Lagrangian Definition and 1000 Threads

Homework Statement The lagrangian is given by: L = -\frac{1}{4} F^2_{\mu \nu} + (\partial_{\mu} \phi_1 - m_1 A_{\mu})^2 + (\partial_{\mu} \phi_2 - m_2 A_{\mu})^2 Homework Equations Find the gauge transformation of the fields that corresponds to a symmetry. Find the combination of scalar...

Lagrangian in classical mechanics equals L=T-V, where T is kinetic energy and V is potencial energy. But, how to compose such a Lagrangian? Everywhere, where I found, it is only assumed and then equation ##d/dt (\partial L/\partial \dot{x})-(\partial L/\partial x)=0## is used. But, why L=T-V, is...

In Lagrangian mechanics the energy E is given as : E = \frac{dL}{d\dot{q}}\dot{q} - L Now in the cases where L have explicit time dependence, E will not be conserved. The notes I am referring to provide these two examples to distinguish between the cases where E is energy and it is not...

I'm trying to understand how to construct effective lagrangians for the hadrons. I understand the procedure for the mesons but I get stuck on baryons. In particular I don't understand how the baryons should transform under a chiral transformation. I mean for the mesons it was easy because they...

Homework Statement Given L (q, dq/dt, t). translation: q ---> q + e (e is infinitesimal constant) show that if ∂L/∂q = 0, then L is symmetry under the above translation. then find conserved quantity. Homework Equations S = ∫ L dt The Attempt at a Solution My attempt is nothing... because I...

Homework Statement A simple pendulum with mass m and length ℓ is suspended from a point which moves horizontally with constant acceleration a > Show that the lagrangian for the system can be written, in terms of the angle θ, L(θ, θ, t˙ ) = m/2(ℓ^2θ˙^2 + a^2t^2 − 2aℓtθ˙ cosθ) + mgℓ cos θ >...

First off, apologies if this is in the wrong forum, if my notation is terrible, or any other signs of noobishness. I just started university and I'm having a hard time with my first Lagrange problems. Help would be very much appreciated. 1. Homework Statement A body of mass m is lying on a...

I am not entirely sure how to convert the conservation of mass and momentum equations into the Lagrangian form using the mass coordinate h. The one dimensional Euler equations given by, \frac{\partial \rho}{\partial t} + u\frac{\partial \rho}{\partial x} + \rho\frac{\partial u}{\partial x} = 0...

Hello, I trying to understood some transition from one equation to another but i need a little help with that. So we have, a Had problems with Latex :).

First, let me take as the definition of a Lagrangian the quantity that when put into the Euler Lagrange equations, it gives the correct equation of motion. It sounds like we need to know the equations of motion first. For example. the Lagrangian for a particle subject to a constant magnetic...

¿How is possible deduce the Lagrangian of the fields of a theory knowing only his Feynman Diagrams?

What exactly was the purpose for the development of Lagrangian mechanics? Does it describe physical systems and situations that Newtonian mechanics cannot? I would also like to know why the Hamiltonian reformulation of mechanics occurred after the development of Lagrangian mechanics.

Homework Statement EDIT: This is a 2D problem, so all of my ##x## variables should be vectors. I just realized this and it may answer my question, I don't know yet though. Two masses, ##m_1## and ##m_2## are connected by a massless spring of spring constant ##k##. The spring is at it's...

How does adding a h.c. term make a Lagrangian real? Like http://isites.harvard.edu/fs/docs/icb.topic521209.files/QFT-Schwartz.pdf on page 99 (11.51)? thanks in advance

Hi everyone, sorry if this is not the right place to post that question but I'm new to this forum, i'll delete if necessary. I am currently trying to learn QFT from Matthew Schwartz's "Quantum field theory and the standard model", quite clear during the first chapters, but i have been...

Does exist a Lagrangian for the Euler equation describing perfect fluid? If so, what is the expression?

So i actually have many words that i know of, and are familiar with such as : The Hamiltonian Operator The Hermitian Operator The Lagrangian Eigen Values/States However, i am struggling with how these things work, and when to apply them, and what they actually mean. Many of the physics...

