International Journal of Modern Physics A

Quark models with four-fermion interaction including derivatives of fields in the strong coupling regime are used to implement composite-Higgs extensions of the Standard Model. In this approach the dynamical breaking of chiral symmetry occurs in two (or more) channels (near polycritical values for coupling constants), giving rise to two (or more) composite Higgs doublets. Two types of models are built for which Flavor Changing Neutral Currents (FCNC) are naturally suppressed. In the first Model I the second Higgs doublet is regarded as a radial excitation of the first one. In the second Model II the quasilocal Yukawa interaction with Higgs doublets reduces at low energies to a conventional local one where each Higgs doublet couples to a definite charge current and its v.e.v. brings the mass either to up- or to down-components of fermion doublets. For the special configuration of four-fermion coupling constants the dynamical CP violation in the Higgs sector appears as a result of complexity of v.e.v. for Higgs doublets.

In this paper we develop an irreducible antifield BRST–anti-BRST formalism for reducible gauge theories.

The Hamiltonian of the N-particle Calogero model can be expressed in terms of generators of a Lie algebra for a definite class of representations. Maintaining this Lie algebra, its representations, and the flatness of the Riemannian metric belonging to the second order differential operator, the set of all possible quadratic Lie algebra forms is investigated. For N = 3 and N = 4 such forms are constructed explicitly and shown to correspond to exactly solvable Sutherland models. The results can be carried over easily to all N.

We study here the relationship between the area preserving diffeomorphism and quantum group with the deformation of symplectic structure and Berry phase in the Landau problem of 2D electron gas in a magnetic field. It is argued that while the area preserving diffeomorphism leads to the quantization of the symmetry , the deformation of the symplectic structure leads to the quantization of the system having the relation Δp. Δ q=2πnℏ, n being an odd integer giving rise to the Berry phase e^i2πμ with n=2μ. A possible link between the deformation parameter q of the deformed algebra with the Berry phase factor arising out of the quantization procedure has been suggested. Finally, the latticization of space associated with the quantum group and its connection with the Z_p spin system is discussed.

We study the possible mixings between gauge vector fields and scalar fields through their self-energies, arising in models with two Higgs doublets. We derive the relevant set of Schwinger–Dyson equations and the Ward identities that compel the longitudinal parts of the field propagators. A linear R_ξ gauge is used and the results are given at all orders in perturbative theory, and some particular aspects of the one-loop case are stressed.

It is well-known that the winding number of the Skyrmion can be identified as the baryon number. We show in this paper that this result can also be established using the Atiyah–Singer index theorem and spectral flow arguments. We argue that this proof suggests that there are light quarks moving in the field of the Skyrmion. We then show that if these light degrees of freedom are averaged out, the low energy excitations of the Skyrmion are in fact spinorial. A natural consequence of our approach is the prediction of a state and its excitations in addition to the nucleon and delta. Using the recent numerical evidence for the existence of Skyrmions with discrete spatial symmetries, we further suggest that the the low energy spectrum of many light nuclei may possess a parity doublet structure arising from a subtle topological interaction between the slow Skyrmion and the fast quarks. We also present tentative experimental evidence supporting our arguments.

We compute the contribution to the modulus of the one-loop effective action in pure non-Abelian Chern–Simons theory in an arbitrary covariant gauge. We find that the results are dependent on both the gauge parameter (α) and the metric required in the gauge fixing. A contribution arises that has not been previously encountered; it is of the form . This is possible as in three dimensions α is dimensionful. A variant of proper time regularization is used to render these integrals well behaved (although no divergences occur when the regularization is turned off at the end of the calculation). Since the original Lagrangian is unaltered in this approach, no symmetries of the classical theory are explicitly broken and ∊_μλν is handled unambiguously since the system is three-dimensional at all stages of the calculation. The results are shown to be consistent with the so-called Nielsen identities which predict the explicit gauge parameter dependence using an extension of BRS symmetry. We demonstrate that this α dependence may potentially contribute to the vacuum expectation values of products of Wilson loops.