Interaction and Renormalization of the Scalar Field Theory

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


In the previous chapter we have covered the quantization of free theories (quadratic actions); now is the time to introduce the interactions. This is where we have to start working perturbatively. The ultimate goal of AQFT is to be able to construct interacting models in 4 spacetime dimensions non-perturbatively, but at the moment no such models are known. The perturbative approach, on the other hand, has proven to be successful in describing many phenomena in particle physics, so it is worthwhile to try to understand its mathematical foundations. It turns out that a careful analysis of the problem and employing some tools from functional analysis allow us to avoid dealing with ill defined “divergent” expressions, as is often done in physics textbooks.


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Copyright information

© The Author(s) 2016

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of YorkYorkUK

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