Lagrangian Definition and 1000 Threads

Homework Statement The polynomial pL(x) is known as Lagranges interpolation formula, and the points (x0; y0), . . . , (xn; yn) are called interpolation points. You will use Lagrange's interpolation formula to interpolate sin x over the range [0; 2pi]. Begin with n + 1 interpolation points...

I have been calculating the currents and associated Noether charges for Lorentz transformations of the Dirac Lagrangian. Up to some spacetime signature dependent overall signs I get for the currents expressions in agreement with Eq. (5.74) in http://staff.science.uva.nl/~jsmit/qft07.pdf . What...

Hi, I have a following question... Can it be that there is given some Lagrangian and instead of considering whole Lagrangian one makes its series expansion and considers only some orders of expansion? Can you bring some examples or why and when does this happen... ? Thank you

Homework Statement Here's the free body diagram with variables. I am looking for the lagrangian mechanics equation. M is mass of the bottom wheel. m is the mass of the top wheel. R is the radius of the bottom wheel. r is the radius of the top wheel. θ_{1} is the angle from vertical of...

Hi, If I have three light quark flavours with massses m_u, m_d,m_s , I want to try and calcuate the masses of the eight pseudogoldstone bosons. I have found from my mass term in the Chiral L that: L_{mass}=-2v^3...

Homework Statement The goal of the question I'm being asked is to show that the covariant derivatives, D_{\mu}, "integrate by parts" in the same manner that the ordinary partial derivatives, \partial_{\mu} do. More precisely, the covariant derivatives act on the complex scalar field...

Homework Statement I have a problem regarding to lagrangian. If L is a Lagrangian for a system of n degrees of freedom satisfying Lagrange's equations, show by direct substitution that L' = L + \frac{d F(q_1,...,q_n,t)}{d t} also satisfies Lagrange's equations where F is any ARBITRARY BUT...

Hi! In some texts (Sakurai - advanced qm and others) I found this expression for the lagrangian of an em field: L=F_{\mu \nu}F_{\mu \nu} but I'm a bit confused... L must be a Lorentz invariant, so I would write instead: L=F_{\mu \nu}F^{\mu \nu} \;\; Which form is the correct one? Or...

Homework Statement I teach myself classical mechanics from David Tong http://www.damtp.cam.ac.uk/user/tong/dynamics.html From the homework set I should verify that the Lagrangian L=\frac{1}{12}m^{2}\dot{x}^{4}+m\dot{x}^{2}V-V^{2} Yields the same equations as the mere...

The Wikipedia article regarding Lagrangian Mechanics mentions that we can essentially derive a new set of equations of motion, thought albeit non-linear ODEs, using Lagrangian Mechanics. My question is: how difficult is it usually to solve these non-linear ODEs? What are the usual numerical...

Hi, If I have the Lagrangian L=i\chi^{\dagger\alpha i}\bar{\sigma}^{\mu}(D_{\mu})_{\alpha}^{\beta}\chi_{\beta i}+i\xi^{\dagger}_{\bar{i}\alpha}\bar{\sigma}^{\mu}(\bar{D}_{\mu})^{\alpha}_{\beta}\xi^{\beta i}-1/4 F^{a\mu\nu}F_{\mu\nu}^{a} where \alpha,\beta are colour indices, and i=1,2 is a...

Please teach me this: Why the Lagrangian in QFT must involve derivative of field? Is it correct that because fermions and bosons(meaning all things) obey Dirac and Klein-Gordon equations,then the corresponding Lagrangians include the derivative of field? (I know that the derivative has a...

Homework Statement A particle of mass m is placed on the inside of a smooth paraboloid of revolution whose equation is cz = x2 + y2 , where c is a constant, at a point P which is at a height H above the horizontal x-y plane. Assuming that the particle starts from rest (a) find the speed...

The stress-energy tensor is usually defined in standard GR treatments as T_{\mu\nu} = -\frac{2}{\sqrt{-g}}\frac{\delta(\sqrt{g}L_m)}{\delta g^{\mu\nu}}) with the Lm the matter Lagrangian. I'm curious what Lm is for a perfect fluid with density ρ and pressure P that would lead to the...

