1
vote
1answer
104 views

Subtlety in derivation of Noether's theorem by Di Francesco

In the book 'Conformal Field Theory' by Di Francesco et al, a derivation of Noether's theorem is demonstrated by imposing that, what I believe is said to be a more elegant approach, the parameter ...
2
votes
0answers
137 views

Question about an integration by parts in Feynman's Quantum Mechanics [closed]

I have begun reading Feynman & Hibbs Quantum Mechanics and Path Integrals. Knowing little about variational calculus or Lagrangians I found the following integration by parts opaque. I think if I ...
1
vote
2answers
87 views

With respect to what quantities do I vary Lagrangians in field theory?

I have recently been wondering, with respect to which quantities (covariant or contravariant) one should vary QFT Lagrangians and whether there is some rule regarding this. Let me give an example ...
2
votes
3answers
282 views

Does a four-divergence extra term in a Lagrangian density matter to the field equations?

Greiner in his book "Field Quantization" page 173, eq.(7.11) did this calculation: ${\mathcal L}^\prime=-\frac{1}{2}\partial_\mu A_\nu\partial^\mu A^\nu+\frac{1}{2}\partial_\mu A_\nu\partial^\nu ...
1
vote
1answer
37 views

Double variation of Schwinger action principle

The Schwinger action principle is given by $$\delta_{1}\big\langle b\big|a\big\rangle= i\int_{t_{a}}^{t_{b}}\text{d}t\,\sum_{c,d}\big\langle b\big|c\big\rangle\big\langle ...
5
votes
0answers
80 views

Optimal tunnel shape for travelling inside the earth [duplicate]

Say you were to travel from Paris to Tokyo by digging a tunnel between both cities. If the tunnel is straight, one can easily compute that the time for travelling from one city to the other ...
2
votes
3answers
393 views

Lagrangian mechanics and time derivative on general coordinates

I am reading a book on analytical mechanics on Lagrangian. I get a bit idea on the method: we can use any coordinates and write down the kinetic energy $T$ and potential $V$ in terms of the general ...
2
votes
1answer
136 views

Varying an action (cosmological perturbation theory)

I am stuck varying an action, trying to get an equation of motion. (Going from eq. 91 to eq. 92 in the image.) This is the action $$S~=~\int d^{4}x \frac{a^{2}(t)}{2}(\dot{h}^{2}-(\nabla h)^2).$$ ...
1
vote
2answers
291 views

Can cos(x) or sin(x) be the function of stationary action?

Is there a way to express $\cos(x(t))$ (or $\sin(x(t))$) as the solution to the Euler-Lagrange equation, in other words is there a sense in which this function is the path of stationary action?
5
votes
1answer
431 views

Lagrangian density for a Piano String

So I'm trying to do this problem where I'm given the Lagrangian density for a piano string which can vibrate both transversely and longitudinally. $\eta(x,t)$ is the transverse displacement and ...
9
votes
4answers
396 views

Is the Lagrangian of a quantum field really a 'functional'?

Weinberg says, page 299, The quantum theory of fields, Vol 1, that The Lagrangian is, in general, a functional $L[\Psi(t),\dot{\Psi}(t)$], of a set of generic fields $\Psi[x,t]$ and their time ...