Modern Physics Letters A

We review a few topics in Planck-scale physics, with emphasis on possible manifestations in relatively low energy. The selected topics include quantum fluctuations of spacetime, their cumulative effects, uncertainties in energy–momentum measurements, and low energy quantum-gravity phenomenology. The focus is on quantum-gravity-induced uncertainties in some observable quantities. We consider four possible ways to probe Planck-scale physics experimentally: (i) looking for energy-dependent spreads in the arrival time of photons of the same energy from GRBs; (ii) examining spacetime fluctuation-induced phase incoherence of light from extragalactic sources; (iii) detecting spacetime foam with laser-based interferometry techniques; (iv) understanding the threshold anomalies in high energy cosmic ray and gamma ray events. Some other experiments are briefly discussed. We show how some physics behind black holes, simple clocks, simple computers, and the holographic principle is related to Planck-scale physics. We also discuss a formulation of the Dirac equation as a difference equation on a discrete Planck-scale spacetime lattice, and a possible interplay between Planck-scale and Hubble-scale physics encoded in the cosmological constant (dark energy).

Field theoretic models possessing a global internal fermionic shift symmetry are considered. When such a symmetry is realized locally, spin-3/2 fields appear naturally as gauge fields. Implementation of the gauging procedure requires not only the usual replacement of ordinary derivatives by covariant derivatives containing the spin-3/2 fields, but also the inclusion of additional monomials. The Higgs mechanism and the high energy Nambu–Goldstone fermion equivalence theorem are explicitly demonstrated.

Events of Au + Au collisions from AGS to RHIC energies by RQMD (v2.4) generator are produced. ratios as functions of rapidity, transverse momentum and centrality at are studied. The dependence on the center of mass energy of ratios is presented, compared with the experimental results. It is shown that ratio from rescattering RQMD is lower than those of the experiments at RHIC energies. We argue that hadronic rescattering at RHIC energies is suppressed compared to AGS, SPS energies.

We study matrix models related to SO/Sp gauge theories with flavors. We give the effective superpotentials for gauge theories with arbitrary tree level superpotential up to first instanton level. For quartic tree level superpotential, we obtained exact one-cut solution. We also derive Seiberg–Witten curve for these gauge theories from matrix model argument.

The concept of a canonical Bäcklund transformation as laid down by Sklyanin is extended to a discrete integral chain, with a Poisson structure which is not canonical in the strict sense. The transformation is induced by an auxiliary Lax operator with a classical r-matrix which is similar in its algebraic structure to that of the original Lax operator governing the dynamics of the chain. Moreover, the transformation can be obtained from a suitable generating function. It is also shown how successive transformations can be composed to construct a new transformation. Finally an inverse transformation is also constructed. The compatibility of the transformation with the "time" part of the Lax equation is explicitly demonstrated. It is also shown that the Bianchi theorem of permutability holds good.