International Journal of Modern Physics A

We discuss some formal aspects of quantum anomalies with an emphasis on the regularization of field theory. We briefly review how ambiguities in perturbation theory have been resolved by various regularization schemes. To single out the true quantum anomaly among ambiguities, the combined ideas of PCAC, soft pion limit and renormalizability were essential. As for the formal treatment of quantum anomalies, we mainly discuss the path integral formulation both in continuum and lattice theories. In particular, we discuss in some detail the recent development in the treatment of chiral anomalies in lattice gauge theory.

We study the effect of magnetic field on the dominant neutrino emission processes in neutron stars. The processes are first calculated for the case when the magnetic field does not exceed the critical value to confine electrons to the lowest Landau state. We consider here magnetic fields up to ~10¹⁹ Gauss. We find that fields of strength 10¹⁵-10¹⁶ Gauss have significant effect on the neutronization process, for the direct URCA process the effect of the magnetic field becomes significant only at ~10¹⁹ Gauss. In order to estimate the effect we derive the composition of cold nuclear matter at high densities and in beta equilibrium, a situation appropriate for neutron stars. The hadronic interactions are incorporated through the exchange of scalar and vector mesons in the framework of relativistic mean field theory. In addition the effects of anomalous magnetic moments of nucleons are also considered.

In terms of the two-variable Hermite polynomials' properties we derive the common eigenstates |q,λ> of two permutable operators (a^†+b)(a+b^†) and a^†a-b^†b, where q is discrete and λ is continuous. These states constitute a complete and orthonormal representation. Applications of the |q,λ> are discussed.

Within the complete heavy quark effective field theory (HQEFT), the QCD sum rule approach is used to evaluate the decay constants including 1/m_Q corrections and the Isgur–Wise function and other additional important wave functions concerned at 1/m_Q for the heavy–light mesons. The number of unknown wave functions or form factors in HQEFT is shown to be much less than the one in the usual heavy quark effective theory (HQET). The values of wave functions at zero recoil are found to be consistent with the ones extracted from the interesting relations (which are resulted from the HQEFT) between the hadron masses and wave functions at zero recoil. The results for the decay constants are consistent with the ones from full QCD sum rule and Lattice calculations. The 1/m_Q corrections to the scaling law are found to be small in HQEFT, which demonstrates again the validity of 1/m_Q expansion in HQEFT. It is also shown that the residual momentum v·k of heavy quark within heavy–light hadrons is indeed around the binding energy of the heavy hadrons, which turns out to be in agreement with the expected one in the HQEFT. Therefore such a calculation provides a consistent check on the HQEFT and shows that the HQEFT is more reliable than the usual HQET for describing a slightly off-mass shell heavy quark within hadron as the usual HQET seems to lead to large 1/m_Q corrections in evaluating the meson decay constants. It is emphasized that the introduction of the "dressed heavy quark" mass is useful for the heavy–light mesons (Qq) with , while for heavy–heavy bound states (ψ₁ψ₂) with masses m₁, , like bottom-charm hadrons or similarly for muonium in QED, one needs to treat both particles as heavy effective particles via 1/m₁ and 1/m₂ expansions and redefine the effective bound states and modified "dressed heavy quark" masses within the HQEFT.

We study the XXZ chain with a boundary at massless regime -1<Δ<1. We give the free field realizations of the boundary vacuum state and its dual. Using these realizations, we give the integral representations for the correlation functions.

Three family SU(3)_C×SU(2)_L×U(1)_Y string models in several constructions generically possess two features: (i) an extra local anomalous U(1)_A and (ii) numerous (often fractionally charged) exotic particles beyond those in the minimal supersymmetric model (MSSM). Recently, we demonstrated that the observable sector effective field theory of such a free fermionic string model can reduce to that of the MSSM, with the standard observable gauge group being just SU(3)_C× SU(2)_L× U(1)_Y and the SU(3)_C× SU(2)_L× U(1)_Y-charged spectrum of the observable sector consisting solely of the MSSM spectrum. An example of a model with this property was shown. We continue our investigation of this model by presenting a large set of different flat directions of the same model that all produce the MSSM spectrum. Our results suggest that even after imposing the conditions for the decoupling of exotic states, there may remain sufficient freedom to satisfy the remaining phenomenological constraints imposed by the observed data.