Algebras generated by geometric scalar forms and their applications in physics and social sciences
Por:
Keller J.
Publicada:
1 ene 2008
Categoría:
Physics and Astronomy (miscellaneous)
Resumen:
The present paper analyzes the consequences of defining that the geometric scalar form is not necessarily quadratic, but in general K-atic, that is obtained from the Kth power of the linear form, requiring {e i; i = 1,...,N; (ei)K = 1} and d? = ?ixiei. We consider the algebras which are thus generated, for positive integer K, a generalization of the geometric algebras we know under the names of Clifford or Grassmann algebras. We then obtain a set of geometric K-algebras. We also consider the generalization of special functions of geometry which corresponds to the K- order scalar forms (as trigonometric functions and other related geometric functions which are based on the use of quadratic forms). We present an overview of the use of quadratic forms in physics as in our general theory, we have called START. And, in order to give an introduction to the use of the more general K-algebras and to the possible application to sciences other than physics, the application to social sciences is considered. For the applications to physics we show that quadratic spaces are a fundamental clue to understand the structure of theoretical physics (see, for example, Keller in ICNAAM 2005 and 2006). © 2008 American Institute of Physics.
Filiaciones:
Keller J.:
Departamento de Física y Química Teórica, Facultad de Química, Universidad Nacional Autónoma de México, AP 70-528, 04510, México D.F., Mexico
Center for Computational Materials Science, General Physics Technical University of Vienna, Gumpendorferstrasse IA, A-1060, Vienna, Austria
|