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Register a new userCP and T violation in non-perturbative chiral gauge theories
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Authors
Werner Kerler
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We give a completely general derivation revealing the precise origin and the quantitative effects of CP and T violations in chiral gauge theories on the lattice.
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We reconsider gauge-transformation properties in chiral gauge theories on the lattice observing all pertinent information and show that these properties are actually determined in a general way for any gauge group and for any value of the index. In our investigations we also clarify several related issues.
Only requiring that Dirac operators decribing massless fermions on the lattice decompose into Weyl operators we arrive at a large class of them. After deriving general relations from spectral representations we study correlation functions of Weyl fermions for any value of the index, stressing the related conditions for basis transformations and getting the precise behaviors under gauge and CP transformations. Using the detailed structure of the chiral projections we also obtain a form of the correlation functions with a determinant in the general case.
We show that gauge-transformation properties of correlation functions in chiral gauge theories on the finite lattice are determined in a general way.
We present a formulation of chiral gauge theories, which admits more general spectra of Dirac operators and reveals considerably more possibilities for the structure of the chiral projections. Our two forms of correlation functions both also apply in the presence of zero modes and for any value of the index. The decomposition of the total set of pairs of bases into equivalence classes is carefully analyzed. Transformation properties are derived.
We present a general formulation of chiral gauge theories, which admits Dirac operators with more general spectra, reveals considerably more possibilities for the structure of the chiral projections, and nevertheless allows appropriate realizations. In our analyses we use two forms of the correlation functions which both also apply in the presence of zero modes and for any value of the index. To account properly for the conditions on the bases the concept of equivalence classes of pairs of them is introduced. The behaviors under gauge transformations and under CP transformations are unambiguously derived.
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