A Note on Kosmann-lie Derivatives of Weyl Spinors

نویسندگان

  • R. A. Sharipov
  • R. A. SHARIPOV
چکیده

Lie derivatives arise in studying continuous symmetries of various geometric structures on manifolds. They are also used in symmetry analysis of ordinary and partial differential equations (see [1]). In general relativity the bundle of Weyl spinors SM is a special geometric structure built over the space-time manifold M . The main goal of this paper is to clarify the procedure of applying Lie derivatives to the basic attributes of this geometric structure, i. e. to the basic spin-tensorial fields associated with the bundle of Weyl spinors.

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

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

A geometric definition of Lie derivative for Spinor Fields

Relying on the general theory of Lie derivatives a new geometric definition of Lie derivative for general spinor fields is given, more general than Kosmann's one. It is shown that for particular infinitesimal lifts, i.e. for Kosmann vector fields, our definition coincides with the definition given by Kosmann more than 20 years ago. 1 Introduction It is known that starting from some works by phy...

متن کامل

Harmonic Spinors on Homogeneous Spaces

Let G be a compact, semi-simple Lie group and H a maximal rank reductive subgroup. The irreducible representations of G can be constructed as spaces of harmonic spinors with respect to a Dirac operator on the homogeneous space G/H twisted by bundles associated to the irreducible, possibly projective, representations of H. Here, we give a quick proof of this result, computing the index and kerne...

متن کامل

Simplification of the covariant derivatives of spinors

Calculating the spinor connection in curved spacetime is a tiresome and fallible task. This pedagogical paper display an equivalent but simple form of the covariant derivative for both the Weyl spinor and the Dirac bispinor, which is more convenient for calculation, and its geometrical meanings are more distinct. PACS numbers: 02.30.Xx, 04.20.Cv

متن کامل

Conformal geometry of the supercotangent and spinor bundles

We study the actions of local conformal vector fieldsX ∈ conf(M, g) on the spinor bundle of (M, g) and on its classical counterpart: the supercotangent bundle M of (M, g). We first deal with the classical framework and determine the Hamiltonian lift of conf(M, g) to M. We then perform the geometric quantization of the supercotangent bundle of (M, g), which constructs the spinor bundle as the qu...

متن کامل

The covariant derivatives and energy momentum tensor of spinors

To understand the coupling behavior of the spinor with spacetime, the explicit form of the energy-momentum tensor of the spinor in curved spacetime is important. This problem seems to be overlooked for a long time. In this paper we derive the explicit form of energy momentum tensors and display some equivalent but simple forms of the covariant derivatives for both the Weyl spinor and the Dirac ...

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

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

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2008