Eigenfunction Expansion for the Three-Dimensional Dirac Operator

نویسندگان

چکیده

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Minimax Principles, Hardy-Dirac Inequalities, and Operator Cores for Two and Three Dimensional Coulomb-Dirac Operators

For n ∈ {2, 3} we prove minimax characterisations of eigenvalues in the gap of the n dimensional Dirac operator with an potential, which may have a Coulomb singularity with a coupling constant up to the critical value 1/(4 − n). This result implies a socalled Hardy-Dirac inequality, which can be used to define a distinguished self-adjoint extension of the Coulomb-Dirac operator defined on C0 (R...

متن کامل

Dimensional Reduction of Dirac Operator

We elaborate an explicit example of dimensional reduction of the free massless Dirac operator with SU(3)-symmetry, defined on 12-dimensional manifold, which is the total space of principle SU(3)-bundle over 4-dimensional manifold. It turns out that after the dimensional reduction we obtain the “usual” Dirac operator, defined on 4-dimensional pseudo-Riemannian (non-flat) manifold but with mass t...

متن کامل

Multilinear Eigenfunction Estimates and Global Existence for the Three Dimensional

— We study nonlinear Schrödinger equations, posed on a three dimensional Riemannian manifold M . We prove global existence of strong H solutions on M = S and M = S × S as far as the nonlinearity is defocusing and sub-quintic and thus we extend results of Ginibre-Velo and Bourgain who treated the cases of the Euclidean space R and the torus T = R/Z respectively. The main ingredient in our argume...

متن کامل

Dirac 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 کامل

Generalized Eigenfunction Expansions for Operator Algebras^)

A generalized eigenfunction expansion may be regarded as a representation for the spectral theorem by a transform technique. These representations have been presented in many forms, an early version of which was the von Neumann "direct integral" decomposition for a class of operator algebras [l9]. In 1953 [17], Mautner applied the von Neumann technique to the class of operators acting in an L2-...

متن کامل

ذخیره 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: Journal of Differential Equations

سال: 2000

ISSN: 0022-0396

DOI: 10.1006/jdeq.1999.3664