Hello! Can someone explain to me what exactly a local gauge invariance is? I am reading my first particle physics book and it seems that putting this local gauge invariance to different lagrangians you obtain most of the standard model. The math makes sense to me, I just don't see what is the...
I'm basically trying to understand the 2-D case of the catenary cable problem. The 1-D case is pretty straightforward, you have a functional of the shape of a cable with a constraint for length and gravity, and you get the explicit function of the shape of a cable.
But if you imagine a square...
Hi, I'm in the masters year of a theoretical physics course which begins this September. I'm reading the classical mechanics notes ahead of time, and I came across the idea of holonomic and non-holonomic constraints. I understand that in the case of a holonomic system, you can use the...
Do I substitute A_\mu + \partial_\mu \lambda everywhere A_\mu appears, then expand out? Do I substitute a contravariant form of the substitution for A^\mu as well? (If so, do I use a metric to convert it first?)
I’m new to Ricci calculus; an explanation as to the meaning of raised and lowered...
The form of the Lagrangian is: L = K - U
When cast in terms of generalized coordinates, the kinetic energy (K) can be a function of the rates of generalized coordinates AND the coordinates themselves (velocity and position); a case would be a double pendulum.
However, the potential energy (U)...
How does one write a Lagrangian of a coherent state of vector fields (of differing energy levels) in terms of the the individual Lagrangians?
I desperately need to know how to know to do this, for a theory of mine to make any progress.
Please stick with me, if I didn't make sense just ask...
Homework Statement
This was supposed to be an easy question. I have a question here that wants you to describe a yoyo's acceleration (in one dimension) using Lagrangian mechanics. I did and got the right answer. Now I want to use Hamilton's equations of motion but I get a wrong number. Here is...
What are Hamiltonian/Lagrangian Mechanics and how are they different from Newtonian?
What are the benefits to studying them and at what year do they generally teach you this at a university?
What are the maths required for learning them?
Homework Statement
Calculate the Lagrangian of this set up:
Imagine having two ropes: They are both attached to the ceiling and have different lengths. One has length b and the other has length 4b. Say they are hooked to the ceiling a distance 4b apart. Now, the ropes are both hooked to a...
Homework Statement
This isn't a homework problem, per se, in that it's not part of a specific class. That being said, the question I would like help with is finding a Lagrangian density from the vertex factor, $$-ig_a\gamma^{\mu}\gamma^5.$$ This vertex would be identical to the QED vertex...
Homework Statement
This is Exercise 1.19 in Goldstein's Classical Mechanics 2nd edition. Self-study, not for a class.
Two mass points of mass ##m_1## and ##m_2## are connected by a string passing through a hole in a smooth table so that ##m_1## rests on the table and ##m_2## hangs suspended...
Homework Statement
A wheel consists of a circular uniform disk with a circular hole in it. The disc is
of radius R and mass per unit area ρ. The hole is of radius ro and an axle of radius ro
passes through it. The centre of the hole is offset radially from the centre of the disk by
ro. The...
Hello everyone!
I have a (supposedly) calculus problem that I just can't seem to figure out. Basically, I'm trying to understand why alternative kinetic energy formulation does not yield the same equations of motion in problem 11 of Goldstein's Classic Mechanics 3 edition.
The text of problem...
Homework Statement
The scenario is a pendulum of length l and mass m2 attached to a mass of m1 which is allowed to slide along the horizontal with no friction. The support mass moves along in the X direction and the pendulum swings through the x-y plane with an angle θ with the vertical. After...
Homework Statement
[/B]
Consider a mass m moving in a frictionless plane that slopes at an angle \alpha with the horizontal.
Write down the Lagrangian \mathcal{L} in terms of coordinates x measured horizontally across the slope, and y,
measured down the slope. (Treat the system as...
Possibly very silly question in QFT. Consider the Lagrangian for a scalar field theory.
A term like
g/φ^2
should be renormalizable on power counting arguments. The mass dimension of g should be
2 (D-1)
where D is the number of space-time dimensions.Does this make sense?
I'm looking for a book that has problems and explanations (not necessarily background theory) about mechanical systems. Consider the picture below for reference.
The idea is I want to get a hold of energy and impulse methods for solving problems like this, eventually the book would have a...
Hi.
I've only ever seen Noether's theorem formulated ond proven in the framework of Lagrangian mechanics. Is it possible to do the same in Newtonian mechanics, essentially only using F=dp/dt ?
The "symmetries" in the usual formulation of the theorem are symmetries of the action with respect to...
Dear all,
If we consider the lagrangian to have both geometric parts (Ricci scalar) and also a field, the action would take the form below:
\begin{equation}
S=\frac{1}{2\kappa}\int{\sqrt{-g} (\ R + \frac{1}{2} g^{\mu\nu} \partial_\mu \phi \partial_\nu \phi -V(\phi)\ )}
\end{equation}
which are...
Hi there,
Over the last couple of weeks, I have been learning about the relativistic description of electromagnetism through Leonard Susskind's Theoretical Minimum lectures, and although I have managed to follow it, there are some parts which I am becoming increasingly confused by, not helped...
Hey I'm trying to follow the derivation given here: http://lampx.tugraz.at/~hadley/ss1/studentpresentations/Bloch08.pdf
Homework Statement
As it says in the pdf: "Based on Noether's theorem construct the energy-momentum tensor for classical electromagnetism from the above Lagrangian. L=-1/4...
I know this has been asked before: "Why is there a negative in the Lagrangian: L = T - V"
I have read the answers and am not happy with them so I tried to formulate my own justification and now ask if anyone could comment on it?
First, I am not happy with those who say "Because it works and...
1.) The Problem Statement:
a.) Find the Lagrangian of a pendulum where the height of the hinge is oscillating in the y direction and is is defined as a function ##y_0=f(t)##
b.) Add a function (a gauge transformation) of the form ##\frac{d F(\theta,t)}{dt}## to the original lagrangian...
Homework Statement
I am asked to find the Hamiltonian of a system with the following Lagrangian:
##L=\frac{m}{2}[l^2\dot\theta^2+\dot{\tilde{y}}^2+2l\dot{\tilde{y}}\dot{\theta}\sin{\theta}]-mg[\tilde{y}-l\cos{\theta}]##
Homework Equations
##H = \dot{q_i}\frac{\partial L}{\partial...
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...
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...
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...
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.'...
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...