scholarly journals Axial anomaly with the overlap-Dirac operator in arbitrary dimensions

2002 ◽  
Vol 2002 (09) ◽  
pp. 025-025 ◽  
Author(s):  
Takanori Fujiwara ◽  
Keiichi Nagao ◽  
Hiroshi Suzuki
Keyword(s):  
Dirac Operator ◽  
Axial Anomaly ◽  
Arbitrary Dimensions

scholarly journals ON INDICES OF THE DIRAC OPERATOR IN A NON-FREDHOLM CASE

1996 ◽  
Vol 11 (12) ◽  
pp. 979-986
Author(s):  
ALEXANDER MOROZ
Keyword(s):  
Dirac Operator ◽  
Heat Kernel ◽  
Continuous Spectrum ◽  
Fredholm Operator ◽  
Axial Anomaly ◽  
Bohm Potential ◽  
Spectral Asymmetry ◽  
Aharonov Bohm ◽  
Dirac Hamiltonian

The Dirac–Hamiltonian with the Aharonov–Bohm potential provides an example of a non-Fredholm operator for which all spectral asymmetry comes entirely from the continuous spectrum. In this case one finds that the use of standard definitions of the resolvent regularized, the heat kernel regularized, and the Witten indices misses the contribution coming from the continuous spectrum and gives vanishing spectral asymmetry and axial anomaly. This behavior in the case of the continuous spectrum seems to be general and its origin is discussed.

scholarly journals Global Symmetries of Naive and Staggered Fermions in Arbitrary Dimensions

2018 ◽  
Vol 175 ◽  
pp. 04006 ◽  
Author(s):  
Mario Kieburg ◽  
Tim R. Würfel
Keyword(s):  
Monte Carlo ◽  
Dirac Operator ◽  
Global Symmetries ◽  
Group Representation ◽  
Arbitrary Dimension ◽  
Continuum Theory ◽  
Staggered Fermions ◽  
Spectral Statistics ◽  
Arbitrary Dimensions ◽  
The Continuum

It is well-known that staggered fermions do not necessarily satisfy the same global symmetries as the continuum theory. We analyze the mechanism behind this phenomenon for arbitrary dimension and gauge group representation. For this purpose we vary the number of lattice sites between even and odd parity in each single direction. Since the global symmetries are manifest in the lowest eigenvalues of the Dirac operator, the spectral statistics and also the symmetry breaking pattern will be affected. We analyze these effects and compare our predictions with Monte-Carlo simulations of naive Dirac operators in the strong coupling limit. This proceeding is a summary of our work [1].

scholarly journals Axial anomaly in lattice abelian gauge theory in arbitrary dimensions

1999 ◽  
Vol 463 (1) ◽  
pp. 63-68 ◽  
Author(s):  
Takanori Fujiwara ◽  
Hiroshi Suzuki ◽  
Ke Wu
Keyword(s):  
Gauge Theory ◽  
Abelian Gauge ◽  
Axial Anomaly ◽  
Abelian Gauge Theory ◽  
Arbitrary Dimensions

NATURAL REGULARIZATION

2007 ◽  
Vol 16 (01) ◽  
pp. 59-67 ◽  
Author(s):  
M. DILLIG
Keyword(s):  
Dimensional Reduction ◽  
Gauge Theories ◽  
Dimensional Regularization ◽  
Feynman Integrals ◽  
Axial Anomaly ◽  
Reduced Integration ◽  
Arbitrary Dimensions ◽  
Integration Space

We formulate natural regularization (NR) as a variant of dimensional regularization (DR). We replace the conventional dimensional reduction by a dimensionless regulator, allowing a transparent regularization of standard D-dimensional Feynman integrals. For arbitrary dimensions, we motivate and demonstrate explicitly the transition from the dimensionally reduced integration space to natural regularization. We establish the relation to cut-off regularization and point out the basic differences from dimensional regularization. Possible applications, such as to the axial anomaly or to gauge theories are briefly touched upon.

Sign in / Sign up

Export Citation Format

Share Document