Effective field theory approach to N=4 supersymmetric Yang-Mills at finite temperature

We study the perturbation expansion of the free energy of N=4 supersymmetric SU(N) Yang-Mills at finite temperature in powers of 't Hooft's coupling g^2 N in the large N limit. Infrared divergences are controlled by constructing a hierarchy of two 3 dimensional effective field theories. This procedure is applied to the calculation of the free energy to order (g^2 N)^(3/2), but it can be extended to higher order corrections.Comment: LaTeX, 10 pages, 1 figure, uses eps

Complexified sigma model and duality

We show that the equations of motion associated with a complexified sigma-model action do not admit manifest dual SO(n,n) symmetry. In the process we discover new type of numbers which we called `complexoids' in order to emphasize their close relation with both complex numbers and matroids. It turns out that the complexoids allow to consider the analogue of the complexified sigma-model action but with (1+1)-worldsheet metric, instead of Euclidean-worldsheet metric. Our observations can be useful for further developments of complexified quantum mechanics.Comment: 15 pages, Latex, improved versio

Equivalence between various versions of the self-dual action of the Ashtekar formalism

Different aspects of the self-dual (anti-self-dual) action of the Ashtekar canonical formalism are discussed. In particular, we study the equivalences and differences between the various versions of such an action. Our analysis may be useful for the development of an Ashtekar formalism in eight dimensions.Comment: 10 pages, Latex, minor correction

About a Coincidente Index for the State of the Economy

The construction of coincident indexes for the economic activity of a country is a common practice since the fifties. The methodologies vary from heuristic methods to probabilistic or statistical ones. In this paper, we present a new procedure for estimating a coincient index of the state of the economy which is optimum in a statiscal sense. This procedure is based on state space models that do possess the steady-state property.We apply our methodology for computing a coincident index for the Colombian economy.State of the economy, Coincidente Index, State Space Models.

Tavis-Cummings models and their quasi-exactly solvable Schrödinger Hamiltonians

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General Approach to Functional Forms for the Exponential Quadratic Operators in Coordinate-Momentum Space

In a recent paper [Nieto M M 1996 Quantum and Semiclassical Optics, 8 1061; quant-ph/9605032], the one dimensional squeezed and harmonic oscillator time-displacement operators were reordered in coordinate-momentum space. In this paper, we give a general approach for reordering multi-dimensional exponential quadratic operator(EQO) in coordinate-momentum space. An explicit computational formula is provided and applied to the single mode and double-mode EQO through the squeezed operator and the time displacement operator of the harmonic oscillator.Comment: To appear in J. Phys. A: Mathematics and Genera