Gauge Invariance, Finite Temperature and Parity Anomaly in D=3

The effective gauge field actions generated by charged fermions in $QED_3$ and $QCD_3$ can be made invariant under both small and large gauge transformations at any temperature by suitable regularization of the Dirac operator determinant, at the price of parity anomalies. We resolve the paradox that the perturbative expansion is not invariant, as manifested by the temperature dependence of the induced Chern-Simons term, by showing that large (unlike small) transformations and hence their Ward identities, are not perturbative order-preserving. Our results are illustrated through concrete examples of field configurations.Comment: 4 pages, RevTe

Seminar on Securities Law

Materials from the UK/CLE Seminar on Securities Law held February 14-15, 1986

As consequências dos acordos de livre comércio sobre o setor de lácteos no Brasil

Este artigo analisa os principais efeitos dos acordos de livre comércio sobre o setor de lácteos no Brasil. Utiliza-se um modelo de equilíbrio parcial formulado como um Problema de Complementaridade Mista (MCP na sigla em inglês) para avaliar mudanças (ganhos e perdas potenciais) em termos de produção, consumo e comércio em cada cenário. Tal modelo considera multirregiões e multiprodutos, o que permite analisar os impactos de políticas de livre comércio para diferentes regiões e diversos produtos lácteos.<br>This paper discusses the main effects of free trade agreements on the dairy sector in Brazil. A partial equilibrium model formulated as a Mixed Complementary Problem (MCP) is used to provide some numerical examples of changes (potential gain and losses) in terms of production, trade and welfare in each scenario. This model also considers a multiregional and a multi-product dimension, which permits to analyze the impact of trade liberalization upon different regions and diverse processed dairy products