Communications in Mathematical Physics

, Volume 304, Issue 1, pp 95–123

Warped Convolutions, Rieffel Deformations and the Construction of Quantum Field Theories

  • Detlev Buchholz
  • Gandalf Lechner
  • Stephen J. Summers
Open AccessArticle

DOI: 10.1007/s00220-010-1137-1

Cite this article as:
Buchholz, D., Lechner, G. & Summers, S.J. Commun. Math. Phys. (2011) 304: 95. doi:10.1007/s00220-010-1137-1

Abstract

Warped convolutions of operators were recently introduced in the algebraic framework of quantum physics as a new constructive tool. It is shown here that these convolutions provide isometric representations of Rieffel’s strict deformations of C*–dynamical systems with automorphic actions of \({\mathbb R^n}\) , whenever the latter are presented in a covariant representation. Moreover, the device can be used for the deformation of relativistic quantum field theories by adjusting the convolutions to the geometry of Minkowski space. The resulting deformed theories still comply with pertinent physical principles and their Tomita–Takesaki modular data coincide with those of the undeformed theory; but they are in general inequivalent to the undeformed theory and exhibit different physical interpretations.

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© The Author(s) 2010

Authors and Affiliations

  • Detlev Buchholz
    • 1
  • Gandalf Lechner
    • 2
  • Stephen J. Summers
    • 3
  1. 1.Institut für Theoretische Physik and Courant Centre “Higher Order Structures in Mathematics”Universität GöttingenGöttingenGermany
  2. 2.Fakultät für PhysikUniversität WienViennaAustria
  3. 3.Department of MathematicsUniversity of FloridaGainesvilleUSA