////////////////////////////////////////////////////////////////////////// // // // Dirac Spinor Algebra Package // // // // The present package implements all the basic algorithms dealing // // with Dirac spinors, which form a fundamental representation of the // // group SL(2,2). The basic classes are DiracSpinor and DiracMatrix, // // which are 4x1 and 4x4 complex matrices, respectively. In this // // context any complex 4x4 matrix that operates on Dirac spinors is // // called a Dirac matrix, and not simply the four or five Dirac gamma // // matrices. The standard representation of Dirac is used for the // // gamma matrices 0-5. The generators of the Lorentz group are the // // Sigma (rotation generators) and Kappa (boost generators) matrices. // // // // The standard matrices are identified by a discrete index of enum // // type EDiracIndex. A EDiracIndex can take on a value from the list // // kDiracOne, kDiracGamma1, kDiracGamma2, kDiracGamma3, // // kDiracGamma4, kDiracGamma5, kDiracSigma1, kDiracSigma2, // // kDiracSigma3, kDiracKappa1, kDiracKappa2, kDiracKappa3. // // The constructor invoked with two EDiracIndex values i,j returns // // i_/2 [TDiracMatrix(i),TDiracMatrix(j)] where [a,b] denotes the com- // // utator of matrices a and b, and i_ is the positive square root of // // -1. In general Dirac matrices describe operators and Dirac spinors // // describe relativistic fermion states. Dirac matrices are also used // // to describe mixed states, ensembles that contain mixtures of // // particles described by more than one Dirac spinor. // // // // Spinors and matrices can be transformed under rotations and boosts // // according to the commutation rules for the group. The most general // // transformation combining rotations and boosts is described by the // // LorentzTransform group defined in TFourVector.h. All angles are // // assumed to be in radians. // // // // This package was developed at the University of Connecticut by // // Richard T. Jones // // // //////////////////////////////////////////////////////////////////////////