TY - JOUR A1 - Ludewig, Matthias A1 - Rosenberger, Elke T1 - Asymptotic eigenfunctions for Schrödinger operators on a vector bundle JF - Reviews in mathematical physics N2 - In the limit (h) over bar -> 0, we analyze a class of Schrödinger operators H-(h) over bar = (h) over bar L-2 + (h) over barW + V .id(epsilon) acting on sections of a vector bundle epsilon over a Riemannian manifold M where L is a Laplace type operator, W is an endomorphism field and the potential energy V has a non-degenerate minimum at some point p is an element of M. We construct quasimodes of WKB-type near p for eigenfunctions associated with the low-lying eigenvalues of H-(h) over bar. These are obtained from eigenfunctions of the associated harmonic oscillator H-p,H-(h) over bar at p, acting on smooth functions on the tangent space. KW - Semi-classical analysis KW - WKB approximation KW - Schrödinger operators KW - semi-classical limit Y1 - 2020 U6 - https://doi.org/10.1142/S0129055X20500208 SN - 0129-055X SN - 1793-6659 VL - 32 IS - 7 PB - World Scientific CY - Singapore ER - TY - JOUR A1 - Ludewig, Matthias A1 - Roos, Saskia T1 - The chiral anomaly of the free fermion in functorial field theory JF - Annales Henri Poincaré : a journal of theoretical and mathematical physics N2 - When trying to cast the free fermion in the framework of functorial field theory, its chiral anomaly manifests in the fact that it assigns the determinant of the Dirac operator to a top-dimensional closed spin manifold, which is not a number as expected, but an element of a complex line. In functorial field theory language, this means that the theory is twisted, which gives rise to an anomaly theory. In this paper, we give a detailed construction of this anomaly theory, as a functor that sends manifolds to infinite-dimensional Clifford algebras and bordisms to bimodules. Y1 - 2020 U6 - https://doi.org/10.1007/s00023-020-00893-6 SN - 1424-0637 SN - 1424-0661 VL - 21 IS - 4 SP - 1191 EP - 1233 PB - Springer International Publishing AG CY - Cham (ZG) ER -