M ar 1 99 9 Unified Descriptions Of All Differential Variational Principles

X iv :p hy si cs /9 90 30 14 v1 [ ph ys ic s. cl as sph ] 8 M ar 1 99 9 Unified Descriptions Of All Differential Variational Principles Y. C. Huang Z. X. Liu X. G. Li Department of Applied Physics, Beijing Polytechnic University, Beijing 100022, P.R. China Department of Physics, Henan Normal University, Xingxiang 453002, P. R. China INFN, Sezione di Catania, Corso Italia 57, I-95129 Catania, Italy Comment: 6pages, Revtex, Email: [email protected] Report-no: BJPU99-01 Subj-class: Classical Physics Abstract A mathematical expression of the quantitative causal principle is given, using the expression this paper shows the unified descriptions of D’Alembert-Lagrange, virtual work, Jourdian, Gauss and general D’Alembert-Lagrange principles of differential style, finds the intrinsic relations among these variational principles, among the conservation quantities and the Noether conservation charges of the all differential variational principles. There are numerous variational principles in physics, they are classified into two kinds, i.e., they are differential and integral variational principles respectively[1, 2]. It is well known that the unified descriptions of the relations among so many scrappy variational principles have not been presented up to now, and the intrinsic relations among the conservation quantities of these principles are not obtained either[3]. On the other hand, in quantum field theory the causal principle demands if the square of the distance of spacetime coordinates of two boson (or fermion) operators is timelike, their commutator (or anticommutator) is not equal to zero, their measures are then coherent, for spacelike no coherent[4]. The dispersion relations can be deduced by the causal principle etc[5], and general scientific theories of physics should satisfy the elementary demand of the causal principle. Therefore, the causal principle is essential to research physical laws. In real physics, the quantitative action (cause) of some quantities must lead to the equal action (result), that is, how much loses (cause), how much gains (result), which is just the quantitative causal principle with the no-loss-no-gain character[6]. Which can be concretely expressed as