Relativistic path integral and relativistic Hamiltonians in QCD and QED

Abstract

The proper-time 4d path integral is used as a starting point to derive the new explicit parametric form of the quark-antiquark Green's function in gluonic and QED fields, entering as a common Wilson loop. The subsequent vacuum averaging of the latter allows to derive the instantaneous Hamiltonian. The explicit form and solutions are given in the case of the $q\bar{q}$ mesons in magnetic field.

Comments: 27 pages,2 figures,misprints corrected