Talk:Nonlocal Lagrangian

Nonlocality, Isotropy and use of the Continuum/Real Line in Physical Theories

A more explicit explanation of Nonlocality would be good. Is the first lagrangian non-local because of the integral (which integrates phi over the whole of space)? I think the second lagrangian could do with more explanation. The action is ok. What constitutes non-locality? For instance, if the field depended upon two points, would that class it as a non-local field? If the field depends on a discrete number of separate points, would that then be non-local?. Then there is the issue of continuum's of points/regions of points. Of course, it is worth asking what integration of a continuum of points actually means if reality is quantised in some sense (though developments in Weyl's tile argument seem to exclude the possibility that reality is discretised - see personal-homepages.mis.mpg.de/fritz/2012/weyl_argument.pdf which states that "the continuum limit of a periodic graph, as experienced by a classical point particle, cannot be isotropic" - which seems to imply that point particles don't exist OR that reality is not the continuum limit of a periodic graph OR potentially that isotropy is an illusion, though I doubt this last possibility, it could be true. If there are other possibilities I hope someone out there could explain them - as I seem to be at a loss as to what periodic structures of space & time could give rise to isotropy).

As per Weyl's tile argument(about space not being quantised if we are to have a notion of distance that is as valid for diagonal lines as for vertical and horizontal ones), the theories associated with these lagrangians ought to be isotropic. — Preceding unsigned comment added by ASavantDude (talk • contribs) 16:46, 3 December 2016 (UTC)[reply]

Pardon me, why is WZW action classified as non-local here? All the terms in it look pretty one-point naively... — Preceding unsigned comment added by 93.175.13.170 (talk) 19:04, 2 April 2022 (UTC)[reply]