Ex-nihilo: Obstacles Surrounding Teaching the Standard Model

The model of the Big Bang is an integral part of the national curriculum for England. Previous work (e.g. Baxter 1989) has shown that pupils often come into education with many and varied prior misconceptions emanating from both internal and external sources. Whilst virtually all of these misconceptions can be remedied, there will remain (by its very nature) the obstacle of ex-nihilo, as characterised by the question `how do you get something from nothing?' There are two origins of this obstacle: conceptual (i.e. knowledge-based) and cultural (e.g. deeply held religious viewpoints). The article shows how the citizenship section of the national curriculum, coming `online' in England from September 2002, presents a new opportunity for exploiting these.Comment: 6 pages. Accepted for publication in Physics E

Exact Solution of the Multi-Allelic Diffusion Model

We give an exact solution to the Kolmogorov equation describing genetic drift for an arbitrary number of alleles at a given locus. This is achieved by finding a change of variable which makes the equation separable, and therefore reduces the problem with an arbitrary number of alleles to the solution of a set of equations that are essentially no more complicated than that found in the two-allele case. The same change of variable also renders the Kolmogorov equation with the effect of mutations added separable, as long as the mutation matrix has equal entries in each row. Thus this case can also be solved exactly for an arbitrary number of alleles. The general solution, which is in the form of a probability distribution, is in agreement with the previously known results--which were for the cases of two and three alleles only. Results are also given for a wide range of other quantities of interest, such as the probabilities of extinction of various numbers of alleles, mean times to these extinctions, and the means and variances of the allele frequencies. To aid dissemination, these results are presented in two stages: first of all they are given without derivations and too much mathematical detail, and then subsequently derivations and a more technical discussion are provided.Comment: 56 pages. 15 figures. Requires Elsevier document clas

Gaudin Hypothesis for the XYZ Spin Chain

The XYZ spin chain is considered in the framework of the generalized algebraic Bethe ansatz developed by Takhtajan and Faddeev. The sum of norms of the Bethe vectors is computed and expressed in the form of a Jacobian. This result corresponds to the Gaudin hypothesis for the XYZ spin chain.Comment: 12 pages, LaTeX2e (+ amssymb, amsthm); to appear in J. Phys.

Tetromino tilings and the Tutte polynomial

We consider tiling rectangles of size 4m x 4n by T-shaped tetrominoes. Each tile is assigned a weight that depends on its orientation and position on the lattice. For a particular choice of the weights, the generating function of tilings is shown to be the evaluation of the multivariate Tutte polynomial Z\_G(Q,v) (known also to physicists as the partition function of the Q-state Potts model) on an (m-1) x (n-1) rectangle G, where the parameter Q and the edge weights v can take arbitrary values depending on the tile weights.Comment: 8 pages, 6 figure

Trade structure, industrial structure, and international business cycles

This paper examines the extent to which the composition of a country's production and trade differs among its trade partners. For example, does the US export the same bundle of goods to the UK as it does to Japan? If we find high dispersion in a country's export and import bundles with its various trading partners, can this be linked to identifiable country characteristics? These findings are important for two reasons. First, they enrich our empirical understanding of the nature of trade. Second, they will stand as a guide for further development of economic theories of the international transmission of business cycles.Trade ; Industrial organization (Economic theory) ; Business cycles

Determinants of Business Cycle Comovement: A Robust Analysis

This paper investigates the determinants of business cycle comovement between countries. Our dataset includes over 100 countries, both developed and developing. We search for variables that are robust' in explaining comovement, using the approach of Leamer (1983). Variables considered are (i) bilateral trade between countries; (ii) total trade in each country; (iii) sectoral structure; (iv) similarity in export and import baskets; (v) factor endowments; and (vi) gravity variables. We find that bilateral trade is robust. However, two variables that the literature has argued are important for business cycles industrial structure and currency unions are found not to be robust.

Baxter equations and Deformation of Abelian Differentials

In this paper the proofs are given of important properties of deformed Abelian differentials introduced earlier in connection with quantum integrable systems. The starting point of the construction is Baxter equation. In particular, we prove Riemann bilinear relation. Duality plays important role in our consideration. Classical limit is considered in details.Comment: 28 pages, 1 figur

General scalar products in the arbitrary six-vertex model

In this work we use the algebraic Bethe ansatz to derive the general scalar product in the six-vertex model for generic Boltzmann weights. We performed this calculation using only the unitarity property, the Yang-Baxter algebra and the Yang-Baxter equation. We have derived a recurrence relation for the scalar product. The solution of this relation was written in terms of the domain wall partition functions. By its turn, these partition functions were also obtained for generic Boltzmann weights, which provided us with an explicit expression for the general scalar product.Comment: 24 page

Excited TBA Equations I: Massive Tricritical Ising Model

We consider the massive tricritical Ising model M(4,5) perturbed by the thermal operator phi_{1,3} in a cylindrical geometry and apply integrable boundary conditions, labelled by the Kac labels (r,s), that are natural off-critical perturbations of known conformal boundary conditions. We derive massive thermodynamic Bethe ansatz (TBA) equations for all excitations by solving, in the continuum scaling limit, the TBA functional equation satisfied by the double-row transfer matrices of the A_4 lattice model of Andrews, Baxter and Forrester (ABF) in Regime III. The complete classification of excitations, in terms of (m,n) systems, is precisely the same as at the conformal tricritical point. Our methods also apply on a torus but we first consider (r,s) boundaries on the cylinder because the classification of states is simply related to fermionic representations of single Virasoro characters chi_{r,s}(q). We study the TBA equations analytically and numerically to determine the conformal UV and free particle IR spectra and the connecting massive flows. The TBA equations in Regime IV and massless RG flows are studied in Part II.Comment: 31 pages, 8 figure

Non perturbative Adler-Bardeen Theorem

The Adler-Bardeen theorem has been proved only as a statement valid at all orders in perturbation theory, without any control on the convergence of the series. In this paper we prove a nonperturbative version of the Adler-Bardeen theorem in $d=2$ by using recently developed technical tools in the theory of Grassmann integration.Comment: 28 pages, 14 figure