Where does Hamilton's Principle come from?

  • #1
Summary:
Hamiltons Principle
Hamiltons Principle and the physcial entity action are the terms in which modern physics is formulated. How do you know that you can always find a Lagrangian for a System which is then used for Hamitlons Principle and the formulation of Action? Why is the action stationary?
 

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  • #2
PeroK
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What have you found so far on this question?
 
  • #3
Thanks! Pretty much nothing, I know classical mechanics, quantum field theory, electromagnetism can formulated this way by I don't see why (I understand the math, I don't see where it comes from).
 
  • #5
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In my opinion, the deepest origin of the Hamiltonian formalism is the symmetry associated with the principle of relativity.

As all inertial observers are equivalent, there has to be a Lie group of transformations connecting different observers. In relativistic physics this is the Poincare group. According to Wigner, transformations from this group are represented by unitary operators in the Hilbert space of any isolated physical system. Generators of this representation form a 10-dimensional Lie algebra of Hermitian operators. The generator of time translations is the Hamiltonian.

This path will lead you to the relativistic Hamiltonian dynamics of Wigner and Dirac.

Eugene.
 

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