On the Effects of the Neumann Boundary Conditions in the Coleman–weinberg Mechanism

Fagundes, F. N.; Oakes, Thiago Luiz Antonacci; Dilem, B. B.; Nogueira, José Alexandre

doi:10.1142/s0217751x10048093

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“…Otherwise, the mechanism cannot be granted to generate mass as pointed out both for the case of the scalar field [21,22] and ColemanWeinberg mechanism [23,24]. About confinement, it should be emphasized that it is the combination of Yukawa-like propagators, showing mass gap, and a running coupling to possibly yield a confining potential [25,26,27].…”

Section: Introductionmentioning

confidence: 99%

Quantum Yang-Mills field theory

Frasca¹

2017

Eur. Phys. J. Plus

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We show that the Dyson-Schwinger set of equations for the YangMills theory can be exactly solved till the two-point function. This is obtained given a set of nonlinear waves solving the classical equations of motion. Translation invariance is maintained by the proper choice of the solution of the equation for the two-point function as devised by Coleman. The computation of the Dyson-Schwinger equations is performed in the same way as devised by Bender, Milton and Savage providing a set of partial differential equations whose proof of existence of the solutions is standard. So, the correlation functions of the theory could be proved to exist and the two-point function manifests a mass gap.

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