Lagrangian Definition and 1000 Threads

Homework Statement So I'm having some difficulty with my QFT assignment. I have to solve the following problem. In three spacetime dimensions (two space plus one time) an antisymmetric Lorentz tensor F^{\mu\nu} = -F^{\nu\mu} is equivalent to an axial Lorentz vector, F^{\mu\nu} =...

We can think of a particle having kinetic and potential energy, T and V. The Hamiltonian is the sum of these, H = T + V. This seems like a sensible enough quantity to think about. However, we can also define the Lagrangian as being the difference between these two quantities, L = T-V...

I'm doing a Lagrangian problem in spherical coordinates, and I was unsure how to express the kinetic energy, so I looked it up and wiki states it should be this: http://en.wikipedia.org/wiki/Lagrangian#In_the_spherical_coordinate_system Which would give me the correct answer, but I'm...

Homework Statement Consider the following Lagrangian of a particle moving in a D-dimensional space and interacting with a central potential field L = 1/2mv2 - k/r Use Noether's theorem to find conserved charges corresponding to the rotational symmetry of the Lagrangian. How many...

Homework Statement A particle of mass 'm' slides on a smooth surface, the shape of which is given by y = Ax^{2} where A is a positive constant of suitable dimensions and y is measured along the vertical direction. The particle is moved slightly away from the position of equilibrium and then...

Homework Statement Find equations of motion (eom) of a particle moving in a D-dimensional flat space with the following Lagrangian L = (1/2)mv2i - k/ra, r = root(x2i), m,k,a are constantsHomework Equations The Attempt at a Solution The equations of motion are given by d/dt(∂L/∂vi) - ∂L/∂xi...

Homework Statement Hi everyone! This is not actually a homework problem, but I thought it was similar to one so I am putting it here. Basically I was watching this youtube video of a falling slinky and I decided I wanted to try modelling it with physical equations: The problem I have...

Please teach me this: Why the renormalization group flow and the fix-point depends only on the basic symmetry but not on the Lagrangian form.In general speaking,the physics laws depend only the basic symmetries?By the way,the Klein-Gordon,linear sigma,nonlinear sigma Lagrangian flow to one...

I'm reading Griffith's Elementary particles and I'm stuck on the math for one of the examples, could anyone show me what I'm missing or point me in the right direction? I attached a pdf (of the word doc I was using) that shows what I did so far since I'm really bad with LaTeX and it would've...

Given an action: S = \int L(q,\dot{q},t) \,dt The variation is: \delta S = \int \left(\frac{\partial L}{\partial q}\delta q+\frac{\partial L}{\partial \dot{q}}\delta\dot{q}\right)\,dt I'm guessing this is some type of chain rule, but I haven't been able to derive it... how is it...

Sorry for a naive question. In EM textbook and QM path integral textbook, the action and Lagrangian in electromagnetic interaction are S = L dt = e(\phi – A v) dt ---equ.(1) But in QFT textbook, the action and Lagrangian density are S = L d^4x = A J d^4x ---equ.(2) As I...

Now bear with me, I'm no expert when it comes to Electroweak Symmetry and Symmetry Breaking; I can only comprehend up to integrating, functions, derivatives, partial derivatives with a small hint of linear algebra and the basic, Hermitian, Hamiltonian, bras and kets. So my questions are the...

Hi, I am trying to obtain a Lagrangian for a particle moving on the surface of a saddle z = x^2 - y^2 I have an added complication that the saddle is rotating with some angular frequency, w, and not sure how to incorporate this rotation into my kinetic and potential terms. This is the...

Hi all, I'm trying to calculate the Feynman Rules for the effective electroweak chiral Lagrangian. For example, this is the first term in the Lagrangian: \begin{eqnarray} \mathcal{L}=\frac{v^2}{4}\text{Tr}(D_{\mu}U D^{\mu}U^{\dagger}) \end{eqnarray} where \begin{eqnarray}...

Suppose I have a mechanical system with l + m degrees of freedom and an associated lagrangian L(\alpha,\beta,\dot{\alpha},\dot{\beta},t) where \alpha\in\mathbb{R}^l and \beta\in\mathbb{R}^m. Now suppose I have a known \mathbb{R}^l-valued function f(t) and define a new lagrangian...

Homework Statement Hello, I would like to derive geodesics equations from hamiltonian H=\frac{1}{2}g^{\mu\nu}p_{\mu}p_{\nu} using hamiltonian equations. A similar case are lagrangian equations. With the definition L=g_{\mu\nu}\dot{x}^\mu\dot{x}^\nu I tried to solve the...

