Integral form of Yang-Mills equations and its gauge invariant conserved charges

Despite the fact that the integral form of the equations of classical electrodynamics is well known, the same is not true for non-Abelian gauge theories. The aim of the present paper is threefold. First, we present the integral form of the classical Yang-Mills equations in the presence of sources and then use it to solve the long-standing problem of constructing conserved charges, for any field configuration, which are invariant under general gauge transformations and not only under transformations that go to a constant at spatial infinity. The construction is based on concepts in loop spaces and on a generalization of the non-Abelian Stokes theorem for two-form connections. The third goal of the paper is to present the integral form of the self-dual Yang-Mills equations and calculate the conserved charges associated with them. The charges are explicitly evaluated for the cases of monopoles, dyons, instantons and merons, and we show that in many cases those charges must be quantized. Our results are important in the understanding of global properties of non-Abelian gauge theories.

No-pole condition in Landau gauge: Properties of the Gribov ghost form factor and a constraint on the 2d gluon propagator

We study general properties of the Landau-gauge Gribov ghost form factor sigma(p(2)) for SU(N-c) Yang-Mills theories in the d-dimensional case. We find a qualitatively different behavior for d = 3, 4 with respect to the d = 2 case. In particular, considering any (sufficiently regular) gluon propagator D(p(2)) and the one-loop-corrected ghost propagator, we prove in the 2d case that the function sigma(p(2)) blows up in the infrared limit p -> 0 as -D(0) ln(p(2)). Thus, for d = 2, the no-pole condition sigma(p(2)) < 1 (for p(2) > 0) can be satisfied only if the gluon propagator vanishes at zero momentum, that is, D(0) = 0. On the contrary, in d = 3 and 4, sigma(p(2)) is finite also if D(0) > 0. The same results are obtained by evaluating the ghost propagator G(p(2)) explicitly at one loop, using fitting forms for D(p(2)) that describe well the numerical data of the gluon propagator in two, three and four space-time dimensions in the SU(2) case. These evaluations also show that, if one considers the coupling constant g(2) as a free parameter, the ghost propagator admits a one-parameter family of behaviors (labeled by g(2)), in agreement with previous works by Boucaud et al. In this case the condition sigma(0) <= 1 implies g(2) <= g(c)(2), where g(c)(2) is a "critical" value. Moreover, a freelike ghost propagator in the infrared limit is obtained for any value of g(2) smaller than g(c)(2), while for g(2) = g(c)(2) one finds an infrared-enhanced ghost propagator. Finally, we analyze the Dyson-Schwinger equation for sigma(p(2)) and show that, for infrared-finite ghost-gluon vertices, one can bound the ghost form factor sigma(p(2)). Using these bounds we find again that only in the d = 2 case does one need to impose D(0) = 0 in order to satisfy the no-pole condition. The d = 2 result is also supported by an analysis of the Dyson-Schwinger equation using a spectral representation for the ghost propagator. Thus, if the no-pole condition is imposed, solving the d = 2 Dyson-Schwinger equations cannot lead to a massive behavior for the gluon propagator. These results apply to any Gribov copy inside the so-called first Gribov horizon; i.e., the 2d result D(0) = 0 is not affected by Gribov noise. These findings are also in agreement with lattice data.

Integrable Models: from Dynamical Solutions to String Theory

We review the status of integrable models from the point of view of their dynamics and integrability conditions. A few integrable models are discussed in detail. We comment on the use it is made of them in string theory. We also discuss the SO(6) symmetric Hamiltonian with SO(6) boundary. This work is especially prepared for the 70th anniversaries of Andr, Swieca (in memoriam) and Roland Koberle.

Gauge and integrable theories in loop spaces

We propose an integral formulation of the equations of motion of a large class of field theories which leads in a quite natural and direct way to the construction of conservation laws. The approach is based on generalized non-abelian Stokes theorems for p-form connections, and its appropriate mathematical language is that of loop spaces. The equations of motion are written as the equality of a hyper-volume ordered integral to a hyper-surface ordered integral on the border of that hyper-volume. The approach applies to integrable field theories in (1 + 1) dimensions, Chern-Simons theories in (2 + 1) dimensions, and non-abelian gauge theories in (2 + 1) and (3 + 1) dimensions. The results presented in this paper are relevant for the understanding of global properties of those theories. As a special byproduct we solve a long standing problem in (3 + 1)-dimensional Yang-Mills theory, namely the construction of conserved charges, valid for any solution, which are invariant under arbitrary gauge transformations. (C) 2012 Elsevier B.V. All rights reserved.

All-loop finiteness of the two-dimensional noncommutative supersymmetric gauge theory

Within the superfield approach, we discuss the two-dimensional noncommutative super-QED. Its all-order finiteness is explicitly shown. Copyright (C) EPLA, 2012

Vortices in the extended Skyrme-Faddeev model

We construct analytical and numerical vortex solutions for an extended Skyrme-Faddeev model in a (3 + 1) dimensional Minkowski space-time. The extension is obtained by adding to the Lagrangian a quartic term, which is the square of the kinetic term, and a potential which breaks the SO(3) symmetry down to SO(2). The construction makes use of an ansatz, invariant under the joint action of the internal SO(2) and three commuting U(1) subgroups of the Poincare group, and which reduces the equations of motion to an ordinary differential equation for a profile function depending on the distance to the x(3) axis. The vortices have finite energy per unit length, and have waves propagating along them with the speed of light. The analytical vortices are obtained for a special choice of potentials, and the numerical ones are constructed using the successive over relaxation method for more general potentials. The spectrum of solutions is analyzed in detail, especially its dependence upon special combinations of coupling constants.

