Lagrangian Definition and 1000 Threads

What is the full Lagrangian of Standard Model?How can we build a Lagrangian that satisfies both the symmetry SU(3) and the symmetry SU(2) at the same time?

Homework Statement [/B] If L is Lagrangian for a (system of) free particle(s) and dL/dt=0, show that any twice differentiable function f(L) gives the same equations of motions. Homework Equations [/B] Euler-Lagrange equations.The Attempt at a Solution Well, after some calculation, I get...

Homework Statement I am trying to calculate the following quantity: $$<0|T\{\phi^\dagger(x_1) \phi(x_2) exp[i\int{L_1(x)dx}]\}|0>$$ where: $$ L_1(x) = -ieA_{\mu}[\phi^* (\partial_\mu \phi ) - (\partial_\mu \phi^*)\phi] $$[/B] I am trying to find an expression including the propagators...

The question revokes around my personal hypothesis that there is two forces connected with the Gravitational Field one obviously attraction between two bodies that is linear and the second is a less powerful repulsive force that emanates in a spiral motion off of rotating bodies that causes the...

Just started with QFT from Zee and am already confused by first equation lol. See attached picture. Does anyone actually understand this? He calls q_a the vertical displacement of particle 'a', and yet he only allows the springs to be horizontally between the particles. So, there should be...

I'm going through Zwiebach Chapter 6 on relativistic strings to try to solve a similar problem. I got all the way to my equation of motion \begin{eqnarray*} \delta S & = & [ p' \delta \theta]_{z 0}^{z 1} + \int_{z 0}^{z 1} d z \left( p - \frac{\partial ( p')}{\partial z} \right) \delta...

I should mention that I'm self-studying this material, not taking it as part of a course, but since this is still a homework-style problem I figured it'd be best to post here. Homework Statement In Peskin and Schroeder problem #11.2, they ask us to consider the Lagrangian: $$\mathcal{L} =...

In http://arxiv.org/abs/hep-th/9506035 the author said after writing this equation: $$\frac{1}{4}\eta^{\mu\nu\lambda\rho} F_{\mu\nu}F_{\lambda\rho} = \eta_{\sigma\tau\alpha\beta}\frac{\partial L}{\partial F_{\sigma\tau}} \frac{\partial L}{\partial F_{\alpha\beta} } + 2C$$ where C was arbitrary...

Homework Statement In a uniform gravitational field, there is a uniform solid disk of of mass M and radius R. A point mass m is glued to the disk at a point that is at a distance a from the center of the disk. The disk rolls without slipping. Find the frequency of small oscillations about the...

Hi, I am trying to figure out how to draw all the three level Feynman diagrams corresponding to this lagrangian density L = \frac{1}{2} \partial _{\mu} \phi \partial^{\mu} \phi - \frac{\mu^2}{2}\phi^2- \frac{\eta}{3!}\phi^3-\frac{\lambda}{4!} \phi^4+i \bar{\psi} \gamma _{\mu} \partial^{\mu}...

Hi all, I've recently been asked for an explanation as to why the Lagrangian is a function of the positions and velocities of the particles constituting a physical system. What follows is my attempt to answer this question. I would be grateful if you could offer your thoughts on whether this is...

The problem goes by this: A sphere of radius ##\rho## is constrained to roll without slipping on the lower half of the inner surface of a hollow cylinder of inside radius R. Determine the Lagrangian function, the equation of constraint, and Lagrange's equations of motion. Find the frequency of...

Hey guys, This is really confusing me cos its allowing me to create factors of 2 from nowhere! Basically, the first term in the Lagrangian for a real Klein-Gordon theory is \frac{1}{2}(\partial_{\mu}\phi)(\partial^{\mu}\phi). Now let's say I wana differentiate this by applying the...

Homework Statement Hey guys! So this question should be simple apparently but I got no idea how to do it. Basically I have the following Lagrangian density \mathcal{L}=\frac{1}{2}(\partial_{\mu}\phi)(\partial^{\mu}\phi)-\frac{m}{2}\phi^{2} which should be invariant under Lorentz...

Homework Statement Find the conserved Noether current j^\mu of the Dirac Lagrangian L = \bar{\psi} ( i \partial_\mu \gamma^\mu - m ) \psi under the transformation: \psi \rightarrow e^{i \alpha} \psi \,\,\,\,\,\,\,\,\,\, \bar{\psi} \rightarrow e^{-i \alpha} \bar{\psi} Homework Equations...

Homework Statement A cylinder on a inclined plane is rolling without slipping. Inclined plane is connected to wall with a spring and cylinder is connected to wall with a spring too. All frictions will be neglected, and all the given data has shown on the image below. As seen above, k2 spring...