Homework Statement a.) Set up the Lagrange Equations of motion in spherical coordinates, ρ,θ, \phi for a particle of mass m subject to a force whose spherical components are F_{\rho},F_{\theta},F_{\phi}. This is just the first part of the problem but the other parts do not seem so bad...

Please teach me this: Does a symmetry of Lagrangian be reserved in each Feynman diagram of perturbative QFT,because even Ward Identity still deduces from U(1) symmetry that we consider each diagram has?. By the way, does effective action reserve the symmetry that Lagrangian has?. Thank...

Hi guys, can you help me with this? I'm supposed to calculate the energy momentum for the classic Maxwell Lagrangian, \mathcal{L}=-\frac{1}{4}F^{\mu\nu}F_{\mu\nu} , where F_{\mu\nu}=\partial_\mu A_\nu-\partial_\nu A_\mu with the well known formula: T^{\sigma\rho}=\frac{\delta\mathcal{L}}{\delta...

Homework Statement |--------------------| m|----------m-------- |m |--------------------| -------> x : positive x-axis This is a picture of a coupled oscillator in equilibrium. All three masses are equal and the spring constant on the long springs are k and the two short...

Homework Statement Q) A child, Alice, on a playground merry-go-round can be modeled as a point mass m on a homogeneous horizontal disc of mass M and radius a. The disc rotates without friction about a vertical axis through its center. Alice clings to a straight railing that extends from the...

Homework Statement "A bead with mass m slides without friction on a wire which lies in a vertical plane near the earth. The wire lies in the x-z plane and is bent into a shape conforming to the parabola az = x2, where a is a positive known constant. (X is horizontal and z is vertical) The...

Please teach me this: Why the Lagrangian in QFT does not include high order derivative of field?Is it correct the reason being all fields obey the only Dirac and Klein-Gordon equations? Thank you very much for your kind helping.

Is anyone good with Lagrangian mechanics applied to constrained systems? I had a question about the Lagrange multiplier method, maybe I should have posted it in this section. https://www.physicsforums.com/showthread.php?t=550139

I know that it works with adding a total time derivative and multiplying the Lagrangian by a constant. are these the only things that can be done to a Lagrangian such that the equations of motion have the same solutions q(t). Thanks!

Man I hate to make two post in one day but I am really stuck! Homework Statement A particle slides on the inside surface if a frictionless cone. The cone is fixed with its tip on the ground and its axis vertical. The half angle of the tip is α. Let r be the distance from the particle to the...

Homework Statement Two equal masses are glued to a massless hoop of radius R that is free to rotate about its center in a vertical plane. The angle between the masses is 2*theta. Find the frequency of small oscillations.Homework Equations \frac{d}{dt} \frac{∂L}{∂\dot{q}}=\frac{∂L}{∂q} The...

In Landau's Mechanics, if an inertial frame \textit{K} is moving with an infinitesimal velocity \textbf{ε} relative to another inertial frame \textit{K'}, then \textbf{v}'=\textbf{v}+\textbf{ε}. Since the equations of motion must have the same form in every frame, the Lagrangian L(v^2) must be...

Hi everyone Homework Statement At first I want to find the langrangian function and the equation of motion for a system which exists of 2 masses(m) coupled by a spring(k). It's moving in 3 dimensions.We shall use cylindrical coordinatesHomework Equations LangrangianThe Attempt at a Solution...

I am trying to find the equations of motion for a test particle in the schwarzschild metric. However, I cannot find the correct first integral for the Lagrangian. The Schwarzschild metric is: ds^2 =...

Homework Statement Hi, i have a quick question to see if I'm on the right track (I totally suck at electrical circuits since i never took a formal course so it might seem elementary to you.. anyway): Three LC systems in parallel with different L and C values, nothing else. closed circuit...

Homework Statement Find the Lagrangian of a simple pendulum of mass m whose point of support moves uniformly on a vertical circle with constant angular velocity. (So basically there is a circle around the origin that spins with a constant angular velocity and the pendulum is attached to the...

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...

Homework Statement I am trying to follow along in my textbook on wireless communications (this is an Electrical Engineering course), and I am having trouble following the mathematics. The idea is to maximize the "capacity" of a channel according to a given constraint. This involves the...

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...