Tagged Questions
0
votes
1answer
75 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
4answers
302 views
Why the Hamiltonian and the Lagrangian are used interchangeably in QFT perturbation calculations
Whenever one needs to calculate correlation functions in QFT using perturbations one encounters the following expression:
$\langle 0| some\ operators \times \exp(iS_{(t)}) |0\rangle$
where, ...
5
votes
2answers
199 views
Can auxiliary fields be thought of as Lagrange multipliers?
In the BRST formalism of gauge theories, the Lautrup-Nakanishi field $B^a(x)$ appears as an auxiliary variable
$$\mathcal{L}_\text{BRST}=-\frac{1}{4}F_{\mu\nu}^a F^{a\,\mu\nu}+\frac{1}{2}\xi B^a B^a + ...
1
vote
1answer
68 views
Smooth trajectory on a smooth manifold
Physicists talk about a smooth trajectory of a particle on a smooth manifold and they label it as q(t) where q_1(t)....q_n(t) are component functions coming from the homeomorphism. I don't see how we ...
5
votes
4answers
727 views
Why can't any term which is added to the Lagrangian be written as a total derivative (or divergence)?
All right, I know there must be an elementary proof of this, but I am not sure why I never came across it before.
Adding a total time derivative to the Lagrangian (or a 4D divergence of some 4 ...
1
vote
2answers
406 views
Geodesics and trajectories
I'm a mathematician studying Arnold's Mathematical Methods of Classical Mechanics.
On p. 83 the following definition is given.
Let $M$ be a differentiable manifold, $TM$ its tangent bundle, and ...
3
votes
2answers
291 views
Variational method applied to brownian motion
It's possible apply the variational method to the brownian motion ? I mean, one of requisites on $y(t)$ is that it must be continuous and $\partial_t{y(t)}$ too, and in this case, $\partial_t{y(t)}$ ...
15
votes
5answers
2k views
Why does calculus of variations work?
How does it make sense to vary the position and the velocity independently?
Edit:
Velocity is the derivative of position, so how can you treat them as independent variables? Doesn't every physics ...
