Collective coordinates of the Skyrme model coupled with fermions

The problem of construction of fiber bundle over the moduli space of the Skyrme model is considered. We analyse an extension of the original Skyrme model which includes the minimal interaction with fermions. An analogy with modili space of the fermion-monopole system is used to construct a fiber bundle structure over the skyrmion moduli space. The possibility of the non-trivial holonomy appearance is considered. It is shown that the effect of the fermion interaction turns the $n$-skyrmion moduli space into a real vector bundle with natural $SO(2n+1)$ connection.Comment: 10 page

Derivative Expansion and the Effective Action for the Abelian Chern-Simons Theory at Higher Orders

We study systematically the higher order corrections to the parity violating part of the effective action for the Abelian Chern-Simons theory in 2+1 dimensions, using the method of derivative expansion. We explicitly calculate the parity violating parts of the quadratic, cubic and the quartic terms (in fields) of the effective action. We show that each of these actions can be summed, in principle, to all orders in the derivatives. However, such a structure is complicated and not very useful. On the other hand, at every order in the powers of the derivatives, we show that the effective action can also be summed to all orders in the fields. The resulting actions can be expressed in terms of the leading order effective action in the static limit. We prove gauge invariance, both large and small of the resulting effective actions. Various other features of the theory are also brought out.Comment: 36 page

Non-trivial Infrared Structure in (2+1)-dimensional Quantum Electrodynamics

We show that the gauge-fermion interaction in multiflavour $(2+1)$-dimensional quantum electrodynamics with a finite infrared cut-off is responsible for non-fermi liquid behaviour in the infrared, in the sense of leading to the existence of a non-trivial fixed point at zero momentum, as well as to a significant slowing down of the running of the coupling at intermediate scales as compared with previous analyses on the subject. Both these features constitute deviations from fermi-liquid theory. Our discussion is based on the leading- $1/N$ resummed solution for the wave-function renormalization of the Schwinger-Dyson equations . The present work completes and confirms the expectations of an earlier work by two of the authors (I.J.R.A. and N.E.M.) on the non-trivial infrared structure of the theory.Comment: 10 pages (LaTex), 5 figures (Postscript

Three-body dispersion-relation N/D equations for the coupled decay channels ppbar (J^{PC}=0^{-+}) --> pi^0 pi^0 pi^0, eta pi^0 pi^0, eta eta pi^0, K Kbar pi^0

During several years the data on different channels ppbar (J^{PC}=0^{-+}) --> 3 mesons presented by Crystal Barrel Collaboration were successfully analyzed by extracting the leading amplitude singularities - pole singularities - with the aim to obtain information about two-meson resonances. But these analyses do not take into account three-body final state interactions (FSI) in an explicitly correct way. This paper is devoted to the consideration of this problem.Comment: 16 pages, no figure

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

Flow Equations for U_k and Z_k

By considering the gradient expansion for the wilsonian effective action S_k of a single component scalar field theory truncated to the first two terms, the potential U_k and the kinetic term Z_k, I show that the recent claim that different expansion of the fluctuation determinant give rise to different renormalization group equations for Z_k is incorrect. The correct procedure to derive this equation is presented and the set of coupled differential equations for U_k and Z_k is definitely established.Comment: 5 page

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

Phase transition in a spring-block model of surface fracture

A simple and robust spring-block model obeying threshold dynamics is introduced to study surface fracture of an overlayer subject to stress induced by adhesion to a substrate. We find a novel phase transition in the crack morphology and fragment-size statistics when the strain and the substrate coupling are varied. Across the transition, the cracks display in succession short-range, power-law and long-range correlations. The study of stress release prior to cracking yields useful information on the cracking process.Comment: RevTeX, 4 pages, 4 Postscript figures included using epsfi

On the Derivative Expansion at Finite Temperature

In this short note, we indicate the origin of nonanalyticity in the method of derivative expansion at finite temperature and discuss some of its consequences.Comment: 7 pages, UR-1363, ER40685-81

Dynamical Symmetry Breaking With a Fourth Generation

Adding a fourth generation to the Standard Model and assuming it to be valid up to some cutoff \Lambda, we show that electroweak symmetry is broken by radiative corrections due to the fourth generation. The effects of the fourth generation are isolated using a Lagrangian with a genuine scalar without self-interactions at the classical level. For masses of the fourth generation consistent with electroweak precision data (including the B \rightarrow K \pi\ CP asymmetries) we obtain a Higgs mass of the order of a few hundreds GeV and a cutoff \Lambda\ around 1-2 TeV. We study the reliability of the perturbative treatment used to obtain these results taking into account the running of the Yukawa couplings of the fourth quark generation with the aid of the Renormalization Group (RG) equations, finding similar allowed values for the Higgs mass but a slightly lower cut-off due to the breaking of the perturbative regime. Such low cut-off means that the effects of new physics needed to describe electroweak interactions at energy above \Lambda\ should be measurable at the LHC. We use the minimal supersymmetric extension of the standard model with four generations as an explicit example of models realizing the dynamical electroweak symmetry breaking by radiative corrections and containing new physics. Here, the cutoff is replaced by the masses of the squarks and electroweak symmetry breaking by radiative corrections requires the squark masses to be of the order of 1 TeV.Comment: 20 pages, 7 figures. New section adde