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Quantum Mechanics with Basic Field Theory by Bipin R. Desai

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41 Lagrangian formulation of classical fields

41.1 Basic structure

 

In Chapter 25 we discussed the Lagrangian method as it applied to nonrelativistic problems. We extend it now to the relativistic domain in which the relativistic wavefunctions, called classical fields, replace their nonrelativistic counterparts with the Lagrangian method formulated in the four-dimensional language.

Let ϕ represent the classical field. We write the Lagrangian density images in terms ϕ and its derivative μ ϕ, and express the Lagrangian as

images

and the action as

The corresponding ...

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