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Most potentials in physics are expressed as a radius or another geometric norm/gauge.

I am looking to understand the significance of the choice of potential functions for force/pressure separation in harmonic analysis before this creates a topology.

To my understanding this is the decision of arbitrary mathematical functions, that are input in to lagrangians/hamiltonians to output the physics action.

To me this is important because if the normed topology is determined arbitrarily then the torsion, curvature or path integral is arbitrary and the physics you are calculating is not accurate.

In a nutshell, as a theoretical physics, how do you have confidence in choosing functions to be computed under laplacians or other transforms?

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