On the Renormalization of the Complex Scalar Free Field Theory
Ruggero Ferrari
TL;DR
This paper demonstrates how to renormalize a complex scalar free field theory in four dimensions using a symmetric subtraction method in polar coordinates, proving the coordinate transformation's existence.
Contribution
It introduces a symmetric subtraction procedure to renormalize a non-renormalizable theory in polar coordinates, with a proof of the coordinate transformation's existence.
Findings
Successful renormalization of the complex scalar free field in polar coordinates.
Validation of the symmetric subtraction method for non-renormalizable theories.
Proof of the coordinate transformation's existence in the renormalization process.
Abstract
Polar coordinates are used for the complex scalar free field in D=4 dimensions. The resulting non renormalizable theory is healed by using a recently proposed symmetric subtraction procedure. The existence of the coordinates transformation is proved by construction.
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