4 ms·
It's a Lagrangian, so this is the function nature tries to minimize. In common everyday systems, the Lagrangian is kinetic energy minus potential energy.
by dhoe 10y ago
It's a Lagrangian, so this is the function nature tries to minimize. In common everyday systems, the Lagrangian is kinetic energy minus potential energy.
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- adrianratnapala 10y agoTrue, but with nitpick that it is the Lagrangian density so nature minimises its total over a region of 4-space. And with the more important nitpick that this Lagrangian is a quantum operator rather than a number. In some sense nature does try to minimise it even so, but I never got an intuitive grasp on what that sense is.
- cygx 10y agoAnd with the more important nitpick that this Lagrangian is a quantum operator rather than a number. I don't think that's true when dealing with the formulation in terms of path integrals as we do here...
- adrianratnapala 10y agoIt's the focus on path integrals that obscures the fact that the Lagrangian is an operator. Except maybe for convenience, there is nothing about such equations that is unique to the path-integral formulation. The fields, the Langragian, and the scattering matrix are all operators; but of course their matrix elements are numbers. The path-integral formulation is a good -- and I think physically well motivated -- trick for calculating those matrix elements in terms of merely fields and their associated Largrangians.
- varjag 10y agoThe text however refers to it as an equation, and that's not an equation.