1
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0answers
67 views

Why does Principle for least action hold for classical fields [duplicate]

Let $\mathscr L (\phi(\mathbf x), \partial \phi(\mathbf x))$ denote the Lagrangian density of field $\phi(\mathbf x)$. Then then actual value of the field $\phi(\mathbf x)$ can be computed from the ...
1
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2answers
157 views

Classical point particles to classical fields

I often hear that in the continuum limit we can study large numbers of particles as fields. I always imagined that by removing all bounds on the number of particles (while keeping total energy, ...
1
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1answer
117 views

How to understand dynamics $\dot x_i=\partial_jA_{ij}$ from skew-symmetric potential $A$?

We speak of a dynamical system with a potential if there is a scalar possibly depending on coordinate such that the vector field is exactly the (negative) gradient of the potential. That means each ...
2
votes
1answer
195 views

Primary constraints for Hamiltonian field theories

I am currently trying to carry out the construction of the generalised Hamiltonian, constraints and constraint algebra, etc for a particular field theory following the procedure in Dirac's "Lectures ...
3
votes
2answers
230 views

Higher order covariant Lagrangian

I'm in search of examples of Lagrangian, which are at least second order in the derivatives and are covariant, preferable for field theories. Up to now I could only find first-order (such at ...
2
votes
1answer
442 views

Texts on field theory in classical physics

I need a very good text on field theory and it should provide good understanding of why this concept cant be ignored?I only need that text which will tell me how field theory is an integral part of ...
3
votes
3answers
297 views

Particles as a limit of classical field theory

A common academic exercise has been to show that classical mechanics is a limit of quantum mechanics, usually by putting $\hbar \rightarrow 0$. Similarly is it possible to show that a limit to field ...