All Questions
16
questions
2
votes
2
answers
165
views
QFT introduction: From point mechanics to the continuum
In any introductory quantum field theory course, one gets introduced with the modification of the classical Lagrangian and the conjugate momentum to the field theory lagrangian (density) and conjugate ...
- 189
4
votes
0
answers
89
views
Why is the action for a field a quadruple integral over spacetime? [duplicate]
I've been trying to get started on classical field theories. As I had been studying classical mechanics from Goldstein, I decided to start from there. Goldstein introduces the action $$S=\int \mathscr{...
- 873
0
votes
0
answers
87
views
Can someone explain the steps? [duplicate]
Can anybody expand the equation .What is ω and is i power of ω in equation 2.2.
And how $f_λ(r_1,r_2,...,r_n,t)=0$;λ=1,2,...,Λ gives the last equation and what $∇_k$ means?
- 1
1
vote
0
answers
70
views
Hamilton's principle for fields
According to Goldstein, Hamilton's principle can be summerized as follows:
The motion of the system from time $t_{1}$ to time $t_{2}$ is such that the line integral (called the action or the action ...
- 1,131
1
vote
0
answers
55
views
Higher Order Equation of Motions from Lagrangian / Action
I'd like to derive the equations of motion for a scalar field in a FLRW universe, where the metric, as well as the field, are perturbed. I think I should get scalar as well as tensorial expressions.
...
- 938
2
votes
1
answer
244
views
Field theory Euler-Lagrange problem term
Consider the following Lagrangian (density)
$$
\mathcal{L} = (\mu/2) (\partial_t q)^2 - (Y/2) (\partial_x q)^2 -\alpha(\partial_x{}^2 q)^2
$$
$\mu, Y, \alpha, q$ are respectively mass/unit length, ...
- 1,031
1
vote
1
answer
145
views
Transformations in classical field theory and configuration space
When transforming a field in classical field theory the transformation of the four-gradient of this field follows automatically. At least this is what i have learned in my lectures.
This circumstance ...
- 2,196
7
votes
0
answers
135
views
Variational principle with $\delta I \neq 0$
In Covariant Phase Space with Boundaries D. Harlow allows boundary terms in the variation of the action. If we have some action $I[\Phi]$ on some spacetime $M$ with boundary $\partial M = \Gamma \cup \...
- 36.4k
0
votes
1
answer
158
views
Question about the concepts of Noether charge and Noether current
I read that a noether current occurs when the lagrangian assume vector values. Well, what are noether current and noether charge in comparison to elementary classical mechanics notions of Noether's ...
- 3,085
2
votes
1
answer
3k
views
Why does a the addition of a total derivative to the Lagrangian leave the equations of motion invariant? [duplicate]
Take a Lagrangian $L \rightarrow L+\partial_{\mu}F^{\mu}$.
If we can show that the total derivative $\partial_{\mu}F^{\mu}$ identically satisfies the Euler-Largrange equation, then we have shown that ...
- 829
0
votes
0
answers
87
views
Lagrangian of Charged Particle Evaluated On-Shell
I am trying to calculate the Lagrangian of a charged particle in background gauge field evaluaed on-shell.
Let $A^{\mu}(x)$ be a gauge field. The action of a charged particle in this background gauge ...
- 2,923
1
vote
0
answers
404
views
From classical mechanics to classical field theory
Suppose I have a system of $N$ classical particles described by the Lagrangian $\mathcal{L}(\mathbf{q}_i,\dot{\mathbf{q}}_i,t)$. Similarly, we can introduce the Hamiltonian of such system via the ...
- 218
2
votes
1
answer
185
views
Why is action a functional of $q$ only?
Action of a particle is written as $$S[q]=\int dt\hspace{0.2cm} L(q(t),\dot{q}(t),t).$$ How can I understand why $S$ is a functional of $q$, and not that of $\dot{q}$? Assuming $L=\frac{1}{2}m\dot{q}^...
- 26.8k
0
votes
0
answers
109
views
General questions about conservation of the action, Noether theorem in classical field theory
In my course, we considered the following Lagrangian :
$$\mathcal{L}(\phi,\phi^*, \partial \phi, \partial \phi^*) = \partial_\mu \phi \partial^\mu \phi^* - m^2 \phi^* \phi $$
We said that we want ...
- 1,450
3
votes
1
answer
556
views
Motivation for the Euler-Lagrange equations for fields
In Lagrangian Mechanics it is possible to motivate the Euler-Lagrange equations by means of D'alembert's principle. This is a quite more natural route to follow than to start postulating the least ...
- 36.4k