A great deal of progress has been made recently in the field of asymptotic formulas that arise
in the theory of Dirac and Laplace type operators. Asymptotic Formulae in Spectral …

A bstract We study the η-invariant of a Dirac operator on a manifold with boundary subject to
local boundary conditions with the help of heat kernel methods. In even dimensions, we …

In the presence of boundaries, the quantum anomalies acquire additional boundary terms.
In odd dimensions, the integrated conformal anomaly, for which the bulk contribution is …

Being motivated by applications to the physics of Weyl semimetals we study spectral
geometry of Dirac operator with an abelian gauge field and an axial vector field. We impose …

We propose a relation between the η invariant on a manifold with boundary, the η invariants
of edge states, and the η invariant in an infinite volume limit. With the example of planar …

We derive a commutative spectral triple and study the spectral action for a rather general
geometric setting which includes the (skew-symmetric) torsion and the chiral bag conditions …

It is known that in the zeta function regularization and in the Fujikawa method chiral anomaly
is defined through a coefficient in the heat kernel expansion for the Dirac operator. In this …

We consider the Atiyah-Patodi-Singer (APS) index theorem corresponding to the chiral
symmetry of a continuum formulation of staggered fermions called K\" ahler-Dirac fermions …

The η invariant plays an important role in Quantum Field Theory. It describes the parity
anomaly [1–3] which leads to a Chern–Simons term in the effective action for gauge fields …

We study asymptotic expansions of the smeared L 2-traces F e− t P^ 2 and FP e− tP^ 2,
where P is an operator of Dirac type and F is an auxiliary smooth endomorphism. We …