Work and energy in inertial and non inertial reference frames

It is usual in introductory courses of mechanics to develop the work and energy formalism from Newton's laws. On the other hand, literature analyzes the way in which forces transform under a change of reference frame. Notwithstanding, no analogous study is done for the way in which work and energy transform under those changes of reference frames. We analyze the behavior of energy and work under such transformations and show explicitly the expected invariance of the formalism under Galilean transformations for one particle and a system of particles. The case of non inertial systems is also analyzed and the fictitious works are characterized. In particular, we show that the total fictitious work in the center of mass system vanishes even if the center of mass defines a non inertial frame. Finally, some subtleties that arise from the formalism are illustrated by examples.Comment: 4 pages, 2 figures. LaTeX2e. Part of the approach has been changed but results are unaltered. Version to appear im American Journal of Physic

The process μ→νeeνˉμ\mu \to \nu_{e}e\bar{\nu}_{\mu} in the 2HDM with flavor changing neutral currents

We consider the process $\mu \to \nu_{e}e\bar{\nu}_{\mu}$in the framework of a two Higgs doublet model with flavor changing neutral currents (FCNC). Since FCNC generates in turn flavor changing charged currents in the lepton sector, this process appears at tree level mediated by a charged Higgs boson exchange. From the experimental upper limit for this decay, we obtain the bound $| \xi_{\mu e}/m_{H^{\pm}}| \leq 3.8\times 10^{-3}$ where$\xi_{\mu e}$refers to the mixing between the first and second lepton generations, and $m_{H^{\pm}}$denotes the mass of the charged Higgs boson. This bound is independent on the other free parameters of the model. In particular, for $m_{H^{\pm}}\simeq 100$GeV we get $| \xi_{e\mu}|$ $\lesssim 0.38$Comment: 2 pages, no figure