In this article [1] we can read an explanation about Wilson's approach to renormalization
I have read that Kenneth G Wilson favoured the path integral/many histories interpretation of Feynman in quantum mechanics to explain it. I was wondering if he did also consider that multiple worlds...
Hello, I have been working on the three-dimensional topological massive gravity (I'm new to this field) and I already faced the first problem concerning the mathematics, after deriving the lagrangian from the action I had a problem in variating it
Here is the Lagrangian
The first variation...
Hello,
I've got to rationally analice the form of the solutions for the equations of motion of a simple pendulum with a varying mass hanging from its thread of length ##l## (being this length constant).
I approached this with lagrangian mechanics, asumming the positive ##y## direction is...
In order to compute de lagrangian in spherical coordinates, one usually writes the following expression for the kinetic energy: $$T = \dfrac{1}{2} m ( \dot{r}^2 + r^2 \dot{\theta}^2 + r^2 \sin^2 \theta \dot{\phi}^2 )\ ,$$ where ##\theta## is the colatitud or polar angle and ##\phi## is the...
I'm reading a book on Classical Mechanics (No Nonsense Classical Mechanics) and one particular section has me a bit puzzled. The author is using the Euler-Lagrange equation to calculate the equation of motion for a system which has the Lagrangian shown in figure 1. The process can be seen in...
Hi, I'm trying to solve a differential geometry problem, and maybe someone can give me a hand, at least with the set up of it.
There is a particle in a 3-dimensional manifold, and the problem is to find the trajectory with the smallest distance for a time interval ##\Delta t=t_{1}-t_{0}##...
Hi!
I am given the lagrangian:
## L = \dot q_1 \dot q_2 - \omega q_1 q_2 ##
(Which corresponds to a 2D harmonic oscillator) And I am given two transformations and I am asked to say if there is a constant of motion associated to each transformation and to find it (if that's the case).
I am...
I am currently studying QFT from this book.
I have progressed to the chapter of QED. In the course, the authors have been writing the Lagrangian for different fields as and when necessary. For example, the Lagrangian for the complex scalar field is $$\mathcal{L} \ = \ (\partial ^\mu...
In "The Theoretical Minimum" (the one on classical mechanics), on page 218, the authors write a Lagrangian
$$L=\frac m 2 (\dot r^2 +r^2\dot \theta ^2)+\frac {GMm} r$$
They then apply the Euler-Lagrange equation ##\frac d {dt}\frac {dL} {d\dot r}=\frac {dL} {dr}## (I know there should be...
The Standard Model Lagrangian contains terms like these:
##-\partial_\mu \phi^+ \partial_\mu\phi^-##
##-\frac{1}{2}\partial_\nu Z^0_\mu\partial_\nu Z^0_\mu##
##-igc_w\partial_\nu Z^0(W^+_\mu W^-_\nu-W^+_\nu W^-_\mu)##
How should one interpret the "derivative particle fields" like...
Alright so I was just messing around with Lagrangian equation, I just learned about it, and I had gotten to this equation of motion:
Mg*sin{α} - 1.5m*x(double dot)=0
I am trying to get velocity, and my first thought was to integrate with dt, but I didn't know how to. And I'm not even sure it's...
I'm reading up a series of papers on hydrodynamical simulations for galaxies and cosmology. They keep mentioning things like "Lagrangian" or "pseudo-lagrangian" or "Eulerian". I tried looking it up on the internet, but the answers are either too broad and could mean a huge number of things in...
I started studying Lagrangian mechanics, and the movement equation is like this:
d/dt (d/dz') L - d/dz L = 0 if the movement is on the z axis.
Now the problem is, let's say L = M(z')2/2 - Mgz. How do we derivate an expression depending of z with respect to z' and also , an expression depending...
Consider two arbitrary scalar multiplets ##\Phi## and ##\Psi## invariant under ##SU(2)\times U(1)##. When writing the potential for this model, in addition to the usual terms like ##\Phi^\dagger \Phi + (\Phi^\dagger \Phi)^2##, I often see in the literature, less usual terms like:
$$\Phi^\dagger...
90 years have gone by since P.A.M. Dirac published his equation in 1928. Some of its most basic consequences however are only discovered just now. (At least I have never encountered this before). We present the Covariant QED representation of the Electromagnetic field.