Hi there - I've been confused for a long time about the following. When we learn how to mop up divergences in QFT, we learn two methods: the Feynman method, and the method of counterterms. In the latter, we add to a Lagrangian containing physical values for the parameters a Lagrangian...

Homework Statement Determine the Hamiltonian corresponding to the an-harmonic oscillator having the Lagrangian L(x,\dot x )=\frac{\dot x ^2}{2}-\frac{\omega ^2 x^2}{2}-\alpha x^3 + \beta x \dot x ^2. Homework Equations H(q,p,t)=\sum p_i \dot q _i -L. p _i=\frac{\partial L}{\partial \dot...

Please teach me this: How do we know a force is strong,week or intermediate by considering the corresponding Lagrangian.It seem that the intensiveness depends on both coupling constant,the form of theory(form of Lagrangian).By the way, the mass of force carrier boson stipulates the range of the...

So I have to find the min and max values of f(x,y,z) = x^4 + y^4 + z^ 4 given the constraint x^2 + y^2 + z^2 = 1. I've found the points (+-1/sqrt(3),1/sqrt(3) ,1/sqrt(3)), (+-1/sqrt(3),-1/sqrt(3) ,1/sqrt(3)) ... etc all of which have the f-value of 1/3 when x =/= 0 & y =/= 0 & z =/= 0 (this...

I've always found that the lagrangian for the Gravitational field is that from the Einstein-Hilbert action: L=R (R is the Ricci scalar; I'm not including the factor of \sqrt{-g}) but when variational principles are applied, we get the vacuum field equations (obviously). I'd like someone...

How to show the Proca equation by using the given Proca Lagrangian? Surely, I know the Euler-Lagrange equation, but I can't solve this differentiation!(TT) The given Proca lagrangian is, \mathcal{L}=...

Hello everyone I have difficulties in understanding some stuff in Lagrangian and Hamiltonian mechanics. This concerns the equations : \dot p = - \frac{\partial H}{\partial q} \frac{d}{dt} \frac{\partial L}{\partial \dot q} = \frac{\partial L}{\partial q} First I have to say that I'm a math...

Does anyone know the Lagrangian for the propagation of light in curved spacetime? I'm disappointed to discover that I don't actually know how to compute the action for a given null curve.

I don't know how to do the 4 questions. And I only have some ideas on questions 1. The details are written on the photos. Thanks for help. Eqtn 2.28 2.36 2.37 are given on the photo.

In most of the physical systems, if we have a Lagrangian L(q,\dot{q}), we can define conjugate momentum p=\frac{\partial L}{\partial{\dot{q}}}, then we can obtain the Hamiltonian via Legendre transform H(p,q)=p\dot{q}-L. A important point is to write \dot{q} as a function of p. However, for the...

Hi All, is there anybody to give me some help on how I can calculate the Euler Lagrangian equation associated with variation of a given functional? I am new with these concepts and have no clue about the procedure. thanks a lot

Hi, I was wondering if anyone had any examples of ALE codes in any dimension and using any method (FEM, FVM, FDM). I just need to know how the mesh velocity and the fluid velocity are dealt with. Many Thanks, H

Is there a systematically way of finding all space-time symmetries of a given Lagrangian? E.g. given a electromagnetic Lagrangian, can I somehow derive that the symmetries in question are conformal ones? Thanks.

So I was lucky enough to visit CERN earlier this year, and they were selling t-shirts with a long equation on them. And I, like an idiot tourist, somehow jumped to the conclusion this was the standard model Lagrangian and got the t-shirt. Well, it's still a pretty cool t-shirt, but then I went...

As is well known, a Dirac Lagrangian can be written in a symmetric form: L = i/2 (\bar\psi \gamma \partial (\psi) - \partial (\bar\psi) \gamma \psi ) - m \bar\psi \psi Let \psi and \psi^\dagger be independent fields. The corresponding canonical momenta are p = i/2 \psi^\dagger...

I'm going through John Taylor's book on Classical Mechanics and am having some difficulty understanding his derivation of momentum conservation in the Lagrangian section. Firstly he starts the section off with assuming that all N particles of a system are moved in space by a distance \epsilon...

We all know that the free Lagrangian for a spin-1/2 Dirac field is \mathcal{L}=\bar\psi(i\gamma_\mu\partial^\mu-m)\psi. But, if I were to invent a Lagrangian, I would have tried \mathcal{L}=\partial_\mu\bar\psi\partial^\mu\psi-m^2\bar\psi\psi. What's wrong with this second Lagrangian? Why...

I am currently reading and trying to solve most of the problems in Carroll's Geometry and Spacetime. I am generally okay at the math (I've done some mathy Riemannian Geometry type stuff), but am not overly good at some of the higher-level physics. Homework Statement (Chapter 1, Question 13)...

