On the Yang-Mills Propagator at Strong Coupling

About twelve years ago, the use of standard functional manipulations was demonstrated to imply an unexpected property satisfied by the fermionic Green’s functions of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>Q</mi><mi>C</mi><mi>D</mi></mrow></semantics></math></inline-formula>. This non-perturbative phenomenon has been dubbed an <i>effective locality</i>. In a much simpler way than in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>Q</mi><mi>C</mi><mi>D</mi></mrow></semantics></math></inline-formula>, the most remarkable and intriguing aspects of effective locality have been presented in a recent publication on the Yang-Mills theory on Minkowski spacetime. While quickly recalled in the current paper, these results are used to calculate the problematic gluonic propagator in the Yang-Mills non-perturbative regime. This paper is dedicated to the memory of Professor Herbert M. Fried (1929–2023), whose inspiring manner, impressive command of functional methods in quantum field theories, enthusiasm for a broad range of topics in Theoretical Physics, and warm friendship are missed greatly by the authors.