International Journal of Modern Physics A

We investigate the effects of the external gravitational and constant magnetic fields to the dynamical symmetry breaking. As simple models of the dynamical symmetry breaking we consider the Nambu–Jona-Lasinio (NJL) model and the supersymmetric Nambu–Jona-Lasinio (SUSY NJL) model nonminimally interacting with the external gravitational field and minimally interacting with constant magnetic field. The explicit expressions for the scalar and spinor Green functions are found to the first order in the space–time curvature and exactly for a constant magnetic field. We obtain the effective potential of the above models from the Green functions in the magnetic field in curved space–time. Calculating the effective potential numerically with the varying curvature and/or magnetic fields we show the effects of the external gravitational and magnetic fields to the phase structure of the theories. In particular, increase of the curvature in the spontaneously broken phase of the chiral symmetry due to the fixed magnetic field makes this phase to be less broken. At the same time the strong magnetic field quickly induces chiral symmetry breaking even in the presence of fixed gravitational field within the nonbroken phase.

We study anti-de Sitter black holes in 2 + 1 dimensions in terms of Chern–Simons gauge theory of the anti-de Sitter group coupled to a source. Taking the source to be an anti-de Sitter state specified by its Casimir invariants, we show how all the relevant features of the black hole are accounted for. The requirement that the source be a unitary representation leads to a discrete tower of excited states which provide a microscopic model for the black hole.

The conformal-gauge two-dimensional quantum gravity is formulated in the framework of the BRS quantization and solved completely in the Heisenberg picture: all n-point Wightman functions are explicitly obtained. The field-equation anomaly is shown to exist as in other gauges, but there is no other subtlety. At the critical dimension D = 26 of the bosonic string, the field-equation anomaly is shown to be absent. However, this result is not equivalent to the statement that the conformal anomaly is proportional to D - 26. The existence of the FP-ghost number current anomaly is seen to be an illusion.

We present numerical calculations of the charge and statistics, as extracted from Berry phases, of the Laughlin quasiparticles, near filling fraction 1/3, and for system sizes of up to 200 electrons. For the quasiholes our results confirm that the charge and statistics parameter are e/3 and 1/3, respectively. For the quasielectron charge we find a slow convergence towards the expected value of -e/3, with a finite size correction for N electrons of approximately -0.13e/N. The statistics parameter for the quasielectrons has no well defined value even for 200 electrons, but might possibly converge to 1/3. The anyon model works well for the quasiholes, but requires singular two-anyon wave functions for modelling two Laughlin quasielectrons.

We investigate the SO(10) unification model in a Lie-algebraic formulation of noncommutative geometry. The SO(10) symmetry is broken by a 45-Higgs and the Majorana mass term for the right neutrinos (126-Higgs) to the standard model structure group. We study the case where the fermion masses are as general as possible, which leads to two 10-multiplets, four 120-multiplets and two additional 126-multiplets of Higgs fields. This Higgs structure differs considerably from the two Higgs multiplets 16 ⊗ 16* and 16^c ⊗ 16* used by Chamseddine and Fröhlich. We find the usual tree level predictions of noncommutative geometry: , and g₂=g₃ as well as m_H≤ m_t.

We reanalyze the time evolution of the system in the language of certain spectral function whose Fourier transforms give the time-dependent survival and transition amplitudes. Approximating the spectral function by a one-pole ansatz we obtain insight into the limitation of the validity of the one-pole approximation. It will be shown that the same validity restrictions apply to the known formulae of the Weisskopf–Wigner approximation as well. The present analysis can also be applied to the effect of so-called vacuum regeneration of K_L and K_S. As a result of this possibility new contributions to the well-known oscillatory terms will enter the time-dependent transition probabilities. It will be shown that the order of magnitude of this new effect is very small and, in principle, its exact determination lies outside the scope of the one-pole ansatz.

By the use of the quasiclassical limit of Baxter's eight-vertex R matrix, an elliptic generalization of the Knizhnik–Zamolodchikov equation is constructed. An integral representation for the solution of this equation is obtained via the off-shell Bethe ansatz. It is shown that there exists a gauge transformation connecting this equation with the Knizhnik–Zamolodchikov–Bernard equation for the SU(2) WZNW model on a torus.

The Klein paradox is reassessed by considering the properties of a finite square well or barrier in the Dirac equation. It is shown that spontaneous positron emission occurs for a well if the potential is strong enough. The vacuum charge and lifetime of the well are estimated. If the well is wide enough, a seemingly constant current is emitted. These phenomena are transient whereas the tunnelling first calculated by Klein is time-independent. Klein tunnelling is a property of relativistic wave equations, not necessarily connected with particle emission. The Coulomb potential is investigated in this context: it is shown that a heavy nucleus of sufficiently large Z will bind positrons. Correspondingly, it is expected that as Z increases the Coulomb barrier will become increasingly transparent to positrons. This is an example of Klein tunnelling.