Quantum field theory in curved spacetime, the operator product expansion, and dark energy

摘要

To make sense of quantum field theory in an arbitrary (globally hyperbolic)curved spacetime, the theory must be formulated in a local and covariant mannerin terms of locally measureable field observables. Since a generic curvedspacetime does not possess symmetries or a unique notion of a vacuum state, thetheory also must be formulated in a manner that does not require symmetries ora preferred notion of a ``vacuum state'' and ``particles''. We propose such aformulation of quantum field theory, wherein the operator product expansion(OPE) of the quantum fields is elevated to a fundamental status, and thequantum field theory is viewed as being defined by its OPE. Since the OPEcoefficients may be better behaved than any quantities having to do withstates, we suggest that it may be possible to perturbatively construct the OPEcoefficients--and, thus, the quantum field theory. By contrast, ground/vacuumstates--in spacetimes, such as Minkowski spacetime, where they may bedefined--cannot vary analytically with the parameters of the theory. We arguethat this implies that composite fields may acquire nonvanishing vacuum stateexpectation values due to nonperturbative effects. We speculate that this couldaccount for the existence of a nonvanishing vacuum expectation value of thestress-energy tensor of a quantum field occurring at a scale much smaller thanthe natural scales of the theory.