Noncommutative theories and general coordinate transformations

The Dirac Equation and General Linear Transformations of Coordinate Systems

The spinor representation of the Lorentz group does not accept simple generalization with the group GL(4,R) of general linear coordinate transformations. The Dirac equation may be written for an arbitrary choice of a coordinate system and a metric, but the covariant linear transformations of the fourcomponent Dirac spinor exist only for isometries. For usual diagonal Minkowski metric the isomet...

Fermions and noncommutative theories

By using a framework where the object of noncommutativity θ represents independent degrees of freedom, we study the symmetry properties of an extended x + θ space-time, given by the group P ’, which has the Poincaré group P as a subgroup. In this process we use the minimal canonical extension of the Doplicher, Fredenhagen and Roberts algebra. It is also proposed a generalized Dirac equation, wh...

Vectors, Matrices and Coordinate Transformations

For our purposes we will think of a vector as a mathematical representation of a physical entity which has both magnitude and direction in a 3D space. Examples of physical vectors are forces, moments, and velocities. Geometrically, a vector can be represented as arrows. The length of the arrow represents its magnitude. Unless indicated otherwise, we shall assume that parallel translation does n...

3D affine coordinate transformations

Landsat MSS Coordinate Transformations

, A number of image a n a l y s i s t a s k s r e q u i r e t h e r e g i s t r a t i o n of a s u r f a c e model w i t h an image. I n t h e case o f s a t e l l i t e images, t h e s u r f a c e model may be a map o r d i g i t a l t e r r a i n model i n t h e form o f surface e l e v a t i o n s on a g r i d o f p o i n t s. We develop here an a f f i n e transformation between coordinates...