of gravity with a constraint by the Lagrange multiplier field. The constraint breaks general covariance or Lorentz symmetry in the ultraviolet region. We report on the $F(R)$ gravity model with the constraint and the proposal of the covariant (power-counting) renormalized gravity model by using the constraint and scalar projectors. We will show that the model admits flat space solution, its gauge-fixing formulation is fully developed, and the only propagating mode is (higher derivative) graviton, while scalar and vector modes do not propagate. The preliminary study of FRW cosmology indicates to the possibility of inflationary universe solution is also given.Comment: 10 pages, to appear in the Proceedings of the QFEXT11 Benasque Conferenc

Antikaon flow in heavy-ion collisions: the effects of absorption and mean fields

We study antikaon flow in heavy-ion collisions at SIS energies based on the relativistic transport model (RVUU 1.0). The production of antikaons from both baryon-baryon and pion-baryon collisions are included. Taking into account only elastic and inelastic collisions of the antikaon with nucleons and neglecting its mean-field potential as in the cascade model, a strong antiflow or anti-correlation of antikaons with respect to nucleons is seen as a result of the strong absorption of antikaons by nucleons. However, the antiflow of antikaons disappears after including also their propagation in the attractive mean-field potential. The experimental measurement of antikaon flow in heavy-ion collision will be very useful in shedding lights on the relative importance of antikaon absorption versus its mean-field potential.Comment: 12 pages, 2 postscript figures omitted in the original submission are included, to appear in Phys. Rev.

Antiproton production in Ni+Ni collisions at 1.85 GeV/nucleon

Antiproton production in Ni+Ni collisions at 1.85 GeV/nucleon is studied in the relativistic Vlasov-Uehling-Uhlenbeck model. The self-energies of the antiproton are determined from the nucleon self-energies by the G-parity transformation. Also, the final-state interactions of the antiproton including both rescattering and annihilation are explicitly treated. With a soft nuclear equation of state, the calculated antiproton momentum spectrum is in good agreement with recent experimental data from the heavy-ion synchrotron at GSI. The effect due to the reduced nucleon and antinucleon masses in a medium is found to be more appreciable than in earlier Bevalac experiments with lighter systems and at higher energies.Comment: 10 pages, 4 figures available upon request to [email protected]. TAMUNT-940

Darboux transformations for a twisted derivation and quasideterminant solutions to the super KdV equation

This paper is concerned with a generalized type of Darboux transformations defined in terms of a twisted derivation $D$ satisfying $D(AB)=D(A)+\sigma(A)B$ where $\sigma$ is a homomorphism. Such twisted derivations include regular derivations, difference and $q$-difference operators and superderivatives as special cases. Remarkably, the formulae for the iteration of Darboux transformations are identical with those in the standard case of a regular derivation and are expressed in terms of quasideterminants. As an example, we revisit the Darboux transformations for the Manin-Radul super KdV equation, studied in Q.P. Liu and M. Ma\~nas, Physics Letters B \textbf{396} 133--140, (1997). The new approach we take enables us to derive a unified expression for solution formulae in terms of quasideterminants, covering all cases at once, rather than using several subcases. Then, by using a known relationship between quasideterminants and superdeterminants, we obtain expressions for these solutions as ratios of superdeterminants. This coincides with the results of Liu and Ma\~nas in all the cases they considered but also deals with the one subcase in which they did not obtain such an expression. Finally, we obtain another type of quasideterminant solutions to the Main-Radul super KdV equation constructed from its binary Darboux transformations. These can also be expressed as ratios of superdeterminants and are a substantial generalization of the solutions constructed using binary Darboux transformations in earlier work on this topic