I know how to solve "typical" Kepler problem but I'm interested in a global view to "binary" systems. For example Earth - Moon. If I set lagrangian of system as ##L=\frac{1}{2}(m_1\dot{r}_1^2 + m_2\dot{r}_2^2)-V(|r_2-r_1|)## there isn't included a spin. My questions are: 1) If it is solved as...

Writing the Lagrangian for 3 masses and 2 springs in a line is easy. KE=1/2(m*v^2) L=KE(m1)+k/2(l1-(x2-x1))^2+KE(m2)+k2/2[L2-(x3-x2)]^2+KE(m3) However, I wish to model non-linear linkages of the above 3 masses and 2 springs. Suppose that the second spring (m2-m3) is angle θ away from the...

What is the interaction Lagrangian of matter and graviton fields?So(on the answer)we can say about the nonrenormalization.Why is the divergence of two gravitons diagram able to be the limit of the coincidence of the verties.So we can say about the nonrenormalization.

I can't find this in any textbook, so I must not understand something about it. What is the Lagrangian of a photon? Would it be just h*nu?

Hello all, If I am having the the effective lagrangian which is actually free + interaction lagrangian (obtained from the minimal substitution for pseudoscalar and vector mesons). then how to compute the vertices of the interaction ? I have taken into consideration of all symmetry breaking...

Homework Statement I have to expand the following term: $$\dfrac{1}{4} F_{\mu\nu}F^{\mu\nu} = \dfrac{1}{4} \left(\partial_{\mu}A_{\nu} - \partial_{\nu}A_{\mu}\right) \left(\partial^{\mu}A^{\nu} - \partial^{\nu}A^{\mu}\right)$$ to get in the end this form...

All I know is that Lagrangian is kinetic energy- potential energy and Hamiltonian is kinetic energy + Potential energy. Why do we calculate the lagrangian or hamiltonian?

If I write the lagrangian for a moving charge with constant angular speed, would a magnetic field be emergent? I would do the math myself, but I'm nowhere near pen and paper.

Hello, everyone. I have a one question which is related to the fermion masses. If you see my latex mathematics, you can know what I want to say. Here, L means SU(2) left-handed lepton doublets and R means SU(2) right-handed lepton singlets. So I am too much confusing to understand this...

What is the quantized form of the strings lagrangian?

Homework Statement Hello, Do you know how to find Lagrangian for 2D Vortices? Homework EquationsThe Attempt at a Solution

(Yes, I have searched the other posts and each one comes up deficient for what I want.) Why must the Lagrangian be extremized? And why it is of the form L = T – V? BUT I HAVE CAVEATS! Please do it from first principles WITHOUT an understanding of F=ma. (And, yes, I understand the calculus...

I've been working through a qft book by Sadovskii (while I wait for my Peskin book to come in) and I've used some later chapters of Griffith's Into to Elementary Particles as an introduction to some qft. My issue with both of these is that, where in classical mechanics we have the Lagrangian...

Homework Statement Hi all, I'm trying to learn how to manipulate tensors and in particular to differentiate expressions. I was looking at a Lagrangian density and trying to apply the Euler-Lagrange equations to it. Homework Equations Lagrangian density: \mathcal{L} = -\frac{1}{2}...

Homework Statement a. Suppose two particles with mass $m$ and coordinates $x_1$, $x_2$ collides elastically, find the lagrangian and prove that the linear momentum is preserved. b. Find new coordiantes (and lagrangian) s.t. the linear momentum is conjugate to the cyclical coordinate. Homework...

Does anyone know where can I find the deduction of all terms of the updated SM lagrangian? Although I have already looked at some lagrangians and theories like local gauge invariance, Yang-Mills theory, feynman rules, spontaneous symmetry-breaking and others, I wanted to see the deduction and...

I am reading the book Supergravity. In chapter 4, section 4.3.2 - Duality for gauge fields and complex scalar: The simplest case of electromagnetic duality in an interacting field theeory occurs with one abelian gauge field ##A_{\mu}(x)## and a complex scalar field ##Z(x)##. The...

http://arxiv.org/abs/1503.08640 New first order Lagrangian for General Relativity Yannick Herfray, Kirill Krasnov (Submitted on 30 Mar 2015) We describe a new BF-type first-order in derivatives Lagrangian for General Relativity. The Lagrangian depends on a connection field as well as a...

