scholarly journals Projective structure, $\widetilde{\operatorname{SL}}(3,\mathbb{R})$ and the symplectic Dirac operator

2016 ◽  
pp. 313-324
Author(s):  
Marie Holíková ◽  
Libor Křižka ◽  
Petr Somberg
Keyword(s):  
Dirac Operator ◽  
Projective Structure ◽  
Symplectic Dirac Operator

scholarly journals Basic Aspects of Symplectic Clifford Analysis for the Symplectic Dirac Operator

2016 ◽  
Vol 27 (2) ◽  
pp. 1103-1132 ◽  
Author(s):  
Hendrik De Bie ◽  
Marie Holíková ◽  
Petr Somberg
Keyword(s):  
Dirac Operator ◽  
Clifford Analysis ◽  
Symplectic Dirac Operator

scholarly journals Higher symmetries of symplectic Dirac operator

2020 ◽  
Vol 209 (1) ◽  
pp. 177-198
Author(s):  
Petr Somberg ◽  
Josef Šilhan
Keyword(s):  
Dirac Operator ◽  
Higher Symmetries ◽  
Symplectic Dirac Operator

A Hodge theoretic projective structure on compact Riemann surfaces

2021 ◽  
Vol 149 ◽  
pp. 1-27
Author(s):  
Indranil Biswas ◽  
Elisabetta Colombo ◽  
Paola Frediani ◽  
Gian Pietro Pirola
Keyword(s):  
Riemann Surfaces ◽  
Projective Structure ◽  
Compact Riemann Surfaces

scholarly journals Extended supersymmetries and the Dirac operator

2005 ◽  
Vol 315 (2) ◽  
pp. 467-487 ◽  
Author(s):  
A. Kirchberg ◽  
J.D. Länge ◽  
A. Wipf
Keyword(s):  
Dirac Operator

scholarly journals Eigenvalue bounds for non-selfadjoint Dirac operators

2021 ◽  
Author(s):  
Piero D’Ancona ◽  
Luca Fanelli ◽  
Nico Michele Schiavone
Keyword(s):  
Dirac Operator ◽  
Discrete Spectrum ◽  
Complex Plane ◽  
Dirac Operators ◽  
Resolvent Estimates ◽  
Eigenvalue Bounds ◽  
Mixed Norms ◽  
Massless Case ◽  
Abstract Version ◽  
Embedded Eigenvalues

AbstractWe prove that the eigenvalues of the n-dimensional massive Dirac operator $${\mathscr {D}}_0 + V$$ D 0 + V , $$n\ge 2$$ n ≥ 2 , perturbed by a potential V, possibly non-Hermitian, are contained in the union of two disjoint disks of the complex plane, provided V is sufficiently small with respect to the mixed norms $$L^1_{x_j} L^\infty _{{\widehat{x}}_j}$$ L x j 1 L x ^ j ∞ , for $$j\in \{1,\dots ,n\}$$ j ∈ { 1 , ⋯ , n } . In the massless case, we prove instead that the discrete spectrum is empty under the same smallness assumption on V, and in particular the spectrum coincides with the spectrum of the unperturbed operator: $$\sigma ({\mathscr {D}}_0+V)=\sigma ({\mathscr {D}}_0)={\mathbb {R}}$$ σ ( D 0 + V ) = σ ( D 0 ) = R . The main tools used are an abstract version of the Birman–Schwinger principle, which allows in particular to control embedded eigenvalues, and suitable resolvent estimates for the Schrödinger operator.

Sign in / Sign up

Export Citation Format

Share Document