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Speaker |
Fang, Yan-Long |
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Coauthors |
Levitin, Michael; Vassiliev, Dmitri |
| Talk Title |
Spectral Analysis Of The Massless Dirac Operator On A 3-manifold |
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Abstract |
The talk mainly concerns on energy spectrum of massless spin-1/2 particles. It will be an overview of a further development of the paper by Robert Downes, Michael Levitin and Dmitri Vassiliev on spectral theory of massless Dirac operator on 3-torus and will also give an insight how spectrum of massless Dirac operator on a 3-manifold interplays with geometric contents of the manifold. In contrast to the Riemann flat manifold, 3-torus, we study the massless Dirac operator on a 3-sphere equipped with standard Riemannian metric. As the asymptotic behaviour of higher eigenvalues has been studied by Dmitri Vassiliev in details and it is know as Weyl law for massless Dirac operator. We will see how the lowest, in terms of modulus, positive and negative eigenvalues relate to characteristic length of the manifold (curved space). Also, we will also answer whether the energy levels of both particle and antiparticle shift symmetrically under arbitrary perturbations. Finally, we will compare our new result with the paper on 3-torus. |
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Talk view |
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