Therefore possess more properties than the more generic objects such as tensors. The word spinor will be used to denote any columnlike function of energy and momentum which, when multiplied by a factor expip x or exp. We define a spinor as a base vector of su2 group representation in two dimensional complex variable space. It is shown that the two complex cartesian components of the electric field of a monochromatic electromagnetic plane wave, with a temporal and spatial dependence of. The fact that the spin representation cannot be obtained from tensors meant that the dirac operator in quantum eld theory must act on spinor elds rather than tensor elds. In 3d, the spinor j 1 2 representation of the spin3 rotation group is constructed from the pauli matrices. Spinor representation of lie algebra for complete linear.
C of the homogeneous lorentz group rather than the lorentz group itself. Information from its description page there is shown below. Spinors can be used without reference to relativity, but they arise naturally in discussions of the lorentz group. Dirac matrices and lorentz spinors university of texas. Cli ord algebras and bilinear forms on spinors honors thesis department of mathematics university of pittsburgh eric o. Commons is a freely licensed media file repository. W e see that the spinor inner products 29 and 31 agree with each other, but whereas the pauli ketvector is a complex 2component column matrix, the correspond ing object in g 3 is the. For so2n the two halfspin representations correspond to the two nodes that branch o. C will be discussed in some detail laterfor now we just mention that it acts most directly on twocomponent, complex vectors, the basic spinors that are analogous to fourvectors for the lorentz group. How to generate spinor representations in any dimension in terms of. The technique enables accordingly to find solutions of the weyl or the dirac equation without making a choice of a special representation for. A spinor type representation is any irreducible representation that doesnt descend to sov. A spinor representation of spinv over the re als is an irreducible representation over the reals whose complexification is a direct sum of spin representations.
Please note that deleting superseded images requires. Representation space has a structure of the fiber space with the space of diagonal matrices as the base and standard spinor space as typical fiber. Cli ord fourier transform and spinor representation of images 3 there are many reasons to believe that such a generalized weierstrass parametrization may reveal to. The vector representation 8 as well as the spin representations 8 are all of dimension 8 and. One could say that a spinor is the most basic sort of mathematical object that can be lorentztransformed. Pdf spinor representation of maxwells equations researchgate. Clifford fourier transform and spinor representation of images.
For the even case of spin2n, we will see that there are two different irreducible halfspinor representations of dimension 2n. Pdf we propose in this paper to introduce a spinor representation for images based on the work of t. A spinor representation of spinv over the reals is an irreducible representation over the reals whose complexi. Cli ord fourier transform and spinor representation of images 3 there are many reasons to believe that such a generalized weierstrass parametrization may reveal to be an e cient tool in the context of image processing.