The axial anomaly and the lattice Dirac sea
(1983) In Nuclear Physics, Section B 221(2). p.381-408- Abstract
In the hamiltonian formulation of fermions coupled to external gauge fields, the axial anomaly has a simple physical interpretation in terms of level shifting at the top of the Dirac sea. We apply this formalism to lattice QED in 1 + 1 and 3 + 1 dimensions, in order to study how the lattice regulation and small fermion mass affect the picture. For a simple choice of the E and B fields, it is possible to accurately follow the time evolution of the (lattice) Dirac sea of Wilson fermions. We find that the Wilson r term plays a role, with respect to the anomaly, which is closely analogous to point-splitting in the continuum. This role is jeopardized whenever the Wilson mass scale r/a is comparable to other physical mass scales in the... (More)
In the hamiltonian formulation of fermions coupled to external gauge fields, the axial anomaly has a simple physical interpretation in terms of level shifting at the top of the Dirac sea. We apply this formalism to lattice QED in 1 + 1 and 3 + 1 dimensions, in order to study how the lattice regulation and small fermion mass affect the picture. For a simple choice of the E and B fields, it is possible to accurately follow the time evolution of the (lattice) Dirac sea of Wilson fermions. We find that the Wilson r term plays a role, with respect to the anomaly, which is closely analogous to point-splitting in the continuum. This role is jeopardized whenever the Wilson mass scale r/a is comparable to other physical mass scales in the problem, as is the case, for example, in strong coupling calculations. Remarkably, we find that hadronic scales of only a few lattice spacings are probably sufficient to guarantee the proper anomaly structure.
(Less)
- author
- Ambjørn, J. ; Greensite, J. and Peterson, C. LU
- publishing date
- 1983-07-11
- type
- Contribution to journal
- publication status
- published
- in
- Nuclear Physics, Section B
- volume
- 221
- issue
- 2
- pages
- 28 pages
- publisher
- North-Holland
- external identifiers
-
- scopus:0000333095
- ISSN
- 0550-3213
- DOI
- 10.1016/0550-3213(83)90585-0
- language
- English
- LU publication?
- no
- id
- fd3c7d21-2c60-4748-8323-4350625c343a
- date added to LUP
- 2019-05-14 16:56:00
- date last changed
- 2021-10-10 04:41:15
@article{fd3c7d21-2c60-4748-8323-4350625c343a,
abstract = {{<p>In the hamiltonian formulation of fermions coupled to external gauge fields, the axial anomaly has a simple physical interpretation in terms of level shifting at the top of the Dirac sea. We apply this formalism to lattice QED in 1 + 1 and 3 + 1 dimensions, in order to study how the lattice regulation and small fermion mass affect the picture. For a simple choice of the E and B fields, it is possible to accurately follow the time evolution of the (lattice) Dirac sea of Wilson fermions. We find that the Wilson r term plays a role, with respect to the anomaly, which is closely analogous to point-splitting in the continuum. This role is jeopardized whenever the Wilson mass scale r/a is comparable to other physical mass scales in the problem, as is the case, for example, in strong coupling calculations. Remarkably, we find that hadronic scales of only a few lattice spacings are probably sufficient to guarantee the proper anomaly structure.</p>}},
author = {{Ambjørn, J. and Greensite, J. and Peterson, C.}},
issn = {{0550-3213}},
language = {{eng}},
month = {{07}},
number = {{2}},
pages = {{381--408}},
publisher = {{North-Holland}},
series = {{Nuclear Physics, Section B}},
title = {{The axial anomaly and the lattice Dirac sea}},
url = {{http://dx.doi.org/10.1016/0550-3213(83)90585-0}},
doi = {{10.1016/0550-3213(83)90585-0}},
volume = {{221}},
year = {{1983}},
}