Dynamical locality of the free scalar field

Abstract

Dynamical locality is a condition on a locally covariant physical theory, asserting that kinematic and dynamical notions of local physics agree. This condition was introduced in [arXiv:1106.4785], where it was shown to be closely related to the question of what it means for a theory to describe the same physics on different spacetimes. In this paper, we consider in detail the example of the free minimally coupled Klein--Gordon field, both as a classical and quantum theory (using both the Weyl algebra and a smeared field approach). It is shown that the massive theory obeys dynamical locality, both classically and in quantum field theory, in all spacetime dimensions $n\ge 2$ and allowing for spacetimes with finitely many connected components. In contrast, the massless theory is shown to violate dynamical locality in any spacetime dimension, in both classical and quantum theory, owing to a rigid gauge symmetry. Taking this into account (equivalently, working with the massless current) dynamical locality is restored in all dimensions $n\ge 2$ on connected spacetimes, and in all dimensions $n\ge 3$ if disconnected spacetimes are permitted. The results on the quantized theories are obtained using general results giving conditions under which dynamically local classical symplectic theories have dynamically local quantizations.

34pp, LaTeX2e. Version to appear in Annales Henri Poincare

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• "Vacuum-like" Hadamard states for quantum fields on curved spacetimes
• Endomorphisms and automorphisms of locally covariant quantum field theories
• Locally covariant quantum field theory and the problem of formulating the same physics in all spacetimes
• Generally covariant dynamical reduction models and the Hadamard condition
• Dynamical locality of the free Maxwell field
• Locally covariant quantum field theory with external sources
• Dynamical locality of the nonminimally coupled scalar field and enlarged algebra of Wick polynomials
• Quantum Field Theory in Curved Spacetime (2nd Edition)
• Snowmass White Paper: The Quest to Define QFT
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• The Semiclassical Einstein Equation on Cosmological Spacetimes
• Strict deformations of quantum field theory in de Sitter spacetime
• Locally covariant quantum field theory and the spin-statistics connection
• Explicit construction of Hadamard states for Quantum Field Theory in curved spacetimes