The most fundamental principle in physics is called 'The Principle of Least Action'. It also happens to be a good principle to live by during these trying times
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the lagrangian is just a function of coordinates and its derivatives; it can be anything. for me, it is just another way to encode equations.
but it CANT be anything, physically. it must be the kinetic minus potential or else the thing your making stationary has no correlation with reality
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like equations cannot be anything for them to match certain physical phenomena. the kinetic minus potential is just another way to express relations between functions and its derivatives
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But doesn’t it need to be THAT PARTICULAR relationship between a function and it’s derivative for it to be useful?
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You can have QFTs with no Lagrangian! It's believed that 6D (2,0) SCFTs have this property. It's operator algebras all the way down.
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I cannot judge that. That is too technical/specific for me. Specially to be judged in a tweet.
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