Showing papers on "Mirror symmetry published in 1974"

Particles and antiparticles

Abstract: In order to elucidate the properties and interrelation of particles and antiparticles, the chapter describes expressions for the operators of the total energy and the total number of particles in the system. The derivation depends on the spin of the particles. To derive the desired expressions, the chapter shows that it is necessary to know that for particles described by Dirac's equation there exists a Hamiltonian. The chapter discusses the relation between the spin and the statistics and the CPT theorem. A universal law of nature is that of relativistic invariance, i.e. invariance under transformations of the Lorentz group. These include both the ordinary three-dimensional rotations and the Lorentz transformations. As well as these transformations, there are others which do not reduce to rotations: spatial inversion and time reversal. The invariance under spatial inversion (P invariance) expresses the mirror symmetry of space. The invariance under time reversal (T invariance) expresses the equivalence of the two directions of time. Both these are valid for phenomena described by the non-relativistic theory. In weak interactions the symmetry between particles and antiparticles expressed by the transformation of charge conjugation (C invariance) is also violated. In the relativistic theory, there is a natural requirement of invariance under a transformation comprising spatial inversion, time reversal and charge conjugation. This is called the CPT theorem.