I was reading that the homogeneity of space can lead to the conclusion that the lagrangian of a free particle is not explicitly dependent on its position. At the moment, this does not come very intuitively to me. By homogeneity, I understand that if you displace the initial position of a...

Homework Statement 'Consider the system consisting of a bead of mass m sliding on a smooth circular wire hoop of mass 2m and radius R in a vertical plane, and the vertical plane containing the hoop is free to rotate about the vertical axis. Determine all relative equilibria of the bead.'...

I was hitting against a wall for the last hours. I am not able to obtain the 1/2 terms in the eq. 5 of this paper and left all in terms of only ##N_i## and ##\overline{N_i}##,neither. Anyone could give me a tip? http://arxiv.org/pdf/hep-ph/0210271v2.pdf Thank you in advance.

Homework Statement A non–uniform disk of mass M and radius R rolls without slipping along a horizontal plane in a straight line as shown in the attachment. The centre of gravity G is displaced a distance a from the centre of the disk. Let θ be the angle between the downward vertical and the...

Hi I began to study the basics of QED. Now I am studying Lagrangian and Hamiltonian densities of Dirac Equation. I'll call them L density and H density for convenience :)Anyway, the derivation of the H density from L density using Legendre transformation confuses me :( I thought because...

In Leonard Susskind's the theoretical minimum, he says, "For any system of particles, if the Lagrangian is invariant under simultaneous translation of the positions of all particles, then momentum is conserved". For a system of two particles moving under a potential which is a function of the...

Homework Statement 1. Two identical blocks A and B with mass m are joined together by a taut string B of length `. Block A moves on a frictionless horizontal table and block B hangs from the string which passes through a small hole in the table as shown in the figure. (a) Using polar...

"The hamiltonian runs over the time axis while the lagrangian runs over the trajectory of the moving particle, the t'-axis." What does the above statement means? Isnt hamiltonian just an operator that corresponds to total energy of a system? How is hamiltonian related to lagrangian intuitively...

This is not a homework equation at all, however I have devised my own example problem in order to convey my misunderstanding. (My question is at the end of the problem) Question that I had come up with: A particle's motion is described in the x direction by the equation x = x(t). The particle's...

Hi, I have a very basic question about the Lagrangian that I can't seem to understand: why is it dependent on both the position function and the time derivative? I know that it is the difference between the kinetic and potential energy, but why? Is there a derivation of this, is it a definition...

Consider a Lagrangian: ##L(x,x',t)## Define now: ##L'(x,x',t) = L + x ## We have seen that Lagrangians can differ up to a total time derivative of some function ##F(x,t)## in such cases and give the same equation. When checking explicitly these two give different equations. Why would it be...

In this process: N*→N+photon If we want to calculate the amplitude with the following interaction Lagrangian: (http://arxiv.org/abs/nucl-th/0205052) If we use functional method,the field operator is not polynomial,how to use "center formula"to bring functional derivative in? Or we must...

Homework Statement [/B] The Lagrangian ##\mathcal{L}\frac{1}{2}(\partial_\mu\phi^\nu)^2+\frac{1}{2}(\partial_\mu\phi^\mu)^2+\frac{m^2}{2}(\phi_\mu\phi^\mu)^2## for the vector field ##\phi^\mu## is not invariant with respect to the gauge transformation ##\phi^\mu\rightarrow...

An example problem in Chapter 7 of "Classical Dynamics of Particles and Systems" by Marion, Thornton uses Lagrangian equations with undetermined multipliers to solve for the motion of a disc rolling down an incline. The resulting Lagrangian equations are: Mg sin α - M d2y/dt2 + λ = 0...

Homework Statement Given the Lagrangian density \Lambda = -\frac{1}{c}j^lA_l - \frac{1}{16 \pi} F^{lm}F_{lm} and the Euler-Lagrange equation for it \frac{\partial }{\partial x^k}\left ( \frac{\partial \Lambda}{\partial A_{i,k}} \right )- \frac{\partial \Lambda}{\partial A_{i}} =0...