Abstract
In the framework of perturbative algebraic quantum field theory (pAQFT) we start with the classical theory, which is subsequently quantized. We work in the Lagrangian framework, but there are some modifications that we need to make to deal with the infinite dimensional character of field theory. In this chapter we give an overview of mathematical structures that will be needed later on to construct models of classical and quantum field theories. Since we do not fix the dynamics yet, the content of this chapter describes the kinematical structure of our model. Readers familiar with some of the concepts we introduce here can skip corresponding sections.
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Notes
- 1.
We say that a subset \(\Gamma \) of \(\widetilde{\Omega }\times (\mathbb {R}^n\setminus \{0\})\) is a cone if \((x,\lambda k)\in \Gamma \) whenever \((x,k)\in \Gamma \), \(\lambda >0\). A cone is said to be closed (open) if it is closed (open) in \(\widetilde{\Omega }\times (\mathbb {R}^n\setminus \{0\})\).
- 2.
This holds true, because \(\mathbb {C}\) is a field of characteristic 0.
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Rejzner, K. (2016). Kinematical Structure. In: Perturbative Algebraic Quantum Field Theory. Mathematical Physics Studies. Springer, Cham. https://doi.org/10.1007/978-3-319-25901-7_3
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