On the theory of coherent pair production in crystals in presence of acoustic waves

The influence of hypersonic waves excited in a single crystal is investigated on the process of electron-positron pair creation by high-energy photons. The coherent part of the corresponding differential cross-section is derived as a function of the amplitude and wave number of the hypersound. The values of the parameters are specified for which the latter affects remarkably on the pair creation cross-section. It is shown that under certain conditions the presence of hypersonic waves can result in enhancement of the process cross-section.Comment: 10 pages, 3 EPS figure

Trace Anomalies and Cocycles of Weyl and Diffeomorphisms Groups

The general structure of trace anomaly, suggested recently by Deser and Shwimmer, is argued to be the consequence of the Wess-Zumino consistency condition. The response of partition function on a finite Weyl transformation, which is connected with the cocycles of the Weyl group in $d=2k$ dimensions is considered, and explicit answers for $d=4,6$ are obtained. Particularly, it is shown, that addition of the special combination of the local counterterms leads to the simple form of that cocycle, quadratic over Weyl field $\sigma$, i.e. the form, similar to the two-dimensional Lioville action. This form also establishes the connection of the cocycles with conformal-invariant operators of order $d$ and zero weight. Beside that, the general rule for transformation of that cocycles into the cocycles of diffeomorphisms group is presented.Comment: 14 page