Tagged Questions
2
votes
2answers
98 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 ...
3
votes
1answer
205 views
Local and Global Symmetries
Could somebody point me in the direction of a mathematically rigorous definition local symmetries and global symmetries for a given (classical) field theory?
Heuristically I know that global ...
1
vote
1answer
175 views
Lorentz Invariant Equation of Motion for Scalar Field
I'm trying to understand why you can't write down a first order equation of motion for a scalar field in special relativity.
Suppose $\phi(x)$ a scalar field, $v^{\mu}$ a 4-vector. According to my ...
3
votes
0answers
88 views
Asymptotic limit of the two kink solution of the sine-gordon equation
I am reading a paper on the sine-gordon model. The solution for a two kink solution is given as:
...
1
vote
4answers
150 views
Cubic term in gauge theories
In ordinary classical gauge theories the term $-\frac{1}{2}\mathrm{Tr}(F_{\mu\nu}F^{\mu\nu})=-\frac{1}{4}F^a_{\mu\nu}F_a^{\mu\nu}$ in the Lagrangian is completely natural. A somehow rare term would be ...
9
votes
3answers
905 views
Why can't General Relativity be written in terms of physical variables?
I am aware that the field in General Relativity (the metric, $g_{\mu\nu}$) is not completely physical, as two metrics which are related by a diffeomorphism (~ a change in coordinates) are physically ...
9
votes
4answers
411 views
Why must the field equations be differential?
In Landau–Lifshitz's Course of Theoretical Physics, Vol. 2 (‘Classical Fields Theory’), Ch. IV, § 27, there is an explanation why the field equations should be linear differential equations. It goes ...
