Narrow Results

In this paper we explore the dependence on the gauge-fixing condition of several quantities in the U(1) Higgs model at finite temperature and chemical potential. We compute the effective potential at the one-loop level, using a gauge-fixing condition that depends on μ and which allows to decouple the contributions of the different fields in the model. In this way we get the mass spectrum and the characterization of the phase transition, pointing out in each case how these quantities depend on the gauge-fixing parameter ξ. When μ vanishes, we agree with previous results if ξ=0. The gauge dependence problem is also analyzed from the perspective of the Nielsen identities.

The contemporary use of Dyson-Schwinger equations in hadronic physics is exemplified via applications to the calculation of pseudoscalar meson masses, and inclusive deep inelastic scattering with a determination of the pion's valence-quark distribution function.

Evolution of structure functions and their moments at low and moderate Q² is studied in the chiral field theory. Evolution equations based on perturbation expansion in the coupling constant of the effective theory are derived and solved for the moments. The kernels of evolution arising from different processes have been calculated with contributions from direct and cross channels, the interference terms being non-negligible in the kinematic regions under consideration. This is shown to lead to flavor-dependence of the kernels which manifests in observable effects. The invalidity of the probabilistic approach to the evolution process is also pointed out.

A mechanism is discussed to obtain light scalar fields from a spontaneously broken continuous symmetry without explicitly breaking it. If there is a continuous manifold of classical vacua in orbit space, its tangent directions describe classically massless fields that may acquire mass from perturbations of the potential that do not break the symmetry. We consider the simplest possible example, involving a scalar field in the adjoint representation of SU(N). We study the scalar mass spectrum and its renormalization group running at one-loop level including scalar and pseudoscalar Yukawa couplings to a massive Dirac fermion.

We explain the origin of the mass for the Nambu–Goldstone bosons when there is a chemical potential in the action which explicitly breaks the symmetry. The method is based on the number of independent histories for the interaction of the pair of Nambu–Goldstone bosons with the degenerate vacuum (triangle relations). The analysis suggests that under some circumstances, pairs of massive Nambu–Goldstone bosons can become a single degree of freedom with an effective mass defined by the superposition of the individual masses of each boson. Possible mass oscillations for the Nambu–Goldstone bosons are discussed.

We consider scalar field theories invariant under extended shift symmetries consisting of higher order polynomials in the spacetime coordinates. These generalize ordinary shift symmetries and the linear shift symmetries of the galileons. We find Wess–Zumino Lagrangians which transform up to total derivatives under these symmetries, and which possess fewer derivatives per field and lower order equations of motion than the strictly invariant terms. In the nonrelativistic context, where the extended shifts are purely spatial, these theories may describe multi-critical Goldstone bosons. In the relativistic case, where the shifts involve the full spacetime coordinate, these theories generally propagate extra ghostly degrees of freedom.

We present some general approach to emergent gauge theories and consider in significant detail the emergent tensor field gravity case. In essence, an arbitrary local theory of a symmetric two-tensor field H_μν in Minkowski spacetime is considered, in which the equations of motion are required to be compatible with a nonlinear σ model type length-fixing constraint leading to spontaneous Lorentz invariance violation, SLIV (M is the proposed scale for SLIV). Allowing the parameters in the Lagrangian to be adjusted so as to be consistent with this constraint, the theory turns out to correspond to linearized general relativity in the weak field approximation, while some of the massless tensor Goldstone modes appearing through SLIV are naturally collected in the physical graviton. The underlying diffeomophism invariance emerges as a necessary condition for the tensor field H_μν not to be superfluously restricted in degrees of freedom, apart from the constraint due to which the true vacuum in the theory is chosen by SLIV. The emergent theory appears essentially nonlinear, when expressed in terms of the pure Goldstone tensor modes and contains a plethora of new Lorentz and CPT violating couplings. However, these couplings do not lead to physical Lorentz violation once this tensor field gravity is properly extended to conventional general relativity.