Minimal Landau background gauge on the lattice

We present the first numerical implementation of the minimal Landau background gauge for Yang-Mills theory on the lattice. Our approach is a simple generalization of the usual minimal Landau gauge and is formulated for the general SU(N) gauge group. We also report on preliminary tests of the method in the four-dimensional SU(2) case, using different background fields. Our tests show that the convergence of the numerical minimization process is comparable to the case of a null background. The uniqueness of the minimizing functional employed is briefly discussed.

Can the `yin and yang` BDNF hypothesis be used to predict the effects of rTMS treatment in neuropsychiatry?

Repetitive transcranial magnetic stimulation (rTMS) is a novel technique of non-invasive brain stimulation which has been used to treat several neuropsychiatric disorders such as major depressive disorder, chronic pain and epilepsy. Recent studies have shown that the therapeutic effects of rTMS are associated with plastic changes in local and distant neural networks. In fact, it has been suggested that rTMS induces long-term potentiation (LTP) and long-term depression (LTD) - like effects. Besides the initial positive clinical results; the effects of rTMS are stilt mixed. Therefore new toots to assess the effects of plasticity non-invasively might be useful to predict its therapeutic effects and design novel therapeutic approaches using rTMS. In this paper we propose that brain-derived neurotrophic factor (BDNF) might be such a tool. Brain-derived neurotrophic factor is a neurotrophin that plays a key role in neuronal survival and synaptic strength, which has also been studied in several neuropsychiatric disorders. There is robust evidence associating BDNF with the LTP/LTD processes, and indeed it has been proposed that BNDF might index an increase or decrease of brain activity - the `yin and yang` BDNF hypothesis. In this article, we review the initial studies combining measurements of BDNF in rTMS clinical trials and discuss the results and potential usefulness of this instrument in the field of rTMS. (C) 2008 Elsevier Ltd. All rights reserved.

MHD numerical simulations of colliding winds in massive binary systems - I. Thermal versus non-thermal radio emission

In the past few decades detailed observations of radio and X-ray emission from massive binary systems revealed a whole new physics present in such systems. Both thermal and non-thermal components of this emission indicate that most of the radiation at these bands originates in shocks. O and B-type stars and WolfRayet (WR) stars present supersonic and massive winds that, when colliding, emit largely due to the freefree radiation. The non-thermal radio and X-ray emissions are due to synchrotron and inverse Compton processes, respectively. In this case, magnetic fields are expected to play an important role in the emission distribution. In the past few years the modelling of the freefree and synchrotron emissions from massive binary systems have been based on purely hydrodynamical simulations, and ad hoc assumptions regarding the distribution of magnetic energy and the field geometry. In this work we provide the first full magnetohydrodynamic numerical simulations of windwind collision in massive binary systems. We study the freefree emission characterizing its dependence on the stellar and orbital parameters. We also study self-consistently the evolution of the magnetic field at the shock region, obtaining also the synchrotron energy distribution integrated along different lines of sight. We show that the magnetic field in the shocks is larger than that obtained when the proportionality between B and the plasma density is assumed. Also, we show that the role of the synchrotron emission relative to the total radio emission has been underestimated.

Bourgin-Yang version of the Borsuk-Ulam theorem for Z(pk)-equivariant maps

Let G = Z(pk) be a cyclic group of prime power order and let V and W be orthogonal representations of G with V-G = W-G = W-G = {0}. Let S(V) be the sphere of V and suppose f: S(V) -> W is a G-equivariant mapping. We give an estimate for the dimension of the set f(-1){0} in terms of V and W. This extends the Bourgin-Yang version of the Borsuk-Ulam theorem to this class of groups. Using this estimate, we also estimate the size of the G-coincidences set of a continuous map from S(V) into a real vector space W'.

Monsplasty for Women After Massive Weight Loss

Ptosis with excess skin in the pubic area is a very common deformity in patients after massive weight loss. This deformity requires adequate surgical treatment whether combined with abdominoplasty or not. The enlarged pubogenital area may lead to psychosocial distress and impaired quality of life. A series of 23 women with a mean age of 39.5 years who previously underwent bariatric surgeries and later presented with pubogenital ptosis underwent monsplasty. The preoperative surgical markings and the surgical technique presented are easily reproducible. In this prospective study, the surgical outcomes were assessed by questionnaires applied to the patients, who scored the following parameters: movement dynamics, aesthetic appearance, sexual performance, improved hygiene, and use of clothing items. Four of the parameters assessed (movement dynamics, aesthetic appearance, hygiene, and use of clothing items) showed clear improvement, with scores ranging from good to very good. A small percentage of the patients (13%) reported fair improvement in sexual performance. The findings showed monsplasty to be a simple and reproducible technique with favorable outcomes and low morbidity rates.

Canonical Quantization of a Massive Weyl Field

We construct a consistent theory of a quantum massive Weyl field. We start with the formulation of the classical field theory approach for the description of massive Weyl fields. It is demonstrated that the standard Lagrange formalism cannot be applied for the studies of massive first-quantized Weyl spinors. Nevertheless we show that the classical field theory description of massive Weyl fields can be implemented in frames of the Hamilton formalism or using the extended Lagrange formalism. Then we carry out a canonical quantization of the system. The independent ways for the quantization of a massive Weyl field are discussed. We also compare our results with the previous approaches for the treatment of massive Weyl spinors. Finally the new interpretation of the Majorana condition is proposed.