# Chiral anomaly for local boundary conditions

@article{Marachevsky2004ChiralAF,
title={Chiral anomaly for local boundary conditions},
author={Valery N. Marachevsky and Dmitri Vassilevich},
journal={Nuclear Physics},
year={2004},
volume={677},
pages={535-552}
}
• Published 1 September 2003
• Mathematics
• Nuclear Physics
19 Citations

### Stability Theorems for Chiral Bag Boundary Conditions

• Mathematics
• 2005
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

• Physics
Journal of Physics A: Mathematical and Theoretical
• 2022
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

• Physics
• 2006
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

• Physics
• 2004
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

• Mathematics
• 2012
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

• Mathematics
• 2006
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

• Mathematics, Physics
• 2004
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

• 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.

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• Mathematics
• 2003
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

### A NOTE ON THE HEAT KERNEL METHOD APPLIED TO FERMIONS

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