Bosonic vacuum wave functions from the BCS-type wave function of the ground state of the massless Thirring model

A BCS-type wave function describes the ground state of the massless Thirring model in the chirally broken phase. The massless Thirring model with fermion fields quantized in the chirally broken phase bosonizes to the quantum field theory of the free massless (pseudo)scalar field (Eur. Phys. J. C20, 723 (2001)). The wave functions of the ground state of the free massless (pseudo)scalar field are obtained from the BCS-type wave function by averaging over quantum fluctuations of the Thirring fermion fields. We show that these wave functions are orthogonal, normalized and non-invariant under shifts of the massless (pseudo)scalar field. This testifies the spontaneous breaking of the field-shift symmetry in the quantum field theory of a free massless (pseudo)scalar field. We show that the vacuum-to-vacuum transition amplitude calculated for the bosonized BCS-type wave functions coincides with the generating functional of Green functions defined only by the contribution of vibrational modes (Eur. Phys. J. C 24, 653 (2002)) . This confirms the assumption that the bosonized BCS-type wave function is defined by the collective zero-mode (hep-th/0212226). We argue that the obtained result is not a counterexample to the Mermin-Wagner-Hohenberg and Coleman theorems.Comment: 9 pages, Latex, no figures, Revised according to the version accepted for publication in Physics Letters

Longitudinal effects of task performance and self-concept on preadolescent EFL learners’ causal attributions of grammar success and failure

Learners’ academic self-concepts and attributions have been widely evidenced to substantially regulate their educational development. Develop­men­tally, they will not only oper­ate in a mu­tually reinforcing manner. Rather, self-concepts will di­­­­rectly affect learners’ out­come attri­bu­­tions in a particular academic set­ting. Current research in the English as a foreign language (EFL) context has increasingly anal­­yzed learners’ attributions and self-concepts on a task-spe­­cific construct level. Never­the­less, there still exist certain research gaps in the field, partic­ularly con­cerning learners’ gram­mar self-con­cept and attributions. There­fore, the present study aimed at anal­yzing lon­gi­tu­dinal re­­lat­ions of prior performance and self-concept with subsequent attri­bu­tions of gram­mar suc­cess and failure in a samp­le of preadolescent EFL learners. Findings demonstrated that attri­bu­tional pat­terns most­­­­ly but not en­tire­ly depended on learn­ers’ grammar self-concept. Poor per­­form­ing learn­ers hold­ing a low self-concept dis­­played a maladaptive attri­bu­tion pattern for ex­­plain­ing both gram­­­mar suc­cess and failure. Though not with respect to all causal factors, these findings largely con­firm the crucial role of task-spe­cific self-concept in longitudinally explaining re­­lated control beliefs in the EFL con­text

A Model for Topological Fermions

We introduce a model designed to describe charged particles as stable topological solitons of a field with values on the internal space S^3. These solitons behave like particles with relativistic properties like Lorentz contraction and velocity dependence of mass. This mass is defined by the energy of the soliton. In this sense this model is a generalisation of the sine-Gordon model from 1+1 dimensions to 3+1 dimensions, from S^1 to S^3. (We do not chase the aim to give a four-dimensional generalisation of Coleman's isomorphism between the Sine-Gordon model and the Thirring model which was shown in 2-dimensional space-time.) For large distances from the center of solitons this model tends to a dual U(1)-theory with freely propagating electromagnetic waves. Already at the classical level it describes important effects, which usually have to be explained by quantum field theory, like particle-antiparticle annihilation and the running of the coupling.Comment: 42 pages, 7 figures, more detailed calculations and comparison to Skyrme model and 't Hooft-Polyakov monopoles adde

Topology and Geometry of the Berkovich Ramification Locus for Rational Functions

Given a nonconstant holomorphic map f: X -> Y between compact Riemann surfaces, one of the first objects we learn to construct is its ramification divisor R_f, which describes the locus at which f fails to be locally injective. The divisor R_f is a finite formal linear combination of points of X that is combinatorially constrained by the Hurwitz formula. Now let k be an algebraically closed field that is complete with respect to a nontrivial non-Archimedean absolute value. For example, k = C_p. Here the role of a Riemann surface is played by a projective Berkovich analytic curve. As these curves have many points that are not algebraic over k, some new (non-algebraic) ramification behavior appears for maps between them. For example, the ramification locus is no longer a divisor, but rather a closed analytic subspace. This article initiates a detailed study of the ramification locus for self-maps f: P^1 -> P^1. This simplest first case has the benefit of being approachable by concrete (and often combinatorial) techniques.Comment: To appear in Manuscripta Mathematica. New results on surplus multiplicities added to section 3.3; a number of equivalent characterizations of tame rational functions added to section 7; shortened section 8 on total ramificatio

Towards transversality of singular varieties: splayed divisors

We study a natural generalization of transversally intersecting smooth hypersurfaces in a complex manifold: hypersurfaces, whose components intersect in a transversal way but may be themselves singular. Such hypersurfaces will be called splayed divisors. A splayed divisor is characterized by a property of its Jacobian ideal. This yields an effective test for splayedness. Two further characterizations of a splayed divisor are shown, one reflecting the geometry of the intersection of its components, the other one using K. Saito's logarithmic derivations. As an application we prove that a union of smooth hypersurfaces has normal crossings if and only if it is a free divisor and has a radical Jacobian ideal. Further it is shown that the Hilbert-Samuel polynomials of splayed divisors satisfy a certain additivity property.Comment: 15 pages, 1 figure; v2: minor revision: inaccuracies corrected and references updated; v3: final version, to appear in Publ. RIM

Intersection-theoretical computations on \Mgbar

We determine necessary conditions for ample divisors in arbitrary genus as well as for very ample divisors in genus 2 and 3. We also compute the intersection numbers $\lambda^9$ and $\lambda_{g-1}^3$ in genus 4. The latter number is relevant for counting curves of higher genus on manifolds, cf. the recent work of Bershadsky et al.Comment: 13 pages, no figures. To appear in "Parameter Spaces", Banach Center Publications, volume in preparation. plain te