Antisymmetric relation

About: Antisymmetric relation is a research topic. Over the lifetime, 3322 publications have been published within this topic receiving 64365 citations. The topic is also known as: antisymmetric property & anti-symmetric property.

Towards extending the Chern-Simons couplings at order $O(\alpha'^2)$

Abstract: Using the compatibility of the anomalous Chern-Simons couplings on D$_p$-branes with the linear T-duality and with the antisymmetric B-field gauge transformations, some couplings have been recently found for $C^{(p-3)}$ at order $O(\alpha'^2)$. We examine these couplings with the S-matrix element of one RR and two antisymmetric B-field vertex operators. We find that the S-matrix element reproduces these couplings as well as some other couplings. Each of them is invariant under the linear T-duality and the B-field gauge transformations.

Heat kernal expansion coefficient. I. An extension

Abstract: The author argues that it is possible to obtain the asymptotic expansion coefficients for an operator with torsion from the expansion coefficients for an operator without torsion. This is possible when both operators act on the same set of eigenfunctions in the same way, and therefore have the same spectrum. The author calculates in four dimensions (a2(- Square Operator +Bk Del k+X)) using the Schwinger-DeWitt ansatz. Then following the argument above he obtains (a2(- Square Operator -Bk Del k+X)) where tildes denote torsion. He compares results with a modest direct calculation using 'toy torsion' (totally antisymmetric and covariantly constant) and obtains agreement. He discusses the results and reviews the literature. He finds no other algorithms for (a2(- Square Operator +Bk Del k+X)) consistent with the limiting case (a2(- Square Operator +Bk Del k+X)). There are three appendices with useful coincidence limits and curvature tensor relations.

Mirror potentials and the fermion problem

Abstract: The exact treatment of fermion systems by Monte Carlo methods has proved to be difficult. We present a new method based on the concept of a ``mirror potential,'' which is a many-body potential that forces the Monte Carlo iteration to have a stable antisymmetric component. The potential may be determined from the wave function and, within the framework of Green's function Monte Carlo, from the random walk whose density converges to the wave function. In certain limits, the method reduces to the fixed node approximation and to transient estimation, so that it subsumes both of them. As a further consequence it offers an approximation analogous to fixed node for treating systems with noncentral forces. The method may prove to be a general one for treating random walkers with nonpositive or complex weights. In support of that we exhibit a successful calculation of a one-dimensional excited state. In this paper we explore the alternative in which the mirror potential is obtained from trial wave functions. This yields an approximation scheme that proves to be accurate in the experiments described here. We present results for a model problem in which four neutrons interact by a spin-independent potential, and compare the results with those of the fixed node method, and the method of transient estimation.