The Deepest Symmetries of Nature: CPT and SUSY

Dezső Horváth
2005 AIP Conference Proceedings  
The structure of matter is related to symmetries on every level of study. CPT symmetry is one of the most important laws of field theory: it states the invariance of physical properties when one simultaneously changes the signs of the charge and of the spatial and time coordinates of particles. Although in general opinion CPT symmetry is not violated in Nature, there are theoretical attempts to develop CPT-violating models. The Antiproton Decelerator at CERN has been built to test CPT
more » ... test CPT invariance. Several observations imply that there might be another deep symmetry, supersymmetry (SUSY), between basic fermions and bosons. SUSY assumes that every fermion and boson observed so far has supersymmetric partners of the opposite nature. In addition to some theoretical problems of the Standard Model of elementary particles, supersymmetry may provide solution to the constituents of the mysterious dark matter of the Universe. However, as opposed to CPT, SUSY is necessarily violated at low energies as so far none of the predicted supersymmetric partners of existing particles was observed experimentally. The LHC experiments at CERN aim to search for these particles. SYMMETRIES IN PARTICLE PHYSICS Symmetries in particle physics are even more important than in chemistry or solid state physics. Just like in any theory of matter, the inner structure of the composite particles are described by symmetries, but in particle physics everything is deduced from the symmetries (or invariance properties) of the physical phenomena or from their violation: the conservation laws, the interactions and even the masses of the particles. The conservation laws are related to symmetries: the Noether theorem states that a global symmetry leads to a conserving quantity. The conservation of momentum and energy are deduced from the translational invariance of space-time: the physical laws do not depend upon where we place the zero point of our coordinate system or time measurement; and the fact that we are free to rotate the coordinate axes at any angle is the origin of angular momentum conservation. The symmetry properties of particles with half-integer spin (fermions) differ from those with integer spin (bosons). The wave function describing a system of fermions changes sign when two fermions switch quantum states whereas in the case of bosons there is no change; all other differences can be deduced from this property.
doi:10.1063/1.2121970 fatcat:z634oat6avbqdbnnv6xl26ocoa