All Questions
Tagged with dof or degrees-of-freedom
473 questions
18
votes
1
answer
4k
views
Gauge fixing and degrees of freedom
Today, my friend (@Will) posed a very intriguing question -
Consider a complex scalar field theory with a $U(1)$ gauge field $(A_\mu, \phi, \phi^*)$. The idea of gauge freedom is that two solutions ...
- 27.7k
14
votes
2
answers
4k
views
Counting degrees of freedom for gravitational waves as a gauge field
Sean Carroll has a new popularization about the Higgs, The Particle at the End of the Universe. Carroll is a relativist, and I enjoyed seeing how he presented the four forces of nature synoptically, ...
user4552
4
votes
1
answer
302
views
How exactly are the degrees of freedom seen by a falling into a black hole observer related to the ones seen by a staying outside observer?
This is some kind of a follow up of this nicely to the point answer to a provocative (but nevertheless upvoted!) question, about the legitimacy of black hole physics. The answer mentions, that the ...
- 9,691
2
votes
1
answer
1k
views
A different proof for 6 degrees of freedom
I want a different proof of 6 degrees of freedom of a solid object made of $N$ particles. I am thinking along these lines:
The definition of rigid body is
$$\left\lvert \vec{r_i}-\vec{r_j} \right\...
- 1,398
4
votes
1
answer
1k
views
Phase Space dimension of Lorenz Strange Attractor
It is often discussed in 3 spatial dimensions and the need for third dimension to prevent self intersection is mentioned. But shouldn't the phase space of the Lorenz system be 6 dimensional, i.e., the ...
- 1,682
4
votes
2
answers
16k
views
The number of degrees of freedom of a monatomic gas
Suppose that I have a monatomic gas sample consisting of $N$ atoms (e.g., $N$ argon atoms); thus there are no vibrations or rotations. How many degrees of freedom does the system have?
Does the ...
- 1,163
3
votes
2
answers
35k
views
Modeling a two-mass, spring, damper system
I'm trying to model a system with two masses, two springs, two dampers, and one applied force using transfer functions. I'll then be inputting it into Simulink.
The system looks like this but there ...
- 85
3
votes
1
answer
1k
views
Propagating degrees of freedom of graviton
What is the best way to see that the number of propagating degrees of freedom or gravitons in 3 dimensions is $0$ ? By graviton I mean the metric and NOT some topologically massive graviton that one ...
- 73
4
votes
1
answer
816
views
Degrees of freedom in the infinite momentum frame
Lenny Susskind explains in this video at about 40min, as an extended object (for example a relativistic string) is boosted to the infinite momentum frame (sometimes called light cone frame), it has no ...
- 9,691
16
votes
7
answers
142k
views
How to deduce $E=(3/2)kT$?
It says in my course notes for undergraduate environmental physics that a particle has so-called "kinetic energy"
$$E=\frac{3}{2}kT=\frac{1}{2}mv^{2}$$
Where does this formula come from? What is $k$?...
- 1,053
3
votes
2
answers
916
views
Path integral on matrix model
I was looking at a 0-dimensional matrix model, where the variables are $N\cdot N$ Hermitean matrices. It had a gauge symmetry, e.g. $U(N)$. And in the path integral, the Faddeev-Popov trick was used. ...
- 461
4
votes
2
answers
379
views
Dark matter: degrees of freedom
I'm afraid this question could sound a little too vague. I don't even know if dark matter (DM) can be genuinely described by quantum field theory, or if quantum field theory should be somehow "...
- 1,544
13
votes
1
answer
2k
views
Clarification on "central charge equals number of degrees of freedom"
It's often stated that the central charge c of a CFT counts the degrees of freedom: it adds up when stacking different fields, decreases as you integrate out UV dof from one fixed point to another, ...
- 461
4
votes
2
answers
7k
views
degree of freedom of a rigid body 5 or 6?
I'm confused here. I have a three particle (rigid) system. What would be the degree of freedom? I found out five. 3 coordinates for center of mass and 2 for describing orientation.
But we have only ...
- 185
6
votes
2
answers
2k
views
Counting degrees of freedom in presence of constraints
In a $N$ dimensional phase space if I have $M$ 1st class and $S$ 2nd class constraints, then I have $N-2M-S$ degrees of freedom in phase space. How can I calculate the degrees of freedom in ...
- 511
10
votes
3
answers
5k
views
Counting degrees of freedom of gauge bosons
Gauge bosons are represented by $A_{\mu}$, where $\mu = 0,1,2,3$. So in general there are 4 degrees of freedom. But in reality, a photon (gauge boson) has two degrees of freedom (two polarization ...
- 867
9
votes
4
answers
4k
views
The number of independent variables in the Lagrangian and Hamiltonian methods in Classical Mechanics
It's told in Landau - Classical Mechanics, that in the Hamiltonian method, generalized coordinates $q_j$ and generalized momenta $p_j$ are independent variables of a mechanical system. Anyway, in the ...
- 757
0
votes
1
answer
198
views
Equipartition theorem for flowing gas
If an ideal gas is flowing with a velocity $v$, how is the equipartition theorem applied.
Normally, we can say that $\frac{1}{2}mv_{x,rms}^2=\frac{1}{2}k_BT$. We can do the same thing for $v_y$ &...
- 19.1k
15
votes
7
answers
20k
views
Degree of freedom paradox for a rigid body
Suppose we consider a rigid body, which has $N$ particles. Then the number of degrees of freedom is $3N - (\mbox{# of constraints})$.
As the distance between any two points in a rigid body is fixed, ...
- 4,932
89
votes
7
answers
14k
views
Do Maxwell's Equations overdetermine the electric and magnetic fields?
Maxwell's equations specify two vector and two scalar (differential) equations. That implies 8 components in the equations. But between vector fields $\vec{E}=(E_x,E_y,E_z)$ and $\vec{B}=(B_x,B_y,B_z)$...
- 9,785
3
votes
1
answer
1k
views
Violations of Dulong-Petit rule as an upper limit to heat capacity
Does any known substance have a heat capacity at constant volume ($C_V$) per mole of atoms greater than $3k_B$ ~ 24.94 J/(mol K)?
In order to count, the substance must actually be made of atoms, that ...
- 7,787
21
votes
1
answer
5k
views
What is the definition of how to count degrees of freedom?
This question resulted, rather as by-product, the discussion on how to count degrees of freedom (DOF). I extend that question here:
Are necessary1 derivatives such as velocities counted as individual ...
- 6,850
7
votes
3
answers
2k
views
What does it mean, when one says that system has $N$ constants of motion?
For example for an isolated system the energy $E$ is conserved. But then any function of energy, (like $E^2,\sin E,\frac{ln|E|}{E^{42}}$ e.t.c.)
is conserved too. Therefore one can make up infinitely ...
- 20.2k