Seminarium "Teoria cząstek elementarnych i kosmologia"

A certain class of renormalizable quantum field theories with purely virtual particles, including quantum gravity, exhibits undesired behaviors, typical of nonrenormalizable theories, and seems to violate positivity bounds. In particular, cross sections can grow as powers of the center-of-mass energy squared. In this talk we argue that the problem should be viewed as a violation of perturbativity, instead of unitarity. Indeed, we show that nonperturbative techniques, such as resummation of self energies, fixes the issue. As an explicit example, we consider a class of O(N) theories, which can be studied exactly to the leading order in the large-N expansion. We show that, after the resummation, the cross sections correctly decrease as inverse powers of the center-of-mass energy squared and that the amplitudes satisfy unitarity. These results are compared to theories with ghosts, where the resummation does not help in improving the high-energy behavior, and to nonrenormalizable theories. Finally, the appearance of new resonances or bound states is discussed.

slides: https://mycloud.fuw.edu.pl/index.php/s/wbQbJP5SzcZiZa7