Space-Time Geometry and Some Applications of Clifford Algebra in Physics

In this paper, we provide some enlightening applications of Clifford algebra in physics. Directly taking the generators of Clifford algebra as tetrad of space-time, we redefine some concepts of field and then discuss the dynamical equation and symmetry by Clifford calculus. Clifford algebra faithfully and exactly reflects intrinsic symmetry of space-time and fields with no more or less contents, and automatically classifies the parameters in field equation by grade, which is a definite guidance to set up dynamical equation and compatible constraints of fields. By insights of Clifford algebra, we discuss the differential connection of fields and torsion in details. The dynamical equation of torsion, the quadratic form of Lagrangian of gravity and first order dynamical equation of gravity in curved space-time are derived. By virtue of this excellent language, physical theories can be well understood by common readers, and some long standing puzzling problems may be easily solved.