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| ON THE KINEMATIC GEOMETRY OF MANY BODY SYSTEMS |
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Citation： |
Wu-Yi HSIANG.ON THE KINEMATIC GEOMETRY OF MANY BODY SYSTEMS[J].Chinese Annals of Mathematics B,1999,20(1):11~28 |
| Page view： 949
Net amount： 723 |
Authors： |
Wu-Yi HSIANG; |
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| Abstract： |
In mechanics, both classical and quantum, one studies the profound
interaction between two types of energy, namely, the kinetic energy and
the potential energy. The former can be organized as the kinematic metric on the
configuration space while the latter can be represented by a suitable potential
function, such as the Newtonian potential in celestial mechanics and the Coulomb
potential in quantum mechanics of atomic and molecular physics. In this paper,
the author studies the kinematic geometry of $n$-body systems.
The main results are
(i) the introduction of a canonical coordinate system which reveals the total
amount of kinematic symmetry by an $SO(3)\times O(n-1)$ action in such a canonical
coordinate representation; (ii) an in depth analysis of the above kinematic system
both in the setting of classical invariant theory and by the technique of
equivariant Riemannian geometry; (iii) a remarkably simple formula for the potential
function in such a canonical coordinate system which reveals the well-fitting
between the kinematic symmetry and the potential energy. |
Keywords： |
Kinematic geometry, Many body system, Configuration space |
Classification： |
53C, 54E, 81V70 |
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