Restricted Weyl symmetry and spontaneous symmetry breakdown of conformal symmetry

In this paper, we elucidate the relation between the restricted Weyl symmetry and spontaneous symmetry breakdown of conformal symmetry. Using a scalar–tensor gravity, we show that the restricted Weyl symmetry leads to spontaneous symmetry breakdown of a global scale symmetry when the vacuum expectation value of a scalar field takes a nonzero value. It is then shown that this spontaneous symmetry breakdown induces spontaneous symmetry breakdown of special conformal symmetry in a flat Minkowski spacetime, but the resultant Nambu–Goldstone boson is not an independent physical mode but expressed in terms of the derivative of the dilaton which is the Nambu–Goldstone boson of the global scale symmetry. In other words, the theories which are invariant under the general coordinate transformation and the restricted Weyl transformation exhibit a Nambu–Goldstone phase where both special conformal transformation and dilatation are spontaneously broken while preserving the Poincaré symmetry.

On trilinear terms in the scalar potential of 3-3-1 gauge models

The trilinear terms of the form [Formula: see text] in the scalar potential of a 3-3-1 gauge model are considered. When looking for the eigenbasis of the massive physical Higgs bosons that survive the spontaneous symmetry breakdown of the model — in light of the observed SM-like Higgs boson with mass [Formula: see text] GeV reported in 2012 at the LHC — one gets a strong constraint to the cubic term. It has to be [Formula: see text], in flagrant contradiction with the large one [Formula: see text] which is propagated in the literature to date.

Critical fermion density for restoring spontaneously broken symmetry

We show how the phenomenon of spontaneous symmetry breakdown is affected by the presence of a sea of fermions in the system. When its density exceeds a critical value, the broken symmetry can be restored. We calculate the critical value and discuss the consequences for three different physical systems: First, for the Standard Model (SM) of particle physics, where the spontaneous symmetry breakdown leads to nonzero masses of intermediate gauge bosons and fermions. The symmetry restoration will greatly enhance various processes with dramatic consequences for the early universe. Second, for the Gell-Mann–Lévy [Formula: see text]-model of nuclear physics, where the symmetry breakdown gives rise to the nucleon and meson masses. The symmetry restoration may have important consequences for formation or collapse of stellar cores. Third, for the superconductive phase of condensed-matter, where the BCS condensate at low-temperature may be destroyed by a too large electron density.

A LAGRANGIAN FOR THE CHIRAL (½, 0) ⊕ (0, ½) QUARTET NUCLEON RESONANCES

We study the nucleon and three N* resonances' properties in an effective linear realization chiral SUL(2)×SUR(2) and UA(1) symmetric Lagrangian. We place the nucleon fields into the so-called "naive" (½, 0) ⊕ (0, ½) and "mirror" (0, ½) ⊕ (½, 0) (fundamental) representations of SUL(2)×SUR(2), two of each — distinguished by their UA(1) chiral properties, as defined by an explicit construction of the nucleon interpolating fields in terms of three quark (Dirac) fields. We construct the most general one-meson–baryon chiral interaction Lagrangian assuming various parities of these four nucleon fields. We show that the observed masses of the four lowest-lying nucleon states can be well reproduced with the effective Lagrangian, after spontaneous symmetry breakdown, without explicit breaking of UA(1) symmetry. This does not mean that explicit UA(1) symmetry breaking does not occur in baryons, but rather that it does not have a unique mass prediction signature that exists, e.g. in the case of spinless mesons. We also consider briefly the axial couplings with chiral representation mixing.

SPONTANEOUS SYMMETRY BREAKDOWN IN FUZZY SPHERES

We study and analyse the questions regarding breakdown of global symmetry on noncommutative sphere. We demonstrate this by considering a complex scalar field on a fuzzy sphere and isolating Goldstone modes. We discuss the role of nonlocal interactions present in these through geometrical considerations.

CLASSICAL SOLUTIONS OF GHOST CONDENSATION MODELS

Motivated by ideas obtained from both ghost condensation and gravitational Higgs mechanism, we attempt to find classical solutions in the unitary gauge in general ghost condensation models. It is shown that depending on the form of scalar fields in an action, there are three kinds of exact solutions, which are (anti-) de Sitter space–time, polynomially expanding universes and flat Minkowski space–time. We briefly comment on gravitational Higgs mechanism in these models where we have massive gravitons of five degrees of freedom and one unitary scalar field (Nambu–Goldstone boson) after spontaneous symmetry breakdown of general coordinate reparametrization invariance. The models at hand are free from the problem associated with the non-unitary propagating mode.