Polarization propagators from the path integral formalism. New insights that may indicate new roads on molecular physics

GUSTAVO A. AUCAR

París

Workshop; "Mathematical challenges in Quantum Electrodynamics".; 2013

Institute Henry Poincare

The polarization propagator written within any of both regimes, relativistic and non-relativistic, was shown to be a sound theoretical device that gives new insights on the understanding of the quantum origin of electronic effects, and also quite accurate results when the calculations are performed at the second-order level of approach, SOPPA1, 2. From the beginning of its relativistic generalization3 it was shown that: a) there are not two but only one formal expression of polarization propagators; b) its NR limit is obtained just making c goes to infinity; c) the magnetic response of any magnetic property usually broken in two magnetic terms, e. g diamagnetic and paramagnetic, become only one, and d) diamagnetic-like terms arise by the consideration of virtual electron-positron pairs. These facts did advice that there should be a deeper mathematical origin and so, new physical insights obtainable by working with such formalism. In this presentation we will give a brief introduction to polarization propagators and show how far away one can go today working with them, till including QED effects. From its deep formal origin one can explain why they have the behavior just found few years ago: polarization propagators do arise from the path integral formalism, which is one of the most used by the QFT community and the closest to the "classical" way of describing physics, though being it purely quantum physics. This formalism can be used as an alternative to the traditional methods for including QED effects on molecular properties. We will also show how to handle the contributions of negative energy states to the electron correlation at a relativistic SOPPA. 1.J. Oddershede, P. Jorgensen and D. L. Yeager, Comp. Phys. Rep. 2, 33 (1984). 2.G. A. Aucar, R. H. Romero and A. F. Maldonado, Int. Rev. on Phys. Chem. 29, 1-64 (2010). 3.J. Oddershede and G. A. Aucar. Int. J. Quantum Chem. 47, 425 (1993).