Seiberg--Witten maps for SO(1,3)\boldsymbol{SO(1,3)} gauge invariance and deformations of gravity

A family of diffeomorphism-invariant Seiberg--Witten deformations of gravity is constructed. In a first step Seiberg--Witten maps for an SO(1,3) gauge symmetry are obtained for constant deformation parameters. This includes maps for the vierbein, the spin connection and the Einstein--Hilbert Lagrangian. In a second step the vierbein postulate is imposed in normal coordinates and the deformation parameters are identified with the components $\theta^{\mu\nu}(x)$ of a covariantly constant bivector. This procedure gives for the classical action a power series in the bivector components which by construction is diffeomorphism-invariant. Explicit contributions up to second order are obtained. For completeness a cosmological constant term is included in the analysis. Covariant constancy of $\theta^{\mu\nu}(x)$, together with the field equations, imply that, up to second order, only four-dimensional metrics which are direct sums of two two-dimensional metrics are admissible, the two-dimensional curvatures being expressed in terms of $\theta^{\mu\nu}$. These four-dimensional metrics can be viewed as a family of deformed emergent gravities.Comment: 1 encapsulated figur

Higher covariant derivative regulators and non-multiplicative renormalization

The renormalization algorithm based on regularization methods with two regulators is analyzed by means of explicit computations. We show in particular that regularization by higher covariant derivative terms can be complemented with dimensional regularization to obtain a consistent renormalized 4-dimensional Yang-Mills theory at the one-loop level. This shows that hybrid regularization methods can be applied not only to finite theories, like \eg\ Chern-Simons, but also to divergent theories.Comment: 12 pages, phyzzx, no figure

Higher covariant derivative Pauli-Villars regularization does not lead to a consistent QCD

We compute the beta function at one loop for Yang-Mills theory using as regulator the combination of higher covariant derivatives and Pauli-Villars determinants proposed by Faddeev and Slavnov. This regularization prescription has the appealing feature that it is manifestly gauge invariant and essentially four-dimensional. It happens however that the one-loop coefficient in the beta function that it yields is not $-11/3,$ as it should be, but $-23/6.$ The difference is due to unphysical logarithmic radiative corrections generated by the Pauli-Villars determinants on which the regularization method is based. This no-go result discards the prescription as a viable gauge invariant regularization, thus solving a long-standing open question in the literature. We also observe that the prescription can be modified so as to not generate unphysical logarithmic corrections, but at the expense of losing manifest gauge invariance.Comment: 43 pages, Latex file (uses the macro axodraw.sty, instructions of how to get it and use it included), FTUAM 94/9, NIKHEF-H 94/2

BRS symmetry versus supersymmetry in Yang-Mills-Chern-Simons theory

We prove that three-dimensional $N=1$ supersymmetric Yang-Mills-Chern-Simons theory is finite to all loop orders. In general this leaves open the possibility that different regularization methods lead to different finite effective actions. We show that in this model dimensional regularization and regularization by dimensional reduction yield the same effective action. Consequently, the superfield approach preserves BRS invariance for this model.Comment: 27 pages, 2 figures, latex2e, uses epsfi

Smarandache's function applied to perfect numbers

Smarandache's function may be defined as follows: S(n) = the smallest positive integer such that S(n)! is divisible by n. In this article we are going to see that the value this function takes when n is a perfect number

On the Surface Tensions of Binary Mixtures

For binary mixtures with fixed concentrations of the species, various relationships between the surface tensions and the concentrations are briefly reviewed

QML and GMM estimators of stochastic volatility models: Response to Andersen and Sorensen

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Quasi-Maximum Likelihood estimation of Stochastic Volatility models

Publicado además en: Recent developments in Time Series, 2003, vol. 2, ISBN13: 9781840649512, pp. 117-134Changes in variance or volatility over time can be modelled using stochastic volatility (SV) models. This approach is based on treating the volatility as an unobserved vatiable, the logarithm of which is modelled as a linear stochastic process, usually an autoregression. This article analyses the asymptotic and finite sample properties of a Quasi-Maximum Likelihood (QML) estimator based on the Kalman filter. The relative efficiency of the QML estimator when compared with estimators based on the Generalized Method of Moments is shown to be quite high for parameter values often found in empirical applications. The QML estimator can still be employed when the SV model is generalized to allow for distributions with heavier tails than the normal. SV models are finally fitted to daily observations on the yen/dollar exchange rate.Publicad