Deformation Quantization

  • Kasia RejznerEmail author
Part of the Mathematical Physics Studies book series (MPST)


The reformulation of classical theory done in Chap.  3 served as a preparation for constructing QFT models. The framework that we are going to use is deformation quantization combined with causal perturbation theory. To quantize a given theory described by the action S we first need to split S into a free part \(S_0\) (at most quadratic in field configurations) and the interaction term \(S_I\). Then, we quantize the theory defined by \(S_0\), using deformation quantization based on a Moyal-type formula, and in the final step we will re-introduce the interaction using causal perturbation theory. This last step will be discussed in Chap.  6, while the present chapter deals with deformation quantization.


Formal Power Series Star Product Field Configuration Deformation Quantization Canonical Poisson Bracket 
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© The Author(s) 2016

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of YorkYorkUK

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