Lagrangian Definition and 1000 Threads

I'm looking for a summary of what invariance or symmetry of the Action in Feynman's path integral has on the equations of motion and on measurement. Do different symmetry groups of the Action integral result in different equations of motion for different particles? Is the least action principle...

I actually have 2 questions. 1)How do you decompose the Lagrangian into kinetic and potential energy? 2)Knowing the Lagrangian, how do we find out if energy of the system is conserved. Example: L=q'^2*sin(q)+q'*exp(q)+q q' is the time derivative of q. Thanks in advance

According to this site http://quantummechanics.ucsd.edu/ph130a/130_notes/node453.html a good choice of Lagrangian for the electromagnetic field is L = - \frac {1}{4} F_{\mu\nu}F_{\mu\nu} + \frac {1}{c} j_\mu A_\mu where F_{\mu \nu} = \frac {\partial A_\nu}{\partial...

Homework Statement Given the Lagrangian density: L= -\frac{1}{2} \partial_{\mu}A_\nu \partial^{\mu}A^\nu -\frac{1}{c}J_\mu A^\mu (a) find the Euler Lagrange equations of motion. Under what assumptions are they the Maxwell equations of electrodynamics? (b) Show that this Lagrangian...

Homework Statement Given the Lagrangian density: L= -\frac{1}{2} \partial_{\mu}A_\nu \partial^{\mu}A^\nu -\frac{1}{c}J_\mu A^\mu (a) find the Euler Lagrange equations of motion. Under what assumptions are they the Maxwell equations of electrodynamics? (b) Show that this Lagrangian...

Hello, Just a few questions about a couple of terms in and not in the SM Lagrangian. I'll talk in particular about these fields, and their representations in SU(3) x SU(2) x U(1) Q (3,2,1/6) (left-handed quarks, fermion) U (3,1,2/3) (right-handed up-quarks, fermion) \phi (1,2,-1/2) (higgs...

Homework Statement Find the Lagrangian and the Lagrangian equations for this pendulum (see the picture). Radius of circle is a, mass of the bob is m and l is the length of the pendulum when it hangs straight down. Homework Equations The Attempt at a Solution I obtain...

I know that, for time-independent potentials, we have E=sum (Vi*partial dL/dVi) - L What if one or more of the potentials are time-dependent? Is the relationship between energy and the lagrangian then "total dE/dt = - partial dL/dt "?

Hey, I was just playing about with some lagrangian mechanics and tried to work out the angular momentum of the earth; Starting with the Lagrangian \mathcal{L} = \left(\frac{1}{2}m (r')^2 + \frac{1}{2}m r^2 (\theta ')^2\right)+\frac{G m M}{r} Applying the Euler Lagrange eqn to prove...

Homework Statement I worked a textbook problem earlier where I had to write the Lagrangian for a pendulum (of mass m and length l) connected to a massless support moving along the x-axis. I chose the angle theta as my generalized coordinate, since the problem specified that the acceleration of...

Euler Lagrange Equation : if y(x) is a curve which minimizes/maximizes the functional : [SIZE="4"]F\left[y(x)\right] = \int^{a}_{b} [SIZE="4"]f(x,y(x),y'(x))dx then, the following Euler Lagrange Differential Equation is true. \frac{\partial}{\partial x} [SIZE="4"]-...

What's the most persuasive argument for using the potential phi and A as independent deegres of freedom in the electromagnetic Lagrangian instead of the more physical field E and B? Why does the cannonical approach break down for E and B?

Homework Statement Assuming that transformation q->f(q,t) is a symmetry of a lagrangian show that the quantity f\frac{\partial L}{\partial q'} is a constant of motion (q'=\frac{dq}{dt}). 2. Noether's theorem http://en.wikipedia.org/wiki/Noether's_theorem The Attempt at a Solution...

I need the general expression for the lagrangian density of a linear elastic solid. I haven't been able to find this anywhere. Thanks.

In flat space time the Lagrangian for the EM potential is (neglecting the source term) \mathcal{L}_{flat}=-\frac{1}{16\pi}(\partial^{\mu}A^{\nu}-\partial^{\nu}A^{\mu})(\partial_{\mu}A_{\nu}-\partial_{\nu}A_{\mu}) which is a scalar for flat spacetime. I would have expected the...

Hi, My question is. Can in principle, a Lagrangian density for some theory be a pseudo-scalar. Normally people say that the Lagrangian needs to be a scalar, but it case it is a pseudo-scalar it would also be a eigaen function of the parity operator. This topic could well be on the...

