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Dirac operators on coset spaces [PDF]
Journal of Mathematical Physics, 2003 The Dirac operator for a manifold Q, and its chirality operator when Q is even dimensional, have a central role in noncommutative geometry. We systematically develop the theory of this operator when Q=G/H, where G and H are compact connected Lie groups and G is simple.
Balachandran, A. P. +3 more
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Topological index theorem on the lattice through the spectral flow of staggered fermions
Physics Letters B, 2015 We investigate numerically the spectral flow introduced by Adams for the staggered Dirac operator on realistic (quenched) gauge configurations. We obtain clear numerical evidence that the definition works as expected: there is a clear separation between ...
V. Azcoiti +3 more
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Unitary Howe dualities in fermionic and bosonic algebras and related Dirac operators
SciPost Physics Proceedings, 2023 In this paper we use the canonical complex structure $\mathbb{J}$ on $\mathbb{R}^{2n}$ to introduce a twist of the symplectic Dirac operator. This can be interpreted as the bosonic analogue of the Dirac operators on a Hermitian manifold.
Guner Muarem
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Advances in Applied Clifford Algebras, 2009 We introduce non-linear Dirac operators in $\mathbb{R}^{n}$ associated to the $p$-harmonic equation and we extend to other contexts including spin manifolds and the sphere.
Nolder, Craig A., Ryan, John
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Dirac operator spectrum on a nilmanifold
Nuclear Physics B, 2022 We obtain the spectrum of the Dirac operator on the three-dimensional Heisenberg nilmanifold M3, and its complete dependence on the metric moduli.
Aldo Deandrea +2 more
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Dirac Operators on Noncommutative Curved Spacetimes
Symmetry, Integrability and Geometry: Methods and Applications, 2013 We study the notion of a Dirac operator in the framework of twist-deformed noncommutative geometry. We provide a number of well-motivated candidate constructions and propose a minimal set of axioms that a noncommutative Dirac operator should satisfy ...
Alexander Schenkel +1 more
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The dirac operator and gravitation [PDF]
Communications in Mathematical Physics, 1995 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Alternatives to the stochastic “noise vector” approach
EPJ Web of Conferences, 2018 Several important observables, like the quark condensate and the Taylor coefficients of the expansion of the QCD pressure with respect to the chemical potential, are based on the trace of the inverse Dirac operator and of its powers.
de Forcrand Philippe, Jäger Benjamin
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Distribution of the Dirac modes in QCD
EPJ Web of Conferences, 2018 It was established that distribution of the near-zero modes of the Dirac operator is consistent with the Chiral Random Matrix Theory (CRMT) and can be considered as a consequence of spontaneous breaking of chiral symmetry (SBCS) in QCD.
Catillo M., Glozman L. Ya.
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DIRAC OPERATOR IN MATRIX GEOMETRY [PDF]
International Journal of Geometric Methods in Modern Physics, 2005 We review the construction of the Dirac operator and its properties in Riemannian geometry, and show how the asymptotic expansion of the trace of the heat kernel determines the spectral invariants of the Dirac operator and its index. We also point out that the Einstein–Hilbert functional can be obtained as a linear combination of the first two ...
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