Semi-Classical Green Kernel Asymptotics for the Dirac Operator
نویسندگان
چکیده
منابع مشابه
Vanishing Theorems for the Half-kernel of a Dirac Operator
We obtain a vanishing theorem for the half-kernel of a Dirac operator on a Clifford module twisted by a sufficiently large power of a line bundle, whose curvature is non-degenerate at any point of the base manifold. In particular, if the base manifold is almost complex, we prove a vanishing theorem for the half-kernel of a spinc Dirac operator twisted by a line bundle with curvature of a mixed ...
متن کاملVanishing Theorems for the Kernel of a Dirac Operator
We obtain a vanishing theorem for the kernel of a Dirac operator on a Clifford module twisted by a sufficiently large power of a line bundle, whose curvature is non-degenerate at any point of the base manifold. In particular, if the base manifold is almost complex, we prove a vanishing theorem for the kernel of a spinc Dirac operator twisted by a line bundle with curvature of a mixed sign. In t...
متن کاملOn the kernel of the affine Dirac operator
Let g be a finite-dimensional semisimple Lie algebra and (· , ·) its Killing form, σ an elliptic automorphism of g, and a a σ-invariant reductive subalgebra of g, such that the restriction of the form (· , ·) to a is non-degenerate. Let L̂(g, σ) and L̂(a, σ) be the associated twisted affine Lie algebras and F σ(p) the σ-twisted Clifford module over L̂(a, σ), associated to the orthocomplement p of ...
متن کاملSemi-classical Asymptotics for the Counting Functions and Riesz Means of Pauli and Dirac Operators with Large Magnetic Fields
We study the asymptotic behavior, as Planck’s constant ~ → 0, of the number of discrete eigenvalues and the Riesz means of Pauli and Dirac operators with a magnetic field μB(x) and an electric field. The magnetic field strength μ is allowed to tend to infinity as ~ → 0. Two main types of results are established: in the first μ~ ≤ constant as ~ → 0, with magnetic fields of arbitrary direction; t...
متن کاملDirac Cohomology for the Cubic Dirac Operator
Let g be a complex semisimple Lie algebra and let r ⊂ g be any reductive Lie subalgebra such that B|r is nonsingular where B is the Killing form of g. Let Z(r) and Z(g) be, respectively, the centers of the enveloping algebras of r and g. Using a Harish-Chandra isomorphism one has a homomorphism η : Z(g) → Z(r) which, by a well-known result of H. Cartan, yields the the relative Lie algebra cohom...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Communications in Partial Differential Equations
سال: 2011
ISSN: 0360-5302,1532-4133
DOI: 10.1080/03605302.2011.600799