Microcausality in Curved Space-Time

Abstract

It is well known that in Lorentz invariant quantum field theories in flat space the commutator of space-like separated local operators vanishes (microcausality). We provide two different arguments showing that this is a consequence of the causal structure of the classical theory, rather than of Lorentz invariance. In particular, microcausality holds in arbitrary curved space-times, where Lorentz invariance is explicitly broken by the background metric. As illustrated by an explicit calculation on a cylinder this property is rather non trivial at the level of Feynman diagrams.

21 pages, 4 figures

References in corpus (6)

• Causality, Analyticity and an IR Obstruction to UV Completion
• Quantum Contributions to Cosmological Correlations
• Quantum Gravitational Optics
• The Refractive Index of Curved Spacetime: the Fate of Causality in QED
• Causality and Micro-Causality in Curved Spacetime
• Bounds on masses of bulk fields in string compactifications

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