Using a renormalization group motivated smoothing technique, we investigate the large scale structure of lattice configurations at finite temperature, concentrating on Abelian monopoles identified in the maximally Abelian, the Laplacian Abelian, and the Polyakov gauge. Monopoles are mostly found in regions of large action and topological charge, rather independent of the gauge chosen to detect ...

We derive a simple efficient algorithm for Abelian periods knowing all Abelian squares in a string. An efficient algorithm for the latter problem was given by Cummings and Smyth in 1997. By the way we show an alternative algorithm for Abelian squares. We also obtain a linear time algorithm finding all “long” Abelian periods. The aim of the paper is a (new) reduction of the problem of all Abelia...

We consider Yang-Mills theory in a general class of Abelian gauges. Exploiting the residual Abelian symmetry on a quantum level, we derive a set of Ward identities in functional form, valid to all orders in perturbation theory. As a consequence, the coupling constant is only renormalised through the Abelian two-point function. This implies that asymptotic freedom in all Abelian gauges can be un...

Return words constitute a powerful tool for studying symbolic dynamical systems. They may be regarded as a discrete analogue of the first return map in dynamical systems. In this paper we investigate two abelian variants of the notion of return word, each of them gives rise to a new characterization of Sturmian words. We prove that a recurrent infinite word is Sturmian if and only if each of it...

General properties of Abelian connection in Fedosov deformation quantization are investigated. Criteria of being a finite series for an Abelian connection are presented. Conditions for different symplectic connections to generate the same correction to the Abelian connection are given. A proof that in 2–dimensional case the Abelian connection is an ifinite series is done. A class of symplectic ...

If A and B are Abelian groups, then Hom(A,B) is also an Abelian group under pointwise addition of functions. In this section we will see how Hom gives rise to classes of functors. Let A denote the category of Abelian groups. A covariant functor T : A → A associates to every Abelian group A an Abelian group T (A), and for every homomorphism f : A → B a homomorphism T (f) : T (A)→ T (B), such tha...

We study non-abelian monogenic algebraic number fields (i.e., non-abelian number fields whose rings of integers have a basis of the form {1, α, α, . . . , αn−1} for some α). There are numerous results about abelian monogenic number fields, yet for the non-abelian case little is understood. As our main result, we find an infinite family of non-abelian monogenic degree 6 number fields.

The dual Meissner effect is observed without monopoles in quenched SU(2) QCD with Landau gauge-fixing. Abelian as well as non-Abelian electric fields are squeezed. Magnetic displacement currents which are time-dependent Abelian magnetic fields play a role of solenoidal currents squeezing Abelian electric fields. Monopoles are not always necessary to the dual Meissner effect. The squeezing of th...

Some theories predict that the filling factor 5/2 fractional quantum Hall state can exhibit non-Abelian statistics, which makes it a candidate for fault-tolerant topological quantum computation. Although the non-Abelian Pfaffian state and its particle-hole conjugate, the anti-Pfaffian state, are the most plausible wave functions for the 5/2 state, there are a number of alternatives with either ...