Dynamical Mass Generation in a Finite-Temperature Abelian Gauge Theory

We write down the gap equation for the fermion self-energy in a finite-temperature abelian gauge theory in three dimensions. The instantaneous approximation is relaxed, momentum-dependent fermion and photon self-energies are considered, and the corresponding Schwinger-Dyson equation is solved numerically. The relation between the zero-momentum and zero-temperature fermion self-energy and the critical temperature T_c, above which there is no dynamical mass generation, is then studied. We also investigate the effect which the number of fermion flavours N_f has on the results, and we give the phase diagram of the theory with respect to T and N_f.Comment: 20 LaTeX pages, 4 postscript figures in a single file, version to appear in Physical Review

Searching for Quantum Solitons in a 3+1 Dimensional Chiral Yukawa Model

We search for static solitons stabilized by heavy fermions in a 3+1 dimensional Yukawa model. We compute the renormalized energy functional, including the exact one-loop quantum corrections, and perform a variational search for configurations that minimize the energy for a fixed fermion number. We compute the quantum corrections using a phase shift parameterization, in which we renormalize by identifying orders of the Born series with corresponding Feynman diagrams. For higher-order terms in the Born series, we develop a simplified calculational method. When applicable, we use the derivative expansion to check our results. We observe marginally bound configurations at large Yukawa coupling, and discuss their interpretation as soliton solutions subject to general limitations of the model.Comment: 27 pp., 7 EPS files; email correspondence to [email protected]

Effect of retardation on dynamical mass generation in two-dimensional QED at finite temperature

The effect of retardation on dynamical mass generation in is studied, in the imaginary time formalism. The photon porarization tensor is evaluated to leading order in 1/N (N is the number of flavours), and simple closed form expressions are found for the fully retarded longitudinal and transverse propagators, which have the correct limit when T goes to zero. The resulting S-D equation for the fermion mass (at order 1/N) has an infrared divergence associated with the contribution of the transverse photon propagator; only the longitudinal contribution is retained, as in earlier treatments. For solutions of constant mass, it is found that the retardation reduces the value of the parameter r (the ratio of twice the mass to the critical temperature) from about 10 to about 6. The gap equation is then solved allowing for the mass to depend on frequency. It was found that the r value remained close to 6. Possibilities for including the transverse propagator are discussed.Comment: 26 pages 8 figure

Effect of Wavefunction Renormalisation in N-Flavour Qed3 at Finite Temperature

A recent study of dynamical chiral symmetry breaking in N-flavour QED$_3$ at finite temperature is extended to include the effect of fermion wavefunction renormalisation in the Schwinger-Dyson equations. The simple ``zero-frequency'' truncation previously used is found to lead to unphysical results, especially as $T \to 0$. A modified set of equations is proposed, whose solutions behave in a way which is qualitatively similar to the $T=0$ solutions of Pennington et al. [5-8] who have made extensive studies of the effect of wavefunction renormalisation in this context, and who concluded that there was no critical $N_c$ (at T=0) above which chiral symmetry was restored. In contrast, we find that our modified equations predict a critical $N_c$ at $T \not= 0$, and an $N-T$ phase diagram very similar to the earlier study neglecting wavefunction renormalisation. The reason for the difference is traced to the different infrared behaviour of the vacuum polarisation at $T=0$ and at $T \not= 0$.Comment: 17 pages + 13 figures (available upon request), Oxford preprint OUTP-93-30P, IFUNAM preprint FT94-39, LaTe

A UV completion of scalar electrodynamics

In previous works, we constructed UV-finite and unitary scalar field theories with an infinite spectrum of propagating modes for arbitrary polynomial interactions. In this paper, we introduce infinitely many massive vector fields into a U(1) gauge theory to construct a theory with UV-finiteness and unitarity.Comment: 25 page

Electric Polarizability of the Nucleon in the Nambu--Jona-Lasinio Model

The electric polarizability of the nucleon is calculated in the soliton approach to the Nambu--Jona-Lasinio model. We analyze the leading-$N_c$ contributions, as well as the effects of rotational $1/N_c$ corrections and $\Delta$-$N$ mass splitting. Our model prediction is substantially reduced compared to other soliton calculations, and is closer to the experimental value.Comment: 16 pages, RevTeX, 3 figures (included, PS, uuencoded), RUB-TPII-55/93 and TPR-93-3

On The Finite Temperature Chern-Simons Coefficient

We compute the exact finite temperature effective action in a 0+1-dimensional field theory containing a topological Chern-Simons term, which has many features in common with 2+1-dimensional Chern-Simons theories. This exact result explains the origin and meaning of puzzling temperature dependent coefficients found in various naive perturbative computations in the higher dimensional models.Comment: 11 pages LaTeX; no figure

Quantum Energies of Strings in a 2+1 Dimensional Gauge Theory

We study classically unstable string type configurations and compute the renormalized vacuum polarization energies that arise from fermion fluctuations in a 2+1 dimensional analog of the standard model. We then search for a minimum of the total energy (classical plus vacuum polarization energies) by varying the profile functions that characterize the string. We find that typical string configurations bind numerous fermions and that populating these levels is beneficial to further decrease the total energy. Ultimately our goal is to explore the stabilization of string type configurations in the standard model through quantum effects. We compute the vacuum polarization energy within the phase shift formalism which identifies terms in the Born series for scattering data and Feynman diagrams. This approach allows us to implement standard renormalization conditions of perturbation theory and thus yields the unambiguous result for this non--perturbative contribution to the total energy.Comment: 26 pages, 20 eps-files combined to 8 figures, minor typos corrected. Version to be published in Nucl. Phys.

From Effective BCS Action to Vortex Dynamics

The topological term in the effective action for the electrically neutral BCS system is discussed. It is applied for the calculation of the transverse force acting on the vortex in the limit of the smooth vortex core and vanishing interlevel distance in the vortex core. The controversy between the topological terms in cond-mat/9703124 and cond-mat/9411047 is resolved.Comment: 9 pages, no Figures, inspired by recent preprint by van Otterlo et al in cond-mat/9703124, corrected after discussion with N.B. Kopni