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Register a new userSome remarks on the spectral functions of the Abelian Higgs Model
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We consider the unitary Abelian Higgs model and investigate its spectral functions at one-loop order. This analysis allows to disentangle what is physical and what is not at the level of the elementary particle propagators, in conjunction with the Nielsen identities. We highlight the role of the tadpole graphs and the gauge choices to get sensible results. We also introduce an Abelian Curci-Ferrari action coupled to a scalar field to model a massive photon which, like the non-Abelian Curci-Ferarri model, is left invariant by a modified non-nilpotent BRST symmetry. We clearly illustrate its non-unitary nature directly from the spectral function viewpoint. This provides a functional analogue of the Ojima observation in the canonical formalism: there are ghost states with nonzero norm in the BRST-invariant states of the Curci-Ferrari model.
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We study vortex solutions in a theory with dynamics governed by two weakly coupled Abelian Higgs models, describing a hidden sector and a visible sector. We analyze the radial dependence of the axially symmetric solutions constructed numerically and discuss the stability of vortex configurations for different values of the model parameters, studying in detail vortex decay into lower energy configurations. We find that even in a weak coupling regime vortex solutions strongly depend on the parameters of both the visible and hidden sectors. We also discuss on qualitative grounds possible implications of the existence of a hidden sector in connection with superconductivity.
Dependence of Greens functions for the Curci-Ferrari model on the parameter resembling the gauge parameter in massless Yang-Mills theories is investigated. It is shown that the generating functional of vertex functions (effective action) depends on this parameter on-shell.
We investigate in detail the phase diagram of the Abelian-Higgs model in one spatial dimension and time (1+1D) on a lattice. We identify a line of first order phase transitions separating the Higgs region from the confined one. This line terminates in a quantum critical point above which the two regions are connected by a smooth crossover. We analyze the critical point and find compelling evidences for its description as the product of two non-interacting systems, a massless free fermion and a massless free boson. However, we find also some surprizing results that cannot be explained by our simple picture, suggesting this newly discovered critical point to be an unusual one.
The two parameters quantum algebra $SU_{p,k}(2)$ can be obtained from a single parameter algebra $SU_q(2)$. This fact gives some relations between $SU_{p,k}(2)$ quantities and the corresponding ones of the $SU_q(2)$ algebra. In this paper are mentioned the relations concerning: Casimir operators, eigenvectors, matrix elements, Clebsch Gordan coefficients and irreducible tensors.
We study the properties of a single magnetic vortex and magnetic vortex lattices in a generalization of the Abelian Higgs model containing the simplest derivative interaction that preserves the $U(1)$ gauge symmetry of the original model. The paper is motivated by the study of finite isospin chiral perturbation theory in a uniform, external : since pions are Goldstone bosons of QCD (due to chiral symmetry breaking by the QCD vacuum), they interact through momentum dependent terms. We introduce a uniform external magnetic field and find the asymptotic properties of single vortex solutions and compare them to the well-known solutions of the standard Abelian Higgs Model. Furthermore, we study the vortex lattice solutions near the upper critical field using the method of successive approximations, which was originally used by Abrikosov in his seminal paper on type-II superconductors. We find the vortex lattice structure, which remains hexagonal as in the standard Abelian Higgs model, and condensation energy of the vortex lattices relative to the normal vacuum (in a uniform magnetic field).
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