My question Does the Sun influence the stability of the Lagrangian points in the Earth-Moon system? Apparently the concept of Lagrangian points works both in the Earth-Moon system and the Earth-Sun system. However, In the Earth-Moon system the Sun, as a third body, has a big influence on...

Homework Statement A bead of mass m is free to move on a stationary frictionless hoop of radius R. The hoop is in a horizontal plane (no need to take gravity into account) and it is located a distance d from a stationary wall. The bead is attached to the wall by a spring (constant k and...

I understand the definitions of both the classical and relativistic (SR) Lagrangians. But I cannot find a precise mathematical definition of Lagrangian Density. Please assist. Thanks in advance.

Homework Statement A ball is sitting on a frictionless seesaw with no inclination at the beginning, and a constant angular velocity \phi. Find the position of the ball as a function of timeHomework Equations L=T-V, T=(m\dot{}x2+m\dot{}y2)/2, V=mgyThe Attempt at a Solution The first problem I...

Homework Statement Find the potential energy density of a hanging string of mass density m/L that has been displaced from equilibrium at a point a distance d up from the bottom of the string. This point is displaced a distance X in the x direction, and a distance Y in the y direction. The...

Homework Statement Show that the complex Klein-Gordon Lagrangian density: L=N\left(\partial_\alpha\phi^{\dagger}(x)\partial^\alpha\phi(x)-\mu^2\phi^{\dagger}(x)\phi(x)\right) is invariant under charge conjugation: \phi(x)\rightarrow C\phi(x)C^{-1}=\eta_c \phi^\dagger (x) Where C...

In Mechanics by Landau-Lifgarbagez there is a step during the derivation of the Lagrangian where.. \int_{t_1}^{t_2} L(q+\delta q, \dot q + \delta \dot q, t ) \, \mathrm{d}t - \int_{t_1}^{t_2} L(q, \dot q, t ) \, dt then they write "when this difference is expanded in powers of...

Hello! I`m looking for Lagrangian Systems with Lagrangian function containing higher derivatives in t. I would be really happy if someone can tell some higher order Lagrangians with physical relevance. Thanks, Viktor

Homework Statement A meter stick stands on a frictionless surface and leans against a frictionless wall as shown. It is released to fall when it makes an angle of 1 degree from the vertical. Use Lagrange and Euler to find how long it takes the stick to fall to the ground. The Attempt...

The Hamiltonian operator in quantum field theory (of Klein Gordon Lagrangian) is H=\frac{1}{2} \int \frac{d^3p}{(2 \pi)^3} \omega_{\vec{p}} a_{\vec{p}}^\dagger a_{\vec{p}} after normal ordering Now we construct energy eigenstates by acting on the vacuum |0 \rangle with a_{\vec{p}}^\dagger...

Hello, is it possible to write a Lagrangian (L) for a simple RC (or RL) circuit? Normally L = kinetic - potential energy, but how would you write this for an RC circuit? thanks!

Please teach me this problem: It seem that following Haag's theorem there not exist quantized equation of motion for interacting fields.So I don't understand how to know the form of interacting Lagrangian has form of product of fields(example Lagrangian of Fermi field interacting with...

1. A rigid straight uniform bar of mass m and length l is attached by a frictionless hinge at one end to a fixed wall so that it can move in a vertical plane. At a distance a from the hinge it is supported by a spring of stiffness constant k, as shown in the figure Ignoring gravitational...

Hello! Can anybody suggest me some articles and books on Lagrangian and Hamiltonian systems with Grasmann variables? Thank you for your help! O

Homework Statement http://img708.imageshack.us/img708/4375/81747300.jpg http://img837.imageshack.us/img837/5850/42434333.jpg [PLAIN][PLAIN]http://img696.imageshack.us/img696/3518/50793668.jpg Homework Equations...

Ive been doing some research on the title concepts... And would love it if someone could answer some questions because I can't seem to find the answer anywhere. 1) How was the lagrangian found? I know its kind of defined, and there are other lagrangians- but is there an idea behind it or was...

Hey, can somebody show me how to derive that the lagrangian in classical phyics is L=T-V i have seen this formula so many times, but i have no idea where it really comes from?

Homework Statement A combination of masses along the z-axis is separated by a distance 'a' with middle mass at origin. The potential is V = \frac{1}{2}kx^2 . What is the force of constraint using Lagrange multiplier? Homework Equations L = T - V + \lambda f The Attempt at a...

