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by hackandthink
1359 days ago
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"All known theories of physics - from classical mechanics all the way to general relativity quantum field theory - can be written in this way: a collection of objects and a recipe to build a Lagrangian from those objects, with the movement of those objects determined by a path that minimizes the Lagrangian." I think Quantum Mechanics doesn't reduce to this, it's a probabilistic theory. A similar take from Peter Woit: https://www.math.columbia.edu/~woit/laguardia.pdf |
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So my understanding is that while the way Lagrangians are written in classical theory doesn't extend directly to quantum mechanics, the concept of a Lagrangian is still useful since the Lagrangian can be fed into the path integral formulation (as opposed to being used as an input to the Euler-Lagrange equations). Also, in quantum field theory the starting point for canonical second quantization is typically a Lagrangian, where the fields are changed to operator fields.
Also, something interesting I came across - the Euler-Lagrange equations do have a quantum analogue as well: https://en.wikipedia.org/wiki/Schwinger%E2%80%93Dyson_equati...