What is the meaning of local field theory in classical field theory?

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SUMMARY

Local field theory, as defined in 'An Introduction to Quantum Field Theory' by Peskin and Schroeder, refers to a framework where the Lagrangian is expressed as a spatial integral of a Lagrangian density. This density is a function of one or more fields and their derivatives, emphasizing the locality of interactions in classical field theory. The concept is crucial for understanding how fields interact at specific points in space and time, distinguishing it from non-local theories.

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In page of 15 of 'An Introduction to Quantum Field Theory,' Peskin and Schroeder writes

In a local field theory the Lagrangian can be written as the spatial integral of a Lagrangian density, ... , which is a function of one of more fields and their derivatives.

Can you explain what the term local field theory means in this context?

P.S. This question is in the 'Classical Physics' site of the forum because it is a question about classical (and not quantum) field theory.
 
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