Verify that the Lagrangian density L= \frac{1}{2} \partial_\mu \phi_a \partial^\mu \phi_a - \frac{1}{2} m^2 \phi_a{}^2 for a triplet of real fields \phi_a (a=1,2,3) is invariant under the infinitesimal SO(3) rotation by \theta \phi_a \rightarrow \phi_a + \theta \epsilon_{abc} n_b \phi_c...

Homework Statement I am trying to get an equation of motion for the following (seemingly simple) setup. You place on a rod on a pivot. The rod's centre of mass is precisely over the pivot. Think of balancing a ruler horizontally on your finger. Gravity, of course acts downward. The...

I have to create a simulation of the pendulum shown in the .pdf at the bottom of the page. The 3 rods are free to rotate around their pivots in a plane. The two edge rods are connected as close to their edges as possible. There is no friction. Unfortunately my equations of motion are spitting...

I'm probably making a mistake, but looking at the free field lagrangian for QED \mathcal{L} \propto (-F^{\mu\nu}F_{\mu\nu}) \propto (\mathbf{E}^2 - \mathbf{B}^2) it appears to me that the action is not bounded from above, nor from below. Does that mean the equations of motion we obtain by...

Homework Statement Eulerian velocity: V_{1}=-z_{1}^{2} V_{1}=\frac{dz_{1}}{dt} z_{1}(t=0)=x_{1} This is supposed to become the Lagrangian velocity of: z_{1}=\frac{x_{1}}{1+tx_{1}} I don't understand how to take the Eulerian velocity and transform it to Lagrangian. Homework EquationsThe...

Homework Statement http://img85.imageshack.us/gal.php?g=hw1y.jpg Its an imageshack gallery Homework Equations Book gives completely irrelevant equations. The Attempt at a Solution I couldn't even solve A. I have no clue how to start this. The instructor isn't providing any...

Find the Euler – Lagrange Equation when L = -1/2 (D_p a_u)(D^p a^u) \sqrt{-g} dx^4 Use g_u_v to raise/lower indices D_p is the covariant derivative I am very new at this notation and am having a lot of trouble getting anywhere with this. I know I have to take the action: S = \int Ldt...

Homework Statement When writing down the Lagrangian and the writing down Euler-Lagrange equation I'm having some difficulties with reasoning something. Homework Equations Lagrangian is: \mathcal{L}=\frac{1}{2}mv^2-q\phi+\frac{q}{c}\vec{v}\cdot\vec{A}. Euler-Lagrange eq...

Homework Statement A spring of rest length L_0 (no tension) is connected to a support at one end and has a mass M attached at the other. Neglect the mass of the spring, the dimension of the mass M, and assume that the motion is confined to a vertical plane. Also, assume that the spring only...

I remember when I learned some basic continuum mechanics, Lagrangian is just a integral of lagrangian density over space, which is quite easy to accept because it's just a continuous version of L=T-U. Now I'm trying to start a bit QFT and notice that Lagrangian is an integral over space-time...

Hi, hopefully someone can check my logic. I have a lever with a mass on top which is rising towards the vertical on a frictionless pivot. The length of the lever can change. (In reality this is a robot rocking onto a foot and straightening its leg). The intention is to bring the lever to a...

In Ryder's text, he defines the dual tensor as the anti-symmetric \tilde F^{\nu \mu} = \epsilon^{\nu \mu \alpha \beta} F_{\alpha \beta}. Later he plops down the complex scalar field Lagrangian as L = (D_\mu \phi)(D^\mu \phi *) - m^2 \phi * \phi - \frac{1}{4} F^{\nu \mu}F_{\nu \mu} where...

The Lagrangian finite strain tensor is defined as: E_{i,j}=\frac{1}{2}\left(\frac{\partial x_k}{\partial X_i}\frac{\partial x_k}{\partial X_j}-\delta _{i,j}\right) Is it in Einstein Notation so that there is a summation symbol missing, i.e. would it be the same thing if one wrote it as...

Hello I am using Landau's mechanics Vol I for classical mechanics. On page 4 he mentions for Lagrangian of a system composed of two systems A and B which are so far away so that their interactions can be neglected. then for the combined system we have L = LA + LB I'm trying to...

Basic exercise for finding a Lagrangian from the Landau's "Mechanics" Hello everyone! Homework Statement I've just started preparing for the classical mechanics course using only Landau & Lifgarbagez, so I'm doing everything according to their formulation. And so I solved an exercise...

Does anyone know where I can find the lagrangian for this? From memory I believe it looks something like S = \frac{1}{2} \int \frac{d\tau}{e}[\dot{X}^2 +i \dot{\psi}{\psi}-2ie\nu \dot{X} \psi] where e is the graviton and nu is the gravitino. Does anyone know of a reference that...