Hey everyone, So I'm just looking around to get a hold of some lagrangian mechanics for the GRE's coming up. Is the lagrangian always dealing with energy? Basically there was a problem I encountered with trying to find the lagrangian of a rolling ball in some setup, and once I knew that it was...

Hello, In the lagrangian of QCD, there is q which is the quark field and it is the fundamental representation of SU(3). This q is multiplied by a gamma matrix and a q bar. So, how can we have a 4x4 matrix multiplying 1x3 matrix? Thanks

Homework Statement See image (I think I forgot to rotate it, careful with your necks!): http://img600.imageshack.us/img600/7888/p1000993t.jpg The system consists of 2 point masses joined by a rigid massless bar of length 2l, which can rotate freely only in the z-x plane. The center of...

According to my CM text, Lagrangian Mechanics can be used to derive Newton's laws. We define the Lagrangian as L=T-V. Now, how do we know what T is? Is it defined to be 1/2mv^2? The only way I know how to derive that is using the work energy theorem which feels like 'cheating' since I am...

Please teach me this: Do the Lagrangian(before broken in symmetry) and corresponding hidden symmetry broken Lagrangian describe the same physics or not?Because the field in the Lagrangian before broken is shifted by a constant in comparision with the field in the broken Lagrangian,but at...

Homework Statement I am trying to prove that Lagrangian L is not uniquely defined, but only up to a time derivative of a function: \frac{d\Lambda}{dt}, \Lambda(\vec{q}, t) So L > L+\frac{d\Lambda}{dt} = L+\frac{\partial \Lambda}{\partial q}~\dot{q}+\frac{\partial \Lambda}{\partial t} But...

Homework Statement I want to check that the QED lagrangian \mathcal{L}=-\frac{1}{4}F^{\alpha\beta}F_{\alpha\beta} + \bar\Psi(i\displaystyle{\not} D - m)\Psi where F^{\alpha\beta} = \partial^\alpha A^\beta - \partial^\beta A^\alpha, \ D^\mu = \partial^\mu - ieA^\mu is invariant under charge...

So I type a differential equation into Wolfram Alpha, like so: And one of the things that W-A outputs is the "Lagrangian" of that equation, which is so: My question is, what is this Lagrangian, what does it describe, and how do I find it?

Hi all, I'm doing some analysis of a bicycle mechanics problem and at one point the approximations I'm making mean that the problem reduces to the classic inverted pendulum. I'm very confused, as the equations I've worked out appear to have an unphysical singularity in them, and I can't see...

Homework Statement In my notes i have the following two equations written with no explanation where thehy came from... can someone help please!? L=(u, x )= -mc\sqrt(u^{\beta} u_\beta)-\frac{q}{c}A^{\alpha}u_\alpha, L(v,r, t) = -mc^2(1-\frac{v^2}{c^2})-\phi +\frac{q}{c}vA L is...

Please teach me this: Why the minima of potential of classical Lagrangian is called the ''vacuum expectation value of Phi(field function)''.Is it really a vacuum expectation value of field operator at the vacuum states(at this state,the potential part of classical Lagrangian equals zero)...

I started to answer this question, and I have quite a bit an answer, but still not complete, let's say that we write a Lagrangian in QFT, which an unknown function of the scalar field \phi and its derivative \partial \phi. We can always Taylor-expand it and get: L(\phi,\partial\phi) = a + b \phi...

Hi, Would someone know where I can find a derivation of the lorentz-invariant lagrangian density? This lagrangian often pops-up in books and papers and they take it for granted, but I was actually wondering if there's a "simple" derivation somewhere... Or does it take a whole theory and...

Homework Statement Trying to solve a Lagrangian, got down this integral. Unfortunately the zeroth-solution isn't good enough since the constant k is close to 1 for our experimental set-up. \int_{0}^{x}dx(\frac{xsin(x)}{1+kcos^2(x)}})^\frac{1}{2} Any hints? I'm not sure where to get...

We were working on some Lagrangian and trying to solve it using an ansatz. Due to some problems in the results we got, we started to doubt the correctness of the method in use. Here is a very simple Lagrangian which shows the problem very easily: L=\frac{1}{2}\dot{x}^{2}-gx We took m=1 for the...

Hi, Hope some one can help me with a problem I am working on: It involves working out: \frac{\delta L}{\delta A_\nu} of the following Lagrangian: L=\frac{1}{4}F_{\mu\nu}F^{\mu\nu} + \frac{1}{2} (D_{\mu} \Psi)^{*} D^{\mu}\Psi The solutions show that this is equal to: \frac{\delta...