N-body Potential Reduction: Can It Be Done?

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SUMMARY

The discussion centers on the feasibility of reducing n-body potentials to functions of pairwise distances, specifically transitioning from f(r1, r2) to f(r12, r13, r23). The inquiry suggests that this reduction may be applicable for three point particles, leveraging the SSS triangle congruence. The author seeks clarity on whether additional constraints are necessary for this reduction, particularly in the context of angular and dihedral potentials.

PREREQUISITES
  • Understanding of n-body potential theory
  • Familiarity with pairwise distance functions in physics
  • Knowledge of triangle congruence principles, specifically SSS
  • Basic concepts of angular and dihedral (torsional) potentials
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  • Research the mathematical foundations of n-body potential reduction
  • Explore the implications of triangle congruence in multi-particle systems
  • Study angular and dihedral potential representations in molecular dynamics
  • Investigate existing models or simulations that utilize pairwise distance functions
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Physicists, mathematicians, and computational scientists interested in potential theory and its applications in multi-body systems.

Päällikkö
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I suppose I could've equally well posted this to the math forum, but here goes...

One often sees the two-body potential f(r1, r2) being reduced to to f(r12). Can this be done in a more general case (can n-body potentials be reduced to just the distances between all the particles, e.g. f(r1, r2) -> f(r12, r13, r23))? I assume that the point particles don't have any internal structure. Do I need to add further constraints? I'm mainly aiming for representations of angular and dihedral (torsional) potentials.

From the looks of it, I'd guess it works at least with 3 point particles, due to the SSS triangle congruence.

Any ideas?
 

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