Homework Statement Ok, so in this system, there are two point particles of mass M connected by massless levers of length L. The pair of masses pivots about the upper point and rotates about the axis at an angular frequency ω. The lower mass is constrained to slide on the vertical axis. The...

Hi guys, have a very tricky question on my HW to find compact group of global symmetry to this Lagrangian of 2 complex scalar fields L={\partial_\mu \phi_1^*}{\partial_\mu \phi_1}+{\partial_\mu \phi_2^*}{\partial_\mu \phi_2}-\lambda(\phi_1^* \phi_1 - \phi_2^* \phi_2 - v^2)^2 and I can't figure...

I have managed to get to the end of Chapter 6 and have done almost all of the exercises (I didn't get anywhere with exercise 5.6 (d) and have seen the Cesarth/TSny exchange and still don't feel I have a satisfactory solution...) but I have hit a bit of a wall with Exercise 7.1 (a).First question...

Homework Statement Note: There is an undertilde under every $$\phi$$ Imagine $$ \phi ^t M \phi $$ . M is a symmetric, real and positive matrix. Prove L is invariant: $$ \mathcal{L} = \phi ^t M \phi + \frac{1}{2} \partial_\mu \phi ^t \partial ^\mu \phi $$ Trick: Counting parameters. Homework...

Anyone can help me how to argue that interaction lagrangian is invariant under gauge transformation?

Okay, so I am trying to understand on how to write Lagrangian in different representations. I know the formula of the SU(3) lagrangian in terms of the 3 and 3* rep. Now presume I have a model in the SU(3) 10 plet rep which includes exotic fermions not in the SM. How would I write out the...

Suppose I come up with a system that has certain number of particles with certain masses and are interconnected between each other in a certain way and are acted by forces which are also part of the system. What's the general rule for finding potential and kinetic energies as functions of...

hi to everyone L=T-V as you know it is the lagrangian equation the effective Lagrangian of the electromagnetic field is given by following relation in gaussian units. L=(1/8pi) (E^2-B^2) how is must calculate this relation? (the energy density of electromagnetic fields is given by u=(1/8pi)...

Homework Statement Take the action S = \int d^4x \frac{1}{2} \left( \partial_{\mu}\phi(x)\partial^{\mu}\phi(x) - m^2\phi^2(x) - g\phi(x)^p \right) , and consider the following transformations: x^{\mu} \rightarrow x^{'\mu} = \lambda x^{\mu} \phi(x) \rightarrow \phi^{'}(x) =...

Given a basic Lagrangian, how would I determine invariant quantities? My hunch says it would be quantities that do not depend on position or time? Saying that, perhaps using the Lagrange equation to solve for equations of motion and along the way whatever terms disappear would be my invariant...

In the lagrangian formalism, we treat the position ##q## and the velocity ##\dot q## as dependent variables and talk about configuration space, which is just the space of positions. In the hamiltonian formalism we talk about canonical positions and momenta, and we consider them independent. Is...

I am having some problem with this attached question. I also attached my answer... My problem is the appearence of the term: 2 e (A \cdot \partial C) |\phi|^2 which shouldn't appear...but comes from cross terms of the: A \cdot A \rightarrow ( A + \partial C) \cdot (A + \partial C) In my...

Hi All, Recently we've been working on the distinction between the Eulerian and Lagrangian approaches in Fluid mechanics. I understand the simpler examples like a running stream of hot water etc. However one example is really tripping me up. So what's confusing me is that in analyzing...

Hi, I have a conceptual question regarding Lagrangian dynamics. It has to do with the potential energy formulation. My instructor today mentioned something in class that does not make much sense to me. Here is he most basic example that illustrates my confusion: Take a simple 1dof...

I want to prove the invariance of the Klein-Gordon Lagrangian \mathcal{L}=\frac 1 2 \partial^\mu \phi \partial_\mu \phi-\frac 1 2 m^2 \phi^2 under a general Lorentz transformation \Lambda^\alpha_\beta but I don't know what should I do. I don't know how to handle it. How should I do it? Thanks

If I stated a problem that you have to find the solution [0,\infty[\;\to\mathbb{R},\quad t\mapsto x(t) to the problem x(0) = x_0 < R \dot{x}(0) = v_0 > 0 m\ddot{x}(t) = -\partial_x U\big(x(t)\big),\quad\quad m>0 where R, v_0, m are some constants, and the function U has been defined...

Homework Statement the question is that there is a particle in 3 spatial Euclidean dimensions in cylindrical coordinates. I want to find a symmetry for the lagrangian if the potential energy is function of r and k.theta+z V=V(r,k.theta+z) Homework Equations k is constant L=T-V...

the question is that there is a particle in 3 spatial Euclidean dimensions in cylindrical coordinates. I want to find a symmetry for the lagrangian if the potential energy is function of r and k.theta+z V=V(r,k.theta+z) any help please ?

