We evaluate the 4-point function of the auxiliary field in the critical O(N) sigma model at O(1/N) and show that it describes the exchange of tensor currents of arbitrary even rank l > 0. These are dual to tensor gauge fields of the same rank in the AdS theory, which supports the recent hypothesis of Klebanov and Polyakov. Their couplings to two auxiliary fields are also derived.
In the one-dimensional periodic potential case, we formulate the condition of Bloch periodicity for the reduced action by using the relation between the wave function and the reduced action established in the context of the equivalence postulate of quantum mechanics. Then, without appealing to the wave function properties, we reproduce the well-known dispersion relations which predict the band structure for the energy spectrum in the Krönig-Penney model.
Fields and their BRST and anti-BRST transformations in gauge-affine gravity are determined by using a superspace formalism. The method is based on the introduction of a basis, instead of the natural one, for differential forms on a (4, 2)-dimensional superspace, whose body is a metric-affine spacetime. This basis is defined after having introduced the coordinate ghost and anti-ghost superfields from a [Formula: see text]-superconnection.
In a stationary case and for any potential, we solve the three-dimensional quantum Hamilton-Jacobi equation in terms of the solutions of the corresponding Schrödinger equation. Then, in the case of separated variables, by requiring that the conjugate momentum be invariant under any linear transformation of the solutions of the Schrödinger equation used in the reduced action, we clearly identify the integration constants successively in one, two and three dimensions. In each of these cases, we analytically establish that the quantum Hamilton-Jacobi equation describes microstates not detected by the Schrödinger equation in the real wave function case.
The main purpose of this work is to give an overview of a generalization of the theory of general relativity, namely metric-affine gravity. We rederive an expression for the Lie derivative of the metric in the case of metric-affine theory and discuss some consequences of such an expression. As a gauge theory of gravitation it may be considered as an upshot of a gauging procedure of the general affine group, or its double covering. A historical approach of such a theory is also contained including the key results. One concludes with some perspectives on the calculation of topological observables in that theory viewed as topological gravity theory.
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