Lagrangian Definition and 1000 Threads

Homework Statement [/B] Find the Cartesian coordinates (x, y, z) of a fixed reference frame expressed in terms of the coordinates (x', y' , z) of a rotating frame, which rotates with the horizontal rod HR. Choose the x' -axis to point along the horizontal rod in the direction OA. Use this to...

Follow along at http://star-www.st-and.ac.uk/~hz4/gr/GRlec4+5+6.pdf and go to PDF page 9 or page 44 of the "slides." I'm trying to see how to go from the first to the third line. If we write the free particle Lagrangian and use q^i-dot and q^j-dot as the velocities and metric g_ij, how is it we...

Homework Statement A long light inflexible rod is free to rotate in a vertical plane about a fixed point O. A particle of mass m is fixed to the rod at a point P a distance ℓ from O. A second particle of mass m is free to move along the rod, and is attracted to the point O by an elastic force...

To make my explanation easier open the ''Generating function approach'' section on this wiki article: http://en.wikipedia.org/wiki/Canonical_transformation The function ##\frac{dG}{dt}## represents the function that always can be added to the Lagrangian without changing the mechanical...

just working my way through Susskind's "Theoretical Minimum". At the Langrangian formalism I'm in novel territory so this may be a dumb question. Kind of multiple choice or fill in a real answer. Why is there no term for the Entropy of a system in the Lagrangian? Is it because time is an...

Homework Statement A long light inflexible rod is free to rotate in a vertical plane about a fixed point O. A particle of mass m is fixed to the rod at a point P a distance l from O. A second particle of mass m is free to move along the rod, and is attracted to the point O by an elastic force...

Homework Statement A long light inflexible rod is free to rotate in a vertical plane about a fixed point O. A particle of mass m is fixed to the rod at a point P a distance ℓ from O. A second particle of mass m is free to move along the rod, and is attracted to the point O by an elastic force...

What's the simplest, most direct way to derive the lagrangian of the SM? I saw earlier today: L[S M] = L[Dirac] + L[mass] + L[Gauge] + L[Gauge/psi] That seems like a good starting point. I like it because it says the SM Lagrangian is simply the sum of four lagrangians. The next step...

I just recently worked through the lagrangian method for describing the motion of a double pendulum. What I want to do now is describe the motion of a double pendulum that has been instantaneously released from the origin and allowed to fly through the air (with the 2 pendulums still connected...

Recommend an easy going introduction to lagrangian and hamiltonian mechanics (for self study)

I was trying to prove all those little things you spend long as the local invariance in the free Lagrangian of electroweak interaction. Taking into account the appropriate SU(2) transformations (without covariant derivatives), came to the following expression \mathcal{L}_{\text{ferm.}} =...

Homework Statement [/B] A circle of radius ##a##, with diameter ##AB##, is drawn on a sheet of paper which lies on a smooth horizontal table. The paper is pivoted with a pin at ##A## and has moment of inertia ##4ma^2## about a vertical axis through ##A##. An insect of mass ##m## walks around...

Hi guys, So I'm trying to understand why the potential energy of a Lagrangian is the way it is. The system I'm considering is a closed necklace of N beads, each of mass m. Each bead interacts only with its nearest neighbour. First let me make some comments: 1) Each bead is labeled with a...

Hi guys, so this is a pretty generic question. Starting off with the classical Lagrangian in a case where there is no interaction or explicit time dependence, the functional form is L=L(x,\dot{x})=L(x,\partial_{t}x). Now when we look at the Lagrangian density in field theory, the functional...

Homework Statement A rod of length ##L## and mass ##M## is constrained to move in a vertical plane. The upper end of the rod slides freely along a horizontal wire. Let ##x## be the distance of the upper end of the rod from a fixed point, and let ##\theta## be the angle between the rod and the...

I was wondering. What's the reason for putting objects in low representations in the SM and not higher ones? So, why fermions in a doublet of SU(2) and not a multiplet? In analogy in SU(5) we put the particles in the 5-plet...

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...

Hello there! It's my first time posting here, I hope you guys will be good to me :). I took a one year break to study a language abroad, and now it seems like I forgot everything math-wise. I'm preparing for a test and I'm having a really hard time doing the following problem. I need to...

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...