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I was watching a clip of a lecture by Richard Feynman (see here), in which he states,

Every theoretical physicist whose any good knows six or seven different theoretical representations for exactly the same physics.

So, I'm wondering, what are some examples of physics problems with six or seven different approaches resulting in the same answer?

Thor Ether
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1 Answers1

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This is just an example: here is a review by Bickers which discusses a dozen of different $1/N$ techniques as applied to Kondo problem. Note that $1/N$ expansion is just one of many approaches to this problem, alongside the simple perturbation theory, several Green's functions formulations, renormalization group, Bethe ansatz and others.

Another example are the variety of methods used to solve problems in quantum transport:

  • Simple Drude-like approaches (equations for the election group velocity and the wave vector)
  • Perturbation theory
  • Kinetic equation
  • Landauer-Büttiker formalism and other approaches based on the scattering matrix
  • Non-equilibrium green's function approaches
  • Quantum Langevin equations
  • Kubo formula
  • Density-matrix equations (master equation, etc.)

And this list is by no means exhaustive.

Urb
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Roger V.
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