International Journal of Modern Physics A

We review recent results obtained in the physics of the thermal Casimir force acting between two dielectrics, dielectric and metal, and between metal and semiconductor. The detailed derivation for the low-temperature behavior of the Casimir free energy, pressure and entropy in the configuration of two real dielectric plates is presented. For dielectrics with finite static dielectric permittivity it is shown that the Nernst heat theorem is satisfied. Hence, the Lifshitz theory of the van der Waals and Casimir forces is demonstrated to be consistent with thermodynamics. The nonzero dc conductivity of dielectric plates is proved to lead to a violation of the Nernst heat theorem and, thus, is not related to the phenomenon of dispersion forces. The low-temperature asymptotics of the Casimir free energy, pressure and entropy are derived also in the configuration of one metal and one dielectric plate. The results are shown to be consistent with thermodynamics if the dielectric plate possesses a finite static dielectric permittivity. If the dc conductivity of a dielectric plate is taken into account this results in the violation of the Nernst heat theorem. We discuss both the experimental and theoretical results related to the Casimir interaction between metal and semiconductor with different charge carrier density. Discussions in the literature on the possible influence of spatial dispersion on the thermal Casimir force are analyzed. In conclusion, the conventional Lifshitz theory taking into account only the frequency dispersion remains the reliable foundation for the interpretation of all present experiments.

We study the critical points of the black hole scalar potential V_BH in N = 2, d = 4 supergravity coupled to n_V vector multiplets, in an asymptotically flat extremal black hole background described by a 2(n_V+1)-dimensional dyonic charge vector and (complex) scalar fields which are coordinates of a special Kähler manifold.

For the case of homogeneous symmetric spaces, we find three general classes of regular attractor solutions with nonvanishing Bekenstein–Hawking entropy. They correspond to three (inequivalent) classes of orbits of the charge vector, which is in a 2(n_V+1)-dimensional representation R_V of the U-duality group. Such orbits are nondegenerate, namely they have nonvanishing quartic invariant (for rank-3 spaces). Other than the ½-BPS one, there are two other distinct non-BPS classes of charge orbits, one of which has vanishing central charge.

The three species of solutions to the N = 2 extremal black hole attractor equations give rise to different mass spectra of the scalar fluctuations, whose pattern can be inferred by using invariance properties of the critical points of V_BH and some group theoretical considerations on homogeneous symmetric special Kähler geometry.

The matrix element of the isoscalar axial vector current, , between nucleon states is computed using the external field QCD sum rule method. The external field induced correlator, , is calculated from the spectrum of the isoscalar axial vector meson states. Since it is difficult to ascertain, from QCD sum rule for hyperons, the accuracy of validity of flavor SU(3) symmetry in hyperon decays when strange quark mass is taken into account, we rely on the empirical validity of Cabbibo theory to determine the matrix element between nucleon states. Combining with our calculation of and the well-known nucleon β-decay constant allows us to determine occurring in the Bjorken sum rule. The result is in reasonable agreement with experiment. We also discuss the role of the anomaly in maintaining flavor symmetry and validity of OZI rule.

We formulate and explore the physical implications of a new translation gauge theory of gravity in flat space–time with a new Yang–Mills action, which involves quadratic gauge curvature and fermions. The theory shows that the presence of an "effective Riemann metric tensor" for the motions of classical particles and light rays is probably the manifestation of the translation gauge symmetry in flat physical space–time. In the post-Newtonian approximation of the tensor gauge field produced by the energy–momentum tensor, the results are shown to be consistent with classical tests of gravity and with the quadrupole radiations of binary pulsars.

The problem of a spinless particle subject to a general mixing of vector and scalar screened Coulomb potentials in a two-dimensional world is analyzed and its bounded solutions are found. Some unusual results, including the existence of a bona fide solitary zero-eigenmode solution, are revealed for the Klein–Gordon equation. The cases of pure vector and scalar potentials, already analyzed in previous works, are obtained as particular cases.

The universe is certainly not yet in a total thermodynamical equilibrium. Thus some law of special initial conditions is needed. A universe or a system imposed to behave periodically will then require "initial conditions." Those initial conditions will not look like the type we already have, which have been suffered the heat death. In other words, the required initial conditions should not have been obtained the maximal entropy — like a random state. The intrinsic periodicity successfully explains why entropy is not maximal but it fails, phenomenologically, in leading to a constant entropy.

The measurement of the exclusive light hadron decays of the ψ″ in e⁺e^- experiments with significant interference between the ψ″ and continuum amplitudes is discussed. The radiative correction and the Monte Carlo simulation are studied. It is possible to verify the destructive interference for the detectors with energy–momentum resolution of (1~2)%.