Modern Physics Letters A

We review the current status of the solar neutrino problem. A survey of the experiments and their results are given, and solar physics crucial to the understanding of these results are discussed. Semi-empirical methods are used to derive bounds on the fluxes of the three most important components (pp, ⁷Be and ⁸B) of the solar neutrino spectrum. The ⁸B neutrinos are directly measured to be about half of the theoretical prediction. Relative to their theoretical predictions, we find the ⁷Be neutrinos to be highly suppressed and the pp neutrinos not suppressed. We are also able to derive a lower bound on the pp flux.

We evaluate the quantum corrections of the Einstein-Hilbert action with boundaries in (2+ε)-dimensional expansion approach. We find the Einstein-Hilbert action with boundaries to be renormalizable to the one-loop order. We compute the geometric entropy beyond the semiclassical approximation. It is found that the exact geometric entropy is related to the string susceptibility by the analytic continuation in the central charge. Our results also show that we can renormalize the divergent quantum corrections for the Bekenstein-Hawking entropy of black holes by the gravitational coupling constant renormalization beyond two dimensions.

We construct the chiral Wess-Zumino term as a solution for the Batalin-Vilkovisky master equation for anomalous two-dimensional gauge theories, working in an extended field-antifield space, where the gauge group elements are introduced as additional degrees of freedom. We analyze the Abelian and the non-Abelian cases, calculating in both cases the BRST generator in order to show the physical equivalence between this chiral solution for the master equation and the usual (nonchiral) one.

The general formula for the universal R-matrix for quantized nontwisted affine algebras, obtained by the first and third authors, is applied to zero central charge, highest weight modules of the quantized affine algebras. It is shown how the universal R-matrix produces the Gauss decomposition of trigonometric R-matrix in tensor product of these modules. In particular, current realization of the universal R-matrix is presented. It gives a new universal presentation for the trigonometric R-matrix with a parameter in tensor product of U_q(sl₂)-Verma modules. Detailed analysis of a scalar factor arising in finite-dimensional representations of the universal R-matrix for any Uq(ĝ) is given. We interpret this scalar factor as a multiplicative bilinear form on highest weight polynomials of irreducible representations and express this form in terms of infinite q-shifted factorials.

The ratio K/π in pp collisions is investigated based on the constraints of the isospin conservation and the strangeness suppression. Numerical results on the ratios of K⁺/π⁺ and K⁻/π⁻ are given for the relationship between the ratio and the multiplicity of produced particles.

The possibility of the existence of “free” Schrödinger anyons is considered. It is shown that special type of contact interactions exists when scattering does not arise. By formulating the problem for the two-particle system with a finite region of interaction which is then allowed to go to zero, it is established that this type of the contact interactions is the analog of the anomalous magnetic moment for fermions in the Aharonov-Bohm field. Finally, we consider connections with the Dirac anyon physics and low energy dynamics of [U(1)]² Chern-Simons solitons.

The link invariant, arising from the cyclic quantum dilogarithm via the particular R- matrix construction is proved to coincide with the invariant of triangulated links in S³ introduced in Ref. 14. The obtained invariant, like Alexander-Conway polynomial, vanishes on disjoint union of links. The R-matrix can be considered as the cyclic analog of the universal R-matrix associated with U_q(sl(2)) algebra.