Tropical Mirror Symmetry in Dimension One

We prove a tropical mirror symmetry theorem for descendant Gromov-Witten invariants of the elliptic curve, generalizing Hurwitz numbers Theorem 2.20 in [B\"ohm J., Bringmann K., Buchholz A., Markwig H., J. Reine Angew. Math. 732 (2017), 211-246, arXiv:1309.5893]. For case version holds on fine level and easily implies equality generating series curve to Feynman integrals. To curves, we investigate bijection between graph covers sets monomials contributing coefficient integral. also soup up traditional approach mathematical physics involving operators Fock space, give proof curve. In this way, shed light intimate relation operator bosonic space approach.