Abstract
In this chapter, we discuss generalize the results in the previous chapter in the view point of the chiral symmetry on a lattice. First, we review the Dirac operator on a lattice and doubler modes. Then we derive the analytical formula connecting the Polyakov loop and the Dirac-eigenmodes which does not have doubler modes such as the Wilson–Dirac operator and overlap-Dirac operator. In particular, the overlap-Dirac operator leads to chiral fermion on a lattice. Our generalized formula also indicates no direct one-to-one correspondence between confinement and chiral symmetry breaking in QCD.
Keywords
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
H.J. Rothe, Lattice Gauge Theories (World Scientific, Singapore, 2012)
H.B. Nielsen, M. Ninomiya, Nucl. Phys. B 185, 20 (1981)
H.B. Nielsen, M. Ninomiya, Nucl. Phys. B 193, 173 (1981)
K.G. Wilson, Phys. Rev. D 10, 2445 (1974)
P.H. Ginsparg, K.G. Wilson, Phys. Rev. D 25, 2649 (1995)
H. Neuberger, Phys. Lett. B 417, 141 (1998)
H. Neuberger, Phys. Lett. B 427, 353 (1998)
M. Luscher, Phys. Lett. B 428, 342 (1998)
S. Aoki et al., Phys. Rev. D 78, 014508 (2008)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2017 Springer Nature Singapore Pte. Ltd
About this chapter
Cite this chapter
Doi, T. (2017). Generalization to Chiral Fermion on the Lattice. In: Lattice QCD Study for the Relation Between Confinement and Chiral Symmetry Breaking. Springer Theses. Springer, Singapore. https://doi.org/10.1007/978-981-10-6596-5_3
Download citation
DOI: https://doi.org/10.1007/978-981-10-6596-5_3
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-10-6595-8
Online ISBN: 978-981-10-6596-5
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)