Annales Henri Poincaré

, Volume 13, Issue 7, pp 1675–1709 | Cite as

Dynamical Locality of the Free Scalar Field

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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 ≥ 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 ≥ 2 on connected spacetimes, and in all dimensions n ≥ 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.

Keywords

Dynamical Locality Spacetime Dimension Weyl Algebra Cauchy Surface Free Scalar 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© Springer Basel AG 2012

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of YorkHeslington, YorkUK
  2. 2.Institut für Theoretische PhysikUniversität LeipzigLeipzigGermany

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