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Feynman Diagrams, Luttinger-Ward Formalism, and Gibbs Measure

2018-06-20 14:00 - 2018-06-20 15:00 Room 29, Quan Zhai, BICMR

\n\tMany-body perturbation theory (MBPT) is widely used in quantum physics, chemistry, and materials science. At the heart of MBPT is the Feynman diagrammatic expansion.  However, for quantum many-body problems, many developments of MBPT are only formally valid. This shortcoming raises both theoretical and practical questions.  By exploring the correspondence between the Feynman diagrammatic expansion and a certain class of Gibbs measures, we provide a relatively concise and self-contained introduction to MBPT, which requires no more knowledge a priori than multivariable calculus. We demonstrate that the resulting models yields diagrammatic expansion that can provide useful insights toward the rigorous understanding of certain topics in MBPT, such as the existence of the Luttinger-Ward functional and the validity of the bold diagrammatic expansion. We also demonstrate that the numerical implementation of MBPT for such Gibbs model, compared to that of the quantum many-body problem, requires significantly reduced effort. (Joint work with Michael Lindsey)<\/span>\n<\/div>