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A four-dimensional approach to quantum field theories. (English) Zbl 1397.81177
Summary: I present a novel Four-Dimensional Regularization/Renormalization approach (FDR) to ultraviolet divergences in field theories which can be interpreted as a natural separation between physical and non physical degrees of freedom. Based on the observation that some infinities can be reabsorbed into the vacuum expectation value of the fields, rather than into the parameters of the Lagrangian, a new type of four-dimensional loop integral is introduced (the FDR integral) which is independent of any UV regulator and respects all properties required by gauge invariance. FDR reproduces the correct ABJ anomaly and no change in the definition of $$\gamma_5$$ is needed. With FDR the possibility is open for an approach to UV infinities in which the renormalization program is substituted by a simple reinterpretation of the appearing loop integrals as FDR ones, leading to important consequences in the context of non-renormalizable field theories. Finally, I show how FDR can also be used to regularize infrared and collinear divergences.

##### MSC:
 81T16 Nonperturbative methods of renormalization applied to problems in quantum field theory 81T18 Feynman diagrams
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