TO: Michael Dütsch, Guest of Institute of Theoretical Physics, University of Göttingen, Germany
FM: Bruce E. Camber
RE: Your book, From Classical Field Theory to Perturbative Quantum Field Theory, 2018, your arXiv articles such as On Gauge Invariance and Spontaneous Symmetry Breaking (1997); and Inspire^HEP, nLab, and ResearchGate.

URL: https://81018.com/dutsch/ Also: http://81018.com/transformation/#12f

First email: 5 August 2019

Reference: https://arxiv.org/abs/1012.5604
Connection between the renormalization groups of Stückelberg-Petermann and Wilson

Dear Prof. Dr. Michael Dütsch:

I have this hunch that the renormalization groups actually tell us
a little something special about the very nature of infinity.

Is that silliness at the outset?

Of course, I thank you for all your very substantial work, especially your work within arXiv particularly the following which are now on my reading list:

• The scaling and mass expansion
• Dimensional Regularization in Position Space…

Thank you.

Most sincerely,
Bruce

Keywords: Finite quantum field theory (FQFT), causal perturbation theory, Scaling (geometry), perturbative quantum field theory,  AQFT,
Main Theorem of Renormalization of Stora and Popineau

Epstein-Glaser renormalization (causal perturbation theory) appears to have no infinities. Renormalization (in $x$-space) amounts to the extension of a distribution which is defined outside the point $x=0$to a distribution which is defined everywhere. This extension is non-unique; the renormalization group describes this indefiniteness.

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