Integrable models with unstable particles

We review some recent results concerning integrable quantum field theories in 1+1 space-time dimensions which contain unstable particles in their spectrum. Recalling first the main features of analytic scattering theories associated to integrable models, we subsequently propose a new bootstrap principle which allows for the construction of particle spectra involving unstable as well as stable particles. We describe the general Lie algebraic structure which underlies theories with unstable particles and formulate a decoupling rule, which predicts the renormalization group flow in dependence of the relative ordering of the resonance parameters. We extend these ideas to theories with an infinite spectrum of unstable particles. We provide new expressions for the scattering amplitudes in the soliton-antisoliton sector of the elliptic sine-Gordon model in terms of infinite products of q-deformed gamma functions. When relaxing the usual restriction on the coupling constants, the model contains additional bound states which admit an interpretation as breathers. For that situation we compute the complete S-matrix of all sectors. We carry out various reductions of the model, one of them leading to a new type of theory, namely an elliptic version of the minimal SO(n)-affine Toda field theory

Finite temperature correlation functions from form factors

We investigate proposals of how the form factor approach to compute correlation functions at zero temperature can be extended to finite temperature. For the two-point correlation function we conclude that the suggestion to use the usual form factor expansion with the modification of introducing dressing functions of various kinds is only suitable for free theories. Dynamically interacting theories require a more severe change of the form factor program

Top incomes and earnings in Portugal 1936-2004

This paper analyzes income and earnings concentration in Portugal from a long-run perspective using personal income and wage tax statistics. Our results suggest that income concentration was much higher during the 1930s and early 1940s than it is today. Top income shares estimated from reported incomes deteriorated during the Second World War, even if Portugal did not take active participation in the conflict. However, the magnitude of the drop was less important than in other European countries. The level of concentration between 1950 and 1970 remained relatively high compared to countries such as Spain, France, UK or the United States. The decrease in income concentration, started very moderately at the end of the 1960s and which accelerated after the revolution of 1974, began to be reversed during the first half of the 1980s. During the last fifteen years top income shares have increased steadily. The rise in wage concentration contributed to this process in a significant way. The evidence since 1989 suggests that the level of marginal tax rate at the top has not been the primary determinant of the level of top reported incomes. Marginal rates have stayed constant in a context of growing top shares.top incomes ; top wages ; concentration ; Portugal

Higher particle form factors of branch point twist fields in integrable quantum field theories

In this paper we compute higher particle form factors of branch point twist fields. These fields were first described in the context of massive 1+1-dimensional integrable quantum field theories and their correlation functions are related to the bi-partite entanglement entropy. We find analytic expressions for some form factors and check those expressions for consistency, mainly by evaluating the conformal dimension of the corresponding twist field in the underlying conformal field theory. We find that solutions to the form factor equations are not unique so that various techniques need to be used to identify those corresponding to the branch point twist field we are interested in. The models for which we carry out our study are characterized by staircase patterns of various physical quantities as functions of the energy scale. As the latter is varied, the beta-function associated to these theories comes close to vanishing at several points between the deep infrared and deep ultraviolet regimes. In other words, renormalisation group flows approach the vicinity of various critical points before ultimately reaching the ultraviolet fixed point. This feature provides an optimal way of checking the consistency of higher particle form factor solutions, as the changes on the conformal dimension of the twist field at various energy scales can only be accounted for by considering higher particle form factor contributions to the expansion of certain correlation functions.Comment: 25 pages, 4 figures; v2 contains small correction

Top incomes and earnings in Portugal 1936-2004

This paper analyzes income and earnings concentration in Portugal from a long-run perspective using personal income and wage tax statistics. Our results suggest that income concentration was much higher during the 1930s and early 1940s than it is today. Top income shares estimated from reported incomes deteriorated during the Second World War, even if Portugal did not take active participation in the conflict. However, the magnitude of the drop was less important than in other European countries. The level of concentration between 1950 and 1970 remained relatively high compared to countries such as Spain, France, UK or the United States. The decrease in income concentration, started very moderately at the end of the 1960s and which accelerated after the revolution of 1974, began to be reversed during the first half of the 1980s. During the last fifteen years top income shares have increased steadily. The rise in wage concentration contributed to this process in a significant way. The evidence since 1989 suggests that the level of marginal tax rate at the top has not been the primary determinant of the level of top reported incomes. Marginal rates have stayed constant in a context of growing top shares.Ce travail présente des séries sur les hauts revenus et les hauts salaires en Portugal entre 1936 et 2004, construites à partir de données fiscales et fichiers administratifs.Le Portugal est un cas spécial de pays doté d'une structure bureaucratique bien organisée en ce qui concerne l'imposition sur le revenu, influencée par la stabilité du régime autoritaire au pouvoir entre 1926 et 1974. Les dossiers administratifs et les données étaient régulièrement publiés depuis 1936. Malheureusement, ces archives et données présentent un blanc entre 1983 et 1988, une période durant laquelle de nombreuses réformes fiscales ont été introduites, ainsi que la transition entre l'ancien et le nouvel impôt sur le revenu réalisée en 1989. Les résultats montrent une relative stabilité des parts des hauts revenus entre la fin de la seconde Guerre mondiale et la fin des années 1960, suivie de dynamiques en forme de U, le bras ascendant du U apparaissant à partir du début des années 1980 quand les réformes ont été introduites afin de satisfaire aux conditions d'accession à la Communauté Economique Européenne. Des données-micro disponibles concernant les salaires mettent aussi à jour une augmentation de la part des hauts salaires

