New Objects in Scattering Theory with Symmetries

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Abstract

We consider 1D quantum scattering problem for a Hamiltonian with symmetries. We show that the proper treatment of symmetries in the spirit of homological algebra leads to new objects, generalizing the well-known T- and K-matrices. Homological treatment implies that old objects and new ones are to be combined in a differential. This differential arises from homotopy transfer of induced interaction and symmetries on solutions of free equations of motion. Therefore, old and new objects satisfy remarkable quadratic equations. We construct an explicit example in SUSY QM on a circle demonstrating nontriviality of the above relation.

About the authors

A. S Losev

Wu Wen-Tsun Key Lab of Mathematics, Chinese Academy of Sciences, 230026, Hefei, People’s Republic of China; National Research University Higher School of Economics, 119048, Moscow, Russia

Email: aslosev2@yandex.ru

T. V Sulimov

Petersburg Branch, Steklov Mathematical Institute, Russian Academy of Sciences, 191023, St. Petersburg, Russia

Author for correspondence.
Email: optimus260@gmail.com

References

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