Resolvent operator of singular Dirac system with transmission conditions

Resolvent Estimates of the Dirac Operator

Non-Perturbative Dirac Operator Resolvent Analysis

We analyze the 1 + 1 dimensional Nambu-Jona-Lasinio model nonperturbatively. In addition to its simple ground state saddle points, the effective action of this model has a rich collection of non-trivial saddle points in which the composite fields σ(x) = 〈ψ̄ψ〉 and π(x) = 〈ψ̄iγ5ψ〉 form static space dependent configurations because of non-trivial dynamics. These configurations may be viewed as one d...

Inverse Problem for Interior Spectral Data of the Dirac Operator with Discontinuous Conditions

In this paper, we study the inverse problem for Dirac differential operators with  discontinuity conditions in a compact interval. It is shown that the potential functions can be uniquely determined by the value of the potential on some interval and parts of two sets of eigenvalues. Also, it is shown that the potential function can be uniquely determined by a part of a set of values of eigenfun...

Dirac systems with regular and singular transmission effects

In this paper, we investigate the spectral properties of singular eigenparameter dependent dissipative problems in Weyl’s limit-circle case with finite transmission conditions. In particular, these transmission conditions are assumed to be regular and singular. To analyze these problems we construct suitable Hilbert spaces with special inner products and linear operators associated with these p...

Submanifold Dirac Operator with Torsion

The submanifold Dirac operator has been studied for this decade, which is closely related to Frenet-Serret and generalized Weierstrass relations. In this article, we will give a submanifold Dirac operator defined over a surface immersed in E with U(1)-gauge field as torsion in the sense of the Frenet-Serret relation, which also has data of immersion of the surface in E. MSC2000: 34L40, 53A05, 5...