Income and wealth concentration in Spain in a historical and fiscal perspective

This paper presents series on top shares of income and wealth in Spain over the 20th century using personal income and wealth tax return statistics. Top income shares are highest in the 1930s, fall sharply during the first two decades of the Franco dictatorship, and have increased slightly since the 1960s, and especially since the mid-1990s. The top 0.01% income share in Spain estimated from income tax data is comparable to estimates for the United States and France over the period 1933-1971. Those findings, along with a careful analysis of all published tax statistics, suggest that income tax evasion and avoidance among top income earners in Spain before 1980 was much less prevalent than previously thought. Wealth concentration has been about stable from 1982 to 2004 as surging real estate prices have benefited the middle class and compensated for a slight increase in financial wealth concentration in the 1990s. We use our wealth series and a simple conceptual model to analyse the effects of the wealth tax exemption of stocks for ownersmanagers introduced in 1994. We show that the reform induced substantial shifting from the taxable to tax exempt status. This shifting has eroded the wealth tax base substantially and hence the tax exemption has generated large efficiency costs.income concentration ; top incomes ; behavioral response

Top incomes and earnings in Portugal 1936-2004

This paper analyzes income and earnings concentration in Portugal from a long-run perspective using personal income and wage tax statistics. Our results suggest that income concentration was much higher during the 1930s and early 1940s than it is today. Top income shares estimated from reported incomes deteriorated during the Second World War, even if Portugal did not take active participation in the conflict. However, the magnitude of the drop was less important than in other European countries. The level of concentration between 1950 and 1970 remained relatively high compared to countries such as Spain, France, UK or the United States. The decrease in income concentration, started very moderately at the end of the 1960s and which accelerated after the revolution of 1974, began to be reversed during the first half of the 1980s. During the last fifteen years top income shares have increased steadily. The rise in wage concentration contributed to this process in a significant way. The evidence since 1989 suggests that the level of marginal tax rate at the top has not been the primary determinant of the level of top reported incomes. Marginal rates have stayed constant in a context of growing top shares.Ce travail présente des séries sur les hauts revenus et les hauts salaires en Portugal entre 1936 et 2004, construites à partir de données fiscales et fichiers administratifs.Le Portugal est un cas spécial de pays doté d'une structure bureaucratique bien organisée en ce qui concerne l'imposition sur le revenu, influencée par la stabilité du régime autoritaire au pouvoir entre 1926 et 1974. Les dossiers administratifs et les données étaient régulièrement publiés depuis 1936. Malheureusement, ces archives et données présentent un blanc entre 1983 et 1988, une période durant laquelle de nombreuses réformes fiscales ont été introduites, ainsi que la transition entre l'ancien et le nouvel impôt sur le revenu réalisée en 1989. Les résultats montrent une relative stabilité des parts des hauts revenus entre la fin de la seconde Guerre mondiale et la fin des années 1960, suivie de dynamiques en forme de U, le bras ascendant du U apparaissant à partir du début des années 1980 quand les réformes ont été introduites afin de satisfaire aux conditions d'accession à la Communauté Economique Européenne. Des données-micro disponibles concernant les salaires mettent aussi à jour une augmentation de la part des hauts salaires

Contribution Ceilings and the Incidence of Payroll Taxes

Social security contributions (SSCs) are typically formally split between employers and employees as payroll taxes, levied on earnings at a constant tax rate that applies only up to a ceiling, above which the marginal tax rate falls to a reduced rate, often 0. Such contribution ceilings create a concave kink point in the budget set of workers and hence should generate a dip in the distribution of earnings around the ceiling through labour supply responses (the reverse of bunching expected at convex kink points) but such a dip is not observed empirically. This paper sets out a new approach to infer the incidence of SSCs that exploits the absence of this dip and the fact that (mechanically) the distributions of labour cost (earnings inclusive of all payroll taxes), gross earnings (net of employer payroll taxes) and net earnings (net of both employer and employee payroll taxes) cannot all be smooth around a kink. The other papers in this special issue apply the method to data for Germany, France, the Netherlands and the UK and all find that distribution of gross earnings is smooth around kinks (implying that the distributions of labour costs and net-of-tax earnings are not) even though the concept of gross earnings is irrelevant in the standard static model of labour supply and demand that dominates the public economics literature. This suggests that other features of the labour market, such as wage bargaining based on the gross earnings concept, are relevant for determining the incidence of SSCs.Fil: Gonzalez Alvaredo, Facundo. Paris School of Economics; Francia. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Breda, Thomas. Paris School of Economics; FranciaFil: Roantree, Barra. Institute for Fiscal Studies; Reino UnidoFil: Saez, Emmanuel. University of California at Berkeley; Estados Unido

Chaos in the thermodynamic Bethe ansatz

We investigate the discretized version of the thermodynamic Bethe ansatz equation for a variety of 1+1 dimensional quantum field theories. By computing Lyapunov exponents we establish that many systems of this type exhibit chaotic behaviour, in the sense that their orbits through fixed points are extremely sensitive with regard to the initial conditions.Comment: 10 pages, Late