Physics:Ginsparg–Wilson equation
In lattice field theory, the Ginsparg–Wilson equation generalizes chiral symmetry on the lattice in a way that approaches the continuum formulation in the continuum limit. The class of fermions whose Dirac operators satisfy this equation are known as Ginsparg–Wilson fermions, with notable examples being overlap, domain wall and fixed point fermions. They are a means to avoid the fermion doubling problem, widely used for instance in lattice QCD calculations.[1] The equation was discovered by Paul Ginsparg and Kenneth Wilson in 1982,Cite error: Closing </ref> missing for <ref> tag[2][3]
- [math]\displaystyle{ D\gamma_5 + \gamma_5 D = a\,D\gamma_5 D\, }[/math]
which recovers the correct continuum expression as the lattice spacing [math]\displaystyle{ a }[/math] goes to zero.
In contrast to Wilson fermions, Ginsparg–Wilson fermions do not modify the inverse fermion propagator additively but multiplicatively, thus lifting the unphysical poles at [math]\displaystyle{ p_\mu = \pi/a }[/math]. The exact form of this modification depends on the individual realisation.
References
- ↑ FLAG Working Group; Aoki, S. (2014). "A.1 Lattice actions". Review of Lattice Results Concerning Low-Energy Particle Physics. Eur. Phys. J. C. 74. pp. 116–117. doi:10.1140/epjc/s10052-014-2890-7.
- ↑ Rothe, Heinz J. (2005). "4 Fermions on the lattice". Lattice Gauge Theories: An Introduction. World Scientific Lecture Notes in Physics (3 ed.). World Scientific Publishing Company. pp. 73–76. ISBN 978-9814365857.
- ↑ Chandrasekharan, S. (2004). "An introduction to chiral symmetry on the lattice". Progress in Particle and Nuclear Physics (Elsevier BV) 53 (2): 373–418. doi:10.1016/j.ppnp.2004.05.003. ISSN 0146-6410. Bibcode: 2004PrPNP..53..373C. http://dx.doi.org/10.1016/j.ppnp.2004.05.003.
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