Constraining Monopoles by Topology: an Autonomous System

We find both analytical and numerical solutions of SU(2) Yang-Mills with an adjoint Higgs field within both closed and open tubes whose sections are spherical caps. This geometry admits a smooth limit in which the space-like metric is flat and, moreover, allows one to use analytical tools which in the flat case are not available. Some of the analytic configurations, in the limit of vanishing Higgs coupling, correspond to magnetic monopoles and dyons living within this tube-shaped domain. However, unlike what happens in the standard case, analytical solutions can also be found in the case in which the Higgs coupling is non-vanishing. We further show that the system admits long-lived breathers.Comment: 20 pages, 9 figures, minor corrections, version accepted in JHE

Casimir energy in the Gribov-Zwanziger approach to QCD

In this paper we study the Casimir energy of QCD within the Gribov-Zwanziger approach. In this model non-perturbative effects of gauge copies are properly taken into account. We show that the computation of the Casimir energy for the MIT bag model within the (refined) Gribov-Zwanziger approach not only gives the correct sign but it also gives an estimate for the radius of the bag.Comment: 5 pages, No figures. The discussion about the constraints on the RGZ parameters (as well as about the corresponding estimates) imposed by the requirement to have the correct behaviour of the Casimir energy has been expanded. Version accepted for publication on Physical Review

Spin-1 gravitational waves and their natural sources

Non-vacuum exact gravitational waves invariant for a non Abelian two-dimensional Lie algebra generated by two Killing fields whose commutator is of light type, are described. The polarization of these waves, already known from previous works, is related to the sources. Non vacuum exact gravitational waves admitting only one Killing field of light type are also discussed.Comment: 10 pages, late

Aristippus and Xenophon as Plato’s contemporary literary rivals and the role of gymnastikè (γυμναστική)

Plato was a Socrates’ friend and disciple, but he wasn’t the only one. No doubt, Socrates had many followers, however, the majority of their work is lost. Was there any antagonism among his followers? Who succeeded in interpreting Socrates? Who could be considered as his successor? Of course, we don’t know if these questions emerged after the death of Socrates, but the Greek doxography suggests that there was a literary rivalry. As we underlined earlier, most unfortunately, we can’t examine all of them thoroughly due to the lack of their work, but we can scrutinize Xenophon’s and Aristippus’ work. All of them, Plato, Xenophon and Aristippus, presented to a certain extent their ideas concerning education. Furthermore, they have not neglected the matter of gymnastikè, but what is exactly the role of physical education in their work? Are there any similarities or any differences between them? Since, Xenophon and Aristippus (as well as Plato) seem to be in favor of gymnastikè, it is necessary to understand its role

Generalized Hedgehog ansatz and Gribov copies in regions with non trivial topologies

In this paper the arising of Gribov copies both in Landau and Coulomb gauges in regions with non-trivial topologies but flat metric, (such as closed tubes S1XD2, or RXT2) will be analyzed. Using a novel generalization of the hedgehog ansatz beyond spherical symmetry, analytic examples of Gribov copies of the vacuum will be constructed. Using such ansatz, we will also construct the elliptic Gribov pendulum. The requirement of absence of Gribov copies of the vacuum satisfying the strong boundary conditions implies geometrical constraints on the shapes and sizes of the regions with non-trivial topologies.Comment: 25 pages; Version accepted for publication on Physical Review D. New References include