Attempt at obtaining bound states from QED Lagrangian : A renormalization flow approach

Roy, Beetehotra (2019) Attempt at obtaining bound states from QED Lagrangian : A renormalization flow approach. Masters thesis, Indian Institute of Science Education and Research Kolkata.

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Abstract

In this project, we wish to show that the positronium atom emerges from the QED Lagrangian as a stable bound state. For this, we first show the development of a nonperturbative RG procedure by applying it on the 1-D Hubbard model. Then we start from QED lagrangian, integrate out the gauge sector, and apply the aformentioned renormalization procedure to the effective theory. We show that the positronium naturally come out of it under non-relativistic approximation, and we are also able to determine the relative energy scales of L-S and S-S coupling, which matches with the literature value. In future, this technique may be helpful in determining the meson and baryon bound states from the QCD Lagrangian.

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