The Higher Spin Dirac Operators. *
نویسنده
چکیده
There is a certain family of conformally invariant first order elliptic systems which include the Dirac operator as its first and simplest member. Their general definition is given and some of their basic properties are described. A special attention is paid to the Rarita-Schwinger operator, the second simplest operator in the row. Its basic properties are described in more details. In the last part indices of discussed operators are computed.
منابع مشابه
Twisted higher spin Dirac operators
In this paper, we define twisted higher spin Dirac operators and explain how these invariant differential operators can be used to define more general higher spin Dirac operators acting on functions f(x) on R which then take values in general half-integer representations for the spin group. Mathematics Subject Classification (2010). 30G35, 42B35.
متن کاملHigher spin Dirac operators
In Clifford analysis, one studies spin-invariant differential operators on spaces of arbitrary dimension m. At the heart of the classical theory lies the well-known Dirac operator, which finds its origin in physics [5]: the Dirac equation describes the behaviour of electrons in the 4-dimensional spacetime. Our aim is to study generalizations of this operator, the so-called higher spin Dirac ope...
متن کاملOn an inductive construction of higher spin Dirac operators
In this contribution, we introduce higher spin Dirac operators, i.e. a specific class of differential operators in Clifford analysis of several vector variables, motivated by equations from theoretical physics. In particular, the higher spin Dirac operator in three vector variables will be explicitly constructed, starting from a description of the so-called twisted Rarita-Schwinger operator.
متن کاملThe Higher Spin Dirac Operators on 3-Dimensional Manifolds
We study the higher spin Dirac operators on 3-dimensional manifolds and show that there exist two Laplace type operators for each associated bundle. Furthermore, we give lower bound estimations for the first eigenvalues of these Laplace type operators.
متن کاملOn Solutions of the Higher Spin Dirac Operators of Order Two
In this paper, we define twisted Rarita-Schwinger operators RTl1 and explain how these invariant differential operators can be used to determine polynomial null solutions of the higher spin Dirac operators Ql1,l2 .
متن کاملOn a special type of solutions of arbitrary higher spin Dirac operators
In this paper an explicit expression is determined for the elliptic higher spin Dirac operator, acting on functions f(x) taking values in an arbitrary irreducible finite-dimensional module for the group Spin(m) characterized by a half-integer highest weight. Also a special class of solutions of these operators is constructed, and the connection between these solutions and transvector algebras i...
متن کامل