Fermion and photon gap-equations in Minkowski space within the Nakanishi integral representation method
Abstract The approach based on the Nakanishi integral representation of n-leg transition amplitudes is extended to the treatment of the self-energies of a fermion and an (IR-regulated) vector boson, in order to pave the way for constructing a comprehensive application of the technique to both gap- a...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2021-01-01
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| Series: | European Physical Journal C: Particles and Fields |
| Online Access: | https://doi.org/10.1140/epjc/s10052-020-08806-x |
| Summary: | Abstract The approach based on the Nakanishi integral representation of n-leg transition amplitudes is extended to the treatment of the self-energies of a fermion and an (IR-regulated) vector boson, in order to pave the way for constructing a comprehensive application of the technique to both gap- and Bethe-Salpeter equations, in Minkowski space. The achieved result, namely a 6-channel coupled system of integral equations, eventually allows one to determine the three Källén–Lehman weights for fully dressing the propagators of fermion and photon. A first consistency check is also provided. The presented formal elaboration points to embed the characteristics of the non-perturbative regime at a more fundamental level. It yields a viable tool in Minkowski space for the phenomenological investigation of strongly interacting theories, within a QFT framework where the dynamical ingredients are made transparent and under control. |
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| ISSN: | 1434-6044 1434-6052 |