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

Relativistic path integral and relativistic Hamiltonians in QCD and QED