Chiral anomaly for local boundary conditions

  title={Chiral anomaly for local boundary conditions},
  author={Valery N. Marachevsky and Dmitri Vassilevich},
  journal={Nuclear Physics},

Stability Theorems for Chiral Bag Boundary Conditions

We study asymptotic expansions of the smeared L2-traces Fe−tP^2 and FPe−tP^2, where P is an operator of Dirac type and F is an auxiliary smooth endomorphism. We impose chiral bag boundary conditions

Heat kernel, effective action and anomalies in noncommutative theories

Being motivated by physical applications (as the 4 model) we calculate the heat kernel coefficients for generalised laplacians on the Moyal plane containing both left and right multiplications. We

Heat kernel, spectral functions and anomalies in Weyl semimetals

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 chiral bag boundary

Finite temperature properties of the Dirac operator with bag boundary conditions

We study the finite temperature free energy and fermion number for Dirac fields in a one-dimensional spatial segment, under local boundary conditions, compatible with the presence of a spectral

Nonsmooth backgrounds in quantum field theory

The one-loop renormalization in field theories can be formulated in terms of the heat kernel expansion. In this paper we calculate leading contributions of discontinuities of background fields and

Spectral Action for Torsion with and without Boundaries

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 on the boundary.

Spectral asymmetry on the ball and asymptotics of the asymmetry kernel

Let be the Dirac operator on a D = 2d dimensional ball with radius R. We calculate the spectral asymmetry for D = 2 and D = 4, when local chiral bag boundary conditions are imposed. With these

Finite-temperature properties of the Dirac operator under local boundary conditions

We study the finite-temperature free energy and fermion number for Dirac fields in a one-dimensional spatial segment, under two different members of the family of local boundary conditions defining a

Chiral Anomaly with MIT Bag Boundary Conditions

After a brief review of the heat kernel approach we obtain a chiral anomaly for local MIT bag boundary conditions.

Remark on the synergy between the heat kernel techniques and the parity anomaly

  • M. KurkovL. Leone
  • Computer Science
    International Journal of Geometric Methods in Modern Physics
  • 2019
It is shown that the gravitational parity anomaly on four-dimensional manifolds with boundaries can be calculated using the general structure of the heat kernel coefficient for mixed boundary conditions, keeping all the weights of various geometric invariants as unknown numbers.



Strong ellipticity and spectral properties of chiral bag boundary conditions

We prove strong ellipticity of chiral bag boundary conditions on even dimensional manifolds. From a knowledge of the heat kernel in an infinite cylinder, some basic properties of the zeta function


The spectrum of the fermionic operators depending on external fields is an important object in quantum field theory. In this paper we prove, using transition to the alternative basis for the

Path Integral Measure for Gauge Invariant Fermion Theories

It is shown that the path-integral measure for gauge-invariant fermion theories is not invariant under the ${\ensuremath{\gamma}}_{5}$ transformation and the Jacobian gives rise to an extra phase