Perturbation theory in the dilation model

It is shown that the ln ? factors, found by Li and Pagels in perturbative expansions in ? around spontaneously broken chiral symmetry limits, become factors of ?^?1 in the dilaton in model. The method also furnishes an improved derivation of the Li-Pagels result.     

Perturbation theory for relativistic Lee model

Proof of convergence of perturbation series for the S matrix elements is given for the relativistic Lee model, subject to the validity of an hypothesis explained in the paper. A proof of isometry for the wave operators is also given.     

Perturbation theory for the anomaly-free chiral Schwinger model

We apply perturbation theory to the gauge invariant version of the chiral Schwinger model. The cancellation of anomalies is shown explicitly in terms of Feynman diagrams. We calculate the exact propagators for the gauge field, for the Wess-Zumino field and for the mixing between these fields. Using these propagators, we demonstrate the existence of a massive state.     

Perturbation theory and the parton model in QCD

We prove that for any process which admits a parton-model interpretation, the naive parton model can be modified to include the effects of QCD interactions to all orders in perturbation theory. This requires that the mass singularities in quark and gluon inclusive cross sections factor into universal functions which renormalize the naive parton model distribution and decay functions. We prove that this factorization takes place for all leading and non-leading logs and thus check consistency of the parton model to all orders in perturbation theory.     

Ginzburg-Landau theory for higher order phase transition

Ginzburg-Landau theory for studying phase transitions of higher order has been derived using coarse graining and lattice formulation within Ehrenfest thermodynamics. Our developed Hamiltonian leads directly to the functional of the system. We studied the evolution of the order parameter using our developed model equations for third and fourth order phase transitions. The periodic nature of the system can be likened to spatially varying periodic soliton/antisoliton lattice of holes in condensate. This is different from what one observes for any conventional solitary wave in the second order phase regime.     

Yang-Lee theory for a nonequilibrium phase transition

To analyze phase transitions in a nonequilibrium system, we study its grand canonical partition function as a function of complex fugacity. Real and positive roots of the partition function mark phase transitions. This behavior, first found by Yang and Lee under general conditions for equilibrium systems, can also be applied to nonequilibrium phase transitions. We consider a one-dimensional diffusion model with periodic boundary conditions. Depending on the diffusion rates, we find real and positive roots and can distinguish two regions of analyticity, which can be identified with two different phases. In a region of the parameter space, both of these phases coexist. The condensation point can be computed with high accuracy.     

Simplifying experiments with a Mandelbrot set model of the phase transition theory

The study of the Mandelbrot set (MS) is a promising new approach to the phase transition theory. We suggest two improvements which drastically simplify the construction of the MS. They could be used to modify existing computer programs so that they start building the MS properly not only for the simplest families. This allows us to add one more parameter to the base function of the MS and demonstrate that this is not enough to make the phase diagram connected. The text was submitted by the author in English.     

Simplifying experiments with a Mandelbrot set model of the phase transition theory

The study of the Mandelbrot set (MS) is a promising new approach to the phase transition theory. We suggest two improvements which drastically simplify the construction of the MS. They could be used to modify existing computer programs so that they start building the MS properly not only for the simplest families. This allows us to add one more parameter to the base function of the MS and demonstrate that this is not enough to make the phase diagram connected.     

Tunneling estimates of paramagnon suppression of superconductivity in transition metals

New experimental estimates are given of the separate electron-phonon (λ_ph) and paramagnon (λ_S) contributions to mass renormalization for the transition metals Nb and V, from recent tunneling results. Our analysis, which is the first of its kind, is based on the recent demonstration of Daams, Mitrovic, and Carbotte of a simple rescaling of the Eliashberg equations using an effective coupling parameter $\text{λ}{}_{\mathrm{ph}}\text{(1+λ}{}_{\mathrm{S}}\text{)}$. The results provide a consistent picture of superconductivity in these transition elements from tunneling, in substantially improved agreement with other measurements. We conclude that spin fluctuations reduce the electron-phonon T_c values in Nb and V by 25% and 45%, respectively.     

Effective scalar field theory for the electroweak phase transition

We investigate an effective model for the finite-temperature symmetry-restoration phase transition of the electroweak theory. It is obtained by dimensional reduction of the (3 + 1)-dimensional full theory and by subsequent integration over all static gauge degrees of freedom. The resulting theory corresponds to a 3-dimensional O(4) ferromagnet containing cubic and quartic terms of the field in its potential function. Possible nonperturbative effects of a magnetic screening mass are parametrically included in the potential. We analyse the theory using mean-field and numerical Monte Carlo (MC) simulation methods. At the value of the physical Higgs mass, m_H = 37 GeV, considered in the present investigation, we find a discontinuous symmetry-restoring phase transition. We determine the critical temperature, order parameter jump, interface tension and latent heat characteristics of the transition. The Monte Carlo results indicate a somewhat weaker first-order phase transition as compared to the mean-field treatment, demonstrating that non-perturbative fluctuations of the Higgs field are relevant. This effect is especially important for the interface tension. Any observation of hard first-order transition could result only from non-perturbative effects related to the gauge degrees of freedom.     

Perturbation theory in the Federbush model: Induced interaction terms

We study elastic scattering and production amplitudes in a theory of two massive spinor fields in two space-time dimensions with a current-pseudocurrent interaction (the Federbush model). In contrast to a claim in the recent literature, the results of perturbation theory in the lowest non-trivial orders are consistent with the explicit solution, although massive-Thirring-coupling counter terms must be introduced in order to reproduce the vanishing particle-antiparticle amplitudes of the exact solution.     

Second order phase transition in two dimensional sine-Gordon field theory—Lattice model

Two dimensional sine-Gordon (SG) field theory on a lattice is studied using the single-site basis variational method of Drell and others. The nature of the phase transition associated with the spontaneous symmetry breakdown in a SG field system is clarified to be of second order. A generalisation is offered for a SG-type field theory in two dimensions with a potential of the from [cos ⁿ (√λ/m)ϕ−1].     

Perturbation theory for kinds

In this paper we prove the validity of formal asymptotic results on perturbation theory for kind solutions of the sine-Gordon equation, originally obtained by McLaughlin and Scott. We prove that for appropriate perturbations, of size in an appropriate norm, slowly varying in time in the rest frame of the kink, the shape of the kink is unaltered in theL norm toO() for a time ofO(1/). The kink parameters, which represent its velocity and centre, evolve slowly in time in the way predicted by the asymptotics. The method of proof uses an orthogonal decomposition of the solution into an oscillatory part and a one-dimensional zero-mode term. The slow evolution of the kink parameters is chosen so as to suppress secular evolution of the zero-mode.Partially supported as a graduate student at Princeton University of NSF grant 215 6211     

Chiral phase transition from string theory

The low energy dynamics of a certain D-brane configuration in string theory is described at weak t'Hooft coupling by a nonlocal version of the Nambu-Jona-Lasinio model. We study this system at finite temperature and strong t'Hooft coupling, using the string theory dual. We show that for sufficiently low temperatures chiral symmetry is broken, while for temperatures larger then the critical value, it gets restored. We compute the latent heat and observe that the phase transition is of the first order.