1 - Definition of the...
Assuming generlized variables, q, we have a Lagrangian in mechanics as the kinetic energy, K, minus potential energy, U, with a dependency form such that
L(q,dq/dt) = K(q, dq/dt) - U(q)
Can someone provide examples of Lagrangians in other disciplines?
Homework Statement
The problem is attached. I'm working on the second system with the masses on a linear spring (not the first system).
I think I solved part (a), but I'm not sure if I did what it was asking for. I'm not sure exactly what the question means by the... L=.5Tnn-.5Vnn. Namely, I'm...
Hi
here is the situation; There's a spherical particle contained with a MEMS sensor (3D accelerometer and gyroscope) moving down a bed. What we want is to estimate the total kinetic energy of the particle. The total kinetic energy has two parts, translational part and rotational part. for the...
Homework Statement
A yoyo falls straight down unwinding as it goes, assume has inner radius a, outer radius b and Inertia I. What is the generalised coordinates and the lagrangian equation of motion?
Homework Equations
L=T-U where T is kinetic energy and U is potential
The Attempt at a...
Homework Statement
I want to show that the propagator of Proca Lagrangian:
\mathcal{L}=-\frac{1}{4}F_{\mu \nu}F^{\mu \nu}+\frac{1}{2}M^2A_\mu A^\mu
Is given by:
\widetilde{D}_{\mu \nu}(k)=\frac{i}{k^2-M^2+i\epsilon}[-g_{\mu\nu}+\frac{k_\mu k_\nu}{M^2}]
Homework Equations
Remember that...
A single particle Hamitonian ##H=\frac{m\dot{x}^{2}}{2}+\frac{m\dot{y}^{2}}{2}+\frac{x^{2}+y^{2}}{2}## can be expressed as: ##H=\frac{p_{x}^{2}}{2m}+\frac{p_{y}^{2}}{2m}+\frac{x^{2}+y^{2}}{2}## or even: ##H=\frac{p_{x}^{2}}{2m}+\frac{p_{y}^{2}}{2m}+\frac{\dot{p_{x}}^{2}+\dot{p_{x}}^{2}}{4}##...
Hello guys,
I've came up with three statements in a discussion with a friend where we were trying to check if we had a clear vision of what isotropy and group invariance would imply in an arbitrary theory of gravity at the level of its matter lagrangian. We got stuck at some point so I came here...
Homework Statement
A bead of mass ##m## slides (without friction) on a wire in the shape, ##y=b\cosh{\frac{x}{b}}.##
Write the Lagrangian for the bead.
Use the Lagrangian method to generate an equation of motion.
For small oscillations, approximate the differential equation neglecting terms...
Homework Statement
A particle of mass ##m## moves without slipping inside a bowl generated by the paraboloid of revolution ##z=b\rho^2,## where ##b## is a positive constant. Write the Lagrangian and Euler-Lagrange equation for this system.
Homework Equations...
Homework Statement
I am given the Hamiltonian of the relativistic free particle. H(q,p)=sqrt(p^2c^2+m^2c^4) Assume c=1
1: Find Ham-1 and Ham-2 for m=0
2: Show L(q,q(dot))=-msqrt(1-(q(dot))^2/c^2)
3: Consider m=0, what does it mean?
Homework Equations
Ham-1: q(dot)=dH/dp
Ham-2: p(dot)=-dH/dq...
Homework Statement
B is 10kg
C is 20kg
can I find a lagrangian for this system? If so how?
Diagram: http://imgur.com/j811rzw
Homework Equations
L=T-V
Kinetic = .5mv^2
Potential = mgh
The Attempt at a Solution
I know the kinetic energy must be 0 right? How could I find the potential?
Homework Statement
Take the x-axis to be pointing perpendicularly upwards.
Mass ##m_1## slides freely along the x-axis. Mass ##m_2## slides freely along the y-axis. The masses are connected by a spring, with spring constant ##k## and relaxed length ##l_0##. The whole system rotates with...
This T-shirt I bought at a physics conference displays the following equation. It looks like the Lagrangian of the Standard Model of particle physics but I only recognise lines 1 (electroweak) and 3 (Higgs mechanism). What are lines 2 and 4 and what is/isn't included? eg. are quarks, gluons...