This is a problem from the Goldstein text. It gives two point masses ##m_1## and ##m_2## connected by a string (negligible mass), where ##m_2## is suspended by the string through a hole in a smooth table; ##m_1## rests on the table. It is important to note that ##m_2## only travels in a vertical...

One way to solve the simple LC circuit with 1 inductor and 1 capacitor is to use the Lagrangian formulation of mechanics and consider charge q as the generalized coordinate. When writing down your Lagrangian, the energy of the inductor \frac{1}{2}L(\frac{dq}{dt})^2 is treated as the kinetic...

I'm reading Leonard Susskind's The Theoretical Minimum Vol. 1. 1. The problem: I'm on the section in which he asks the readers to derive the Lagrangian for a particle on a rotating carousel in polar coordinates. 2. Relevant ideas: The same Lagrangian in Cartesian coordinates is given as...

Homework Statement So I just learned how to derive the equation of motion under the Lagrangian formulation which involves finding the euler-lagrange equation when setting the change in action to zero, chain rule, integration by parts etc.. Then I learned how to find the equations of motion...

Hi all, I have a (hopefully) quick conceptual question that I'd like to clear up with your help. Is the following argument for why we treat position and velocity as independent variables in the Lagrangian correct? (referring to classical mechanics) : The Lagrangian, \mathcal{L} of a given...

Homework Statement Consider the following Lagrangian for a massive vector field $A_{\mu}$ in Euclidean space time: $$\mathcal L = \frac{1}{4} F^{\alpha \beta}F_{\alpha \beta} + \frac{1}{2}m^2 A^{\alpha}A_{\alpha}$$ where ##F_{\alpha \beta} = \partial_{\alpha}A_{\beta} -...

[SIZE="4"]Definition/Summary The Lagrangian is a function that summarizes equations of motion. It appears in the action, a quantity whose extremum (minimum or maximum) yields the classical equations of motion by use of the Euler-Lagrange equation. In quantum mechanics, the action, and thus...

This isn't really a homework question, but may be similar to a typical example problem so I posted it here. Homework Statement I want to find the max and min dot product of a 3d vector and all points in a sphere constrained by angles in spherical coordinates. Homework Equations A point...

Hi guys. I hope this isn't a bad place to post my question, which is: I'm reading some lecture notes on Lagrangian mechanics, and we've just derived the Euler-Lagrange equations of motion for a particle in an electromagnetic field. It reads: m \ddot{\vec{r}} = -\frac{e}{c} \frac{\partial...

Greetings, I have two semi-related questions. 1. When making the Lagrangian formalism of electrodynamics, why is it that we use the Lagrangian density \mathcal{L}, rather than the plain old regular Lagrangian L? Is this something that is necessary, or is it more that it is just very...

I have just started studying Lagrangian Mechanics, and I can find decent material on the internet that describes the theory behind it, several proofs on equivalence and even some good solved examples. However, I would really appreciate if someone could recommend a book that has some of the...

I got this Lagrangian on the exam and it just seems weird to me: L = \frac{m}{2}(ẋ²+ẏ²) – eBẋy What I mean by "asymmetric" is that it doesn't seem to behave in a same way on x as on y, because there is ẋ in the last term and y but there is no ẏ and x. Deriving Euler-Lagrange equations I get: ẍ...

http://imgur.com/QhYG54l The image seems to be not showing here is the link : http://imgur.com/QhYG54lWhat does Landau mean here by the Lagrangian remaining ''unchanged''. Is it the value of the lagrangian as a function that may not change or is it the form that may not change? Also how does...

Hello everyone, I've been having trouble with the following reasoning for a while. The book I use for learning is Landau and Lifschitz vol1. When the concept of the Lagrangian is introduced in textbooks it is some abstract function of the position vector, velocity vector and time. Then they try...

Hello everyone! I was reading the following review: http://relativity.livingreviews.org/open?pubNo=lrr-2009-4&amp;page=articlesu23.html And I got stuck at the first equation; (10.1) So how I understand this is that there are two variations, \tilde{q}(t)=q(t)+\delta q(t)...

Homework Statement Prove that under an infinitesimal Lorentz transformation: x^\mu \to x^\mu+\omega^\mu_\nu x^\nu so: \phi\to\phi-\omega^\mu_\nu x^\nu\partial_\mu\phi the Lagrangian varies as: \delta \mathcal{L}=-\partial_\mu(\omega^\mu_\nu x^\nu \mathcal{L}) The Attempt at a...