By Kennison L. S.

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LODI RIZZIN112,7, M. MACRi2,3, N. MADSEN'l, G. MANUZ102,3, D. MITCHARD5, P. MONTAGNA7,8, H. PRUYS4, C. REGENFUS4, A. ROTOND1738, G. TESTERA213, A. VARIOLA5, L. VENTURELL112,7, D. P. VAN DER WERF5, Y. YAMAZAKI', AND N. ZURL0'2,7 Department of Physics, CERN, 1211 Genive 23, Switzerland Dipartimento d i Fisica, Universitci d i Genova, 16146 Genova, Italy 31NFN Sezione d i Genova, 16146 Genova, Italy Physik-Institut, University of Zurich, 8057 Zurich, Switzerland 5Department of Physics, University of Wales Swansea, Swansea SA2 8PP, UK 61nstituto d i Fisica, Universidade Federal do Rio de Janeiro, Rio de Janeiro 21945-9'70, Brazil Dipartimento d i Fisica Nucleare e Teorica, Universith d i Pavia, 2'7100 Pavia, Italy 81NFN Sezione da Pavia, 27100 Pavia, Italy Atomic Physics Laboratory, RIKEN, Saitama 351-0198, Japan loDepartment of Physics, University of Tokyo, Tokyo 113-0033, Japan l1Department of Physics and Astronomy, University of Aarhus, 8000 Aarhus C, Denmark 12Dipartimento d i Chimica e Fisica per l'lngegneria e per i Materiali, Universitd d i Brescia, 251 23 Brescia, Italy ' (ATHENA Collaboration) Atomic systems of antiparticles are the laboratories of choice for tests of C P T symmetry with antimatter.

Our aproach also can be used for a unified description of tests for charge conservation which is one of the basic principles in the construction of physical theories. 1. Methods of phenomenological generalizations of dynamical equations The current phenomenological generalizations of dynamical equations like the Dirac or the Maxwell equation have the status of a test theory and provide a link between the full quantum gravity formalism and the language which is appropriate to describe experiments.