Quantum particles in general spacetimes - a tangent bundle formalism

Abstract

Using tangent bundle geometry we construct an equivalent reformulation of classical field theory on flat spacetimes which simultaneously encodes the perspectives of multiple observers. Its generalization to curved spacetimes realizes a new type of non-minimal coupling of the fields, and is shown to admit a canonical quantization procedure. For the resulting quantum theory we demonstrate the emergence of a particle interpretation, fully consistent with general relativistic geometry. The path-dependency of parallel transport forces each observer to carry his own quantum state; we find that the communication of the corresponding quantum information may generate extra particles on curved spacetimes. A speculative link between quantum information and spacetime curvature is discussed which might lead to novel explanations for quantum decoherence and vanishing interference in double-slit or interaction-free measurement scenarios, in the mere presence of additional observers.