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

SOME EXPRESSIONS OF THE SMARANDACHE PRIME FUNCTION

The main purpose of this paper is using elementary arithmetical functions to give some expressions of the Smarandache Prime Function P(n)

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

A Congruence with Smarandache's Function

Smarandache's function is defined thus: S( n) = is the smallest integer such that S( n)! is divisible by n

Regularization and Renormalization of Chern-Simons Theory

We analyze some features of the perturbative quantization of Chern-Simons theory (CST) in the Landau gauge. In this gauge the theory is known to be perturbatively finite. We consider the renormalization scheme in which the renormalized parameter $k$ equals the bare or classical one and show that it constitutes a natural parametrization for the quantum theory. The reason is that, although in this renormalization scheme the value of the Green functions depends on the regularization used, comparison among different regularization methods shows that the observables (Wilson loops) are the same function of the shifted monodromy parameter $k+c_v$ for all BRS invariant regulators used so far for CST. We also discuss a particular BRS invariant regularization prescription in which CST is perturbatively defined as the large mass limit of dimensionally regularized topologically massive Yang-Mills theory. With this regularization prescription the radiative corrections induced by two-loop contributions do not entail observable consequences since they can be reabsorbed by a finite rescaling of the fields only. This very mechanism is conjectured to take place at higher perturbative orders. Talk presented by G.G. at the NATO AWR on ``Low dimensional Topology and Quantum Field Theory'', 6-13 September 1992, Cambridge (UK).Comment: 10 pages, Phyzzx, LPTHE 92-4