Authors: Johan Noldus
In this letter we study two different aspects of general covariance, first we quantize a reparametrization invariant theory, the free particle in Minkowski spacetime and point out in detail where this theory fails (notably these comments appear to be missing in the literature). Second we study the covariance of quantum field theory and show how it connects to causality, the outcome of this study is that QFT is what we shall call ultra weakly covariant with respect to the background spacetime. Third, we treat the question of whether evolution in quantum theory (apart from the measurement act) needs to be unitary, it is easily shown that a perfectly satisfying probabilistic interpretation exists which does not require unitary evolution. Fourth, we speculate on some modifications quantum theory should undergo in order for it to be generally covariant. This paper is primarily written for the student who wishes to study quantum gravity.
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