On the spectrum of the two-dimensional periodic Dirac operator

1999 ◽  
Vol 118 (1) ◽  
pp. 1-11 ◽  
Author(s):  
L. I. Danilov
Keyword(s):  
Dirac Operator ◽  
Two Dimensional ◽  
Periodic Dirac Operator

scholarly journals Spectrum of the Dirac operator coupled to two-dimensional quantum gravity

2002 ◽  
Vol 630 (1-2) ◽  
pp. 339-358 ◽  
Author(s):  
L. Bogacz ◽  
Z. Burda ◽  
C. Petersen ◽  
B. Petersson
Keyword(s):  
Quantum Gravity ◽  
Dirac Operator ◽  
Two Dimensional

FERMIONIC ZERO MODES IN SELF-DUAL VORTEX BACKGROUND ON A SPHERE

2007 ◽  
Vol 22 (21) ◽  
pp. 3643-3653 ◽  
Author(s):  
YU-XIAO LIU ◽  
LI ZHAO ◽  
LI-JIE ZHANG ◽  
YI-SHI DUAN
Keyword(s):  
Riemann Surface ◽  
Dirac Equation ◽  
Dirac Operator ◽  
Topological Structure ◽  
The Self ◽  
Two Dimensional ◽  
Zero Modes ◽  
Self Duality ◽  
Effective Lagrangian ◽  
Topological Term

We study fermionic zero modes in the self-dual vortex background on an extra two-dimensional Riemann surface in 5+1 dimensions. Using the generalized Abelian Higgs model, we obtain the inner topological structure of the self-dual vortex and establish the exact self-duality equation with topological term. Then we analyze the Dirac operator on an extra sphere and the effective Lagrangian of four-dimensional fermions with the self-dual vortex background. Solving the Dirac equation, the fermionic zero modes on a sphere in two simple cases are obtained.

scholarly journals A Note on the Three Dimensional Dirac Operator with Zigzag Type Boundary Conditions

2021 ◽  
Vol 15 (3) ◽  
Author(s):  
Markus Holzmann
Keyword(s):  
Dirac Operator ◽  
Boundary Conditions ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Dirichlet Laplacian ◽  
Open Set ◽  
Type Boundary ◽  
Infinite Multiplicity ◽  
Zigzag Type

AbstractIn this note the three dimensional Dirac operator $$A_m$$ A m with boundary conditions, which are the analogue of the two dimensional zigzag boundary conditions, is investigated. It is shown that $$A_m$$ A m is self-adjoint in $$L^2(\Omega ;{\mathbb {C}}^4)$$ L 2 ( Ω ; C 4 ) for any open set $$\Omega \subset {\mathbb {R}}^3$$ Ω ⊂ R 3 and its spectrum is described explicitly in terms of the spectrum of the Dirichlet Laplacian in $$\Omega $$ Ω . In particular, whenever the spectrum of the Dirichlet Laplacian is purely discrete, then also the spectrum of $$A_m$$ A m consists of discrete eigenvalues that accumulate at $$\pm \infty $$ ± ∞ and one additional eigenvalue of infinite multiplicity.

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