Quantum field theory on curved spacetime
Robert Wald, University of Chicago rmwa@midway.uchicago.edu A program on ``Quantum field theory on curved space times'' was held at the Erwin Schroedinger Institute in Vienna, Austria from July 1 through August 31, 2002. The main goal of this program was to bring together researchers with expertise in general relativity and researchers with expertise in mathematical aspects of quantum field theory, in order to address some problems of mutual interest in quantum field theory in curved spacetime. Approximately 25 researchers in quantum field theory in curved spacetime and related areas participated in the program. The following is a brief summary of some of the main topics and results discussed during the program. It is well known that in quantum field theory in flat or curved spacetime, the expected energy density at a point can be made arbitrarily negative. However, during the past ten years, some global restrictions on negative energy have been derived. In particular, ``quantum inequalities'' have been derived, which put a lower bound on the energy density measured along the worldline of an observer with a (smooth, compact support) ``sampling function'' . Originally, such bounds were derived by non-rigorous methods in certain special cases, but recently a rigorous and completely general derivation of quantum inequalities has been given using the methods of microlocal analysis. Many issues remain open, however, such as the derivation of optimal bounds and whether some version may hold of the average null energy condition (which asserts the non-negativity of the integral over a complete null geodesic of the stress energy tensor contracted twice with the tangent to the null geodesic). These issues were explored in seminars by Ford, Fewster, Roman, Flanagan, and Pfenning. In research arising directly from discussions occurring during the program, progress also was made toward deriving quantum inequalities for quantities other than the stress-energy tensor. | |
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