The Generalized Gell-Mann–Low Theorem for Relativistic Bound States

ar X iv : h ep - p h / 05 06 12 3 v 1 1 3 Ju n 20 05 Bound states in Yukawa theory Axel

A generalization of the Gell-Mann–Low Theorem is applied to bound state calculations in Yukawa theory. The resulting effective Schrödinger equation is solved numerically for two-fermion bound states with the exchange of a massless boson. The complete low-lying bound state spectrum is obtained for different ratios of the constituent masses. No abnormal solutions are found. We show the consistenc...

Fine and hyperfine structure in different bound systems

We demonstrate that the generalized Gell-Mann–Low theorem permits for a systematic expansion around the nonrelativistic limit when applied to bound states in the Wick-Cutkosky model, Yukawa theory, and QED (in Coulomb gauge). We apply this expansion to obtain new results for the fine and hyperfine structure of bound states in the cases of the Wick-Cutkosky model and Yukawa theory, and reproduce...

Muonium spectrum beyond the nonrelativistic limit

A generalization of the Gell-Mann–Low theorem is applied to the antimuon-electron system. The bound state spectrum is extracted numerically. As a result, fine and hyperfine structure are reproduced correctly near the nonrelativistic limit (and for arbitrary masses). We compare the spectrum for the relativistic value α = 0.3 with corresponding calculations in light-front quantization.

Expression of a Tensor Commutation Matrix in Terms of the Generalized Gell-Mann Matrices

We have expressed the tensor commutation matrix n ⊗ n as linear combination of the tensor products of the generalized Gell-Mann matrices. The tensor commutation matrices 3 ⊗ 2 and 2 ⊗ 3 have been expressed in terms of the classical Gell-Mann matrices and the Pauli matrices. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use,...

Adiabatic approximation, Gell-Mann and Low theorem and degeneracies: A pedagogical example