PHOTON WITHOUT THE POINCAR ´ E GROUP * Magdalena Gusiew-Czud˙ zak Uniwersytet Wroclawski, Instytut Fizyki Teoretycznej plac Maxa Borna 9, 50204 Wroc law, Poland, gusiew@ift.uni.wroc.pl and Zbigniew Oziewicz † Universidad Nacional Aut´onoma de M´ exico, Facultad de Estudios Superiores C.P. 54714 Cuautitl´ an Izcalli, Apartado Postal # 25, Estado de M´ exico oziewicz@servidor.unam.mx We believe that the theory of the elementary particles can be based on the Clifford bi- gebra which consists of the Clifford algebra and of the Clifford co-gebra as a new kind of an interaction or as a new kind of an internal structure. We belive that all particles, including photon and graviton, must be identified with the Clifford modules and their tensor products instead of the Poincar´ e or the Lorentz modules. 1999 PACS: 02.10.Tq 2000 Mathematical Subject Classification: 15A66; 16W30 KEYWORDS. Clifford al-gebra, Clifford co-gebra, Clifford bi-gebra, spinor, photon The sixth problem: Axioms of the physics. Mathematicians must consider all theories logically possible. David Hilbert, Congress of Mathematicians, Paris 1900. The axiomatic basis of theoretical physics must not be obtained from experiments, but must be freely invented by the human mind. Albert Einstein, Herbert Spence Lecture at Oxford, 1933. * In: Valeri V. Dvoeglazov, Editor, “Photon: Old Problems in Light of New Ideas”, in series ‘Contemporary Foundamental Physics’, Nova Science Books and Jrnls Publishers, Commack, New York, 2000. ISBN 1-56072-810-8. † Supported by el Consejo Nacional de Ciencia y Tecnolog´ ıa (CONACyT) de M´ exico, Grant # 27670 E (1999-2000) and by UNAM, DGAPA, Programa de Apoyo a Proyectos de Investigaci´on e Innovaci´on Tecnol´ogica, Proyecto IN-109599 (1999-2002). Zbigniew Oziewicz is a member of Sistema Nacional de Investigadores, M´ exico. 494