Questions tagged [lagrangian-formalism]
For questions involving the Lagrangian formulation of a dynamical system. Namely, the application of an action principle to a suitably chosen Lagrangian or Lagrangian Density in order to obtain the equations of motion of the system.
275 questions from the last 365 days
1
vote
0
answers
54
views
Canonical Electromagnetic Stress-EnergyTensor and Conservation Laws with Sources
Given the expression for the canonical Stress-Energy Tensor as:
$$T^{\mu \nu}=\partial^\mu \phi \frac{\partial \mathcal{L}}{\partial (\partial_\nu \phi)}-g^{\mu\nu}\mathcal{L}$$
where $\phi$ is a ...
- 11
1
vote
0
answers
67
views
How the energy-momentum tensor comes from the action in Kalb-Ramond (KR) gravity? [closed]
The action
\begin{align}\label{action}
S=\int d^4x\sqrt{-g}\bigg[\frac{1}{2\kappa}\bigg(R-\varepsilon\, B^{\mu\lambda}B^\nu\, _\lambda R_{\mu\nu}\bigg)-\frac{1}{12}H_{\lambda\mu\nu}H^{\lambda\mu\nu}-V(...
- 19
0
votes
0
answers
102
views
Where do experiments enter the renormalization procedure? [duplicate]
I'm studying the renormalization of scalar quantum field theories ($\lambda\phi^4$ in particular). I'm considering renormalization by counterterms with the old non-Wilsonian interpretation of ...
- 864
5
votes
0
answers
156
views
Structure of Higgs potential
The Higgs potential is written as
$V(\phi) = -\mu^2 |\phi|^2 + \lambda^2 |\phi|^4$,
where $|\phi|^2 = \phi^\dagger \phi $ and $ \phi $ is a complex scalar doublet.
My question is: why do we not ...
- 51
-1
votes
1
answer
136
views
Sign confusion in Relativistic Lagrangian and Lorentz Force Derivation [duplicate]
This is a rewrite of the original question and calculation, which should be now correct and focusses on the core issues of possible confusion:
I was confronted with some confusion regarding the ...
- 39
3
votes
1
answer
69
views
How to minimise jettisoned mass spent for a body with continuous but variable thrust?
In general I would like to know how to minimise fuel mass spent for an orbiting body that continuously jettisons its mass (i.e. ion thruster) so as to perform efficient transfer maneuver in ...
- 43
1
vote
0
answers
63
views
Deriving the full crystal Hamiltonian from a Lagrangian density
I'm trying to understand the connection between field-theoretic Lagrangians and the standard Hamiltonians used in solid-state physics. In particular, consider a full crystal Hamiltonian of the form:
$ ...
6
votes
4
answers
350
views
Is there a version of Hamilton's Principle of Stationary Action when only initial conditions are known and the final end state is unknown? [duplicate]
Consider a dynamical system with Lagrangian $L$ and configuration space $X$, we are interested in trajectories of this system over a time interval $q:[t_0,t_1]\rightarrow X$.
When one has the ...
- 153
-1
votes
1
answer
84
views
How does the relativistic action logically follow from the nonrelativistic action, and why is proper time involved? [closed]
In nonrelativistic mechanics, the action for a particle of mass $m$ moving in a potential $V(\mathbf{x})$ is
$$
S_{\text{classical}} = \int \left(\frac{1}{2} m \mathbf{v}^2 - V(\mathbf{x}) \right) dt.\...
- 127
2
votes
0
answers
41
views
Proof for scalar field VEV solving classical equations of motion to lowest order [duplicate]
Page 370 (start of section 11.4) of Peskin and Schroeder claims that the VEV of a scalar field in the presence of an external source,
$$\phi_\text{cl} \equiv \langle 0_J|\phi(x)|0_J\rangle,\tag{11.46}$...
- 147
0
votes
0
answers
26
views
Accounting for magnetic forces in Lagrangian mechanics [duplicate]
For conservative forces the Euler-Lagrange equation is used to find the relevant details about the system. However magnetic forces are not conservative do not perform any work on an moving charged ...
2
votes
1
answer
125
views
On the interpretation of spontaneous symmetry breaking (SSB) and fields
I am a math student taking a course in fundamental interactions and I have two questions about the interpretation of the spontaneous symmetry breaking (SSB). For contest we started with a classical ...
1
vote
1
answer
90
views
Doubt about Lagrangian transformation between reference frames (Susskind, Classical Mechanics, The Theoretical Minimum, pag.117)
I'm working through Susskind's Classical Mechanics book and I reached the point where he explains how to transform the action (and Lagrangian) when changing reference frames. However, I believe there ...
- 111
0
votes
0
answers
71
views
EOM of Nambu-Goto in second fundamental form
I am computing the EOM of the Nambu-Goto action $$S[X] = -T\int d^2 \sigma \sqrt{-\det{(\partial_a X^\mu \partial_b X_\mu)}}$$ and I want to write this in a specific form using the second fundamental ...
- 688
2
votes
2
answers
91
views
How is using the principal axis frame in the Lagrangian allowed?
The kinetic energy of a fixed, rotating rigid body is
$$
T =\frac{1}{2}\mathbf{\omega}\mathbf{I}\mathbf{\omega}=\frac{1}{2}I_{xx}\omega_x^2 +\frac{1}{2}I_{yy}\omega_y^2 + \frac{1}{2}I_{zz}\omega_z^2 + ...
- 187