All Questions
Tagged with dof or degrees-of-freedom
473 questions
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Counting degrees of freedom without fixing the gauge?
In electrodynamics, the current-current interaction in the momentum space is described by
$$p^2 A_\mu J^\mu = J_\mu J^\mu \, ,$$
where $J$ denotes an arbitrary external current. Since photon-...
user20250
1
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1
answer
213
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Independent Quantities in Canonical Transformations
I was looking through some lecture slides and I came across this page:
I understand that the equation highlighted blue (top right corner) is obtained from the Principle of Least Action. Given a ...
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1
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Gauge theory and eliminating unphysical degrees of freedom
In free space we can express Maxwell's equations as
\begin{align}
\varepsilon^{abcd}\partial_bF_{cd}=0 ~~\text{ and }~~ \partial_aF^{ab}=0 \tag{1}
\end{align}
where $F^{ab}=-F^{ba}$. The most general ...
- 609
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0
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452
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Are there fundamental differences between finite and infinite systems?
Most sources on classical field theory introduce classical fields as a limit of a system with $N$ particles constrained in some way in a lattice where a continuum limit involving $N$, lattice size and ...
- 1,774
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2
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Rotation About Axis of Diatomic Molecule [duplicate]
While counting the degrees of freedom of a diatomic molecule, We neglect the rotation about the axis of the molecule stating the reason that it's energy is negligible. I agree with this reasoning, and ...
- 1,108
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3
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How many dimensions are there in the electric field?
I am not a physicist. I am buying some polariser for my camera. Circular polariser intrigues me. Basically you pass light through a linear polariser, then through a waveplate, you get circular ...
- 41
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2
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176
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Amplitudes of Fourier expansion of a vector as the generalized coordinates
On page 14, under the subtopic "Constraints", when discussing about generalized coordinates, Goldstein says the following:
All sorts of quantities may be impressed to serve as generalized ...
- 459
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0
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Is there an equivalency between fluctuation and effective degrees of freedom?
Is it possible to use the fluctuation-dissipation theorem to introduce a new "fictitious" degree of freedom (d.o.f) for an existing coordinate/d.o.f which fluctuates a lot?
Consider a non ...
- 3,406
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Propagating degrees of freedom of gravitational field
I'm following Carroll's Spacetime and Geometry, chapter on Linearized Gravity, pag. 282. He splits up the metric perturbation in scalar, vector and tensor components, writes the Einstein tensor with ...
- 633
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3
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1k
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When is time a degree of freedom?
When is time a degree of freedom? I was doing a problem, and made a mistake and said that
$\vec{\nabla} \cdot \vec{F}(\vec{r},t) = \frac{\partial F(\vec{r},t)}{\partial x} + \frac{\partial F(\vec{r},...
- 63
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Goldstone Theorem and Degree of Freedom Counting
When a continuous global symmetry is broken, we lose one degree of freedom.
We also gain a massless spin 0 boson, called a Goldstone boson.
We then say the number of degrees of freedom is the same.
...
- 1,345
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2
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657
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Degrees of freedom of this tensor
I would like to know the degrees of freedom (dof) of the tensor $f$:
\begin{equation}
f_{\mu \nu} = \partial_\mu \xi_\nu+\partial_\nu \xi_\mu
\end{equation}
in 4 dimensions using the common index ...
- 655
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1
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Dimension of motions of an atom vs a molecule wrt energy/heat calculation
I had just started a course on Climate change and it helped me refresh the notion of heat.
Heat as given by the equation,
$E = \frac 1 2 kT$
is the amount of energy of a particle at a given ...
- 153
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3
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2k
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Question about physical degree of freedom in Maxwell Theory: Why Coulomb gauge can fix all redundant degree of freedom
Given $4$-potential $A^\mu(x)=(\phi(x),\mathbf{A}(x))$, the vacuum Maxwell equations:
$$\nabla^2\phi+\frac{\partial}{\partial t}(\nabla\cdot \mathbf{A} )=0$$
$$\nabla^2 \mathbf{A} -\frac{\partial^2 \...
user153663
2
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1
answer
2k
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Degrees of freedom of neutrinos
In cosmology, in $g_{eff}$, the number of relativistic degrees of freedom, one finds that the contribution of neutrinos is 2 ($\frac{7}{8}\times 2$ more precisely) but what is due this 2 factor to ? ...
- 157
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How many degrees of freedom for the spin 1/2?
I count four but most of the documentation I read, says just one.
1) One degree of freedom for the spin measurement outcome, either up or down.
3) three degrees of freedom for the unit quaternion ...
- 1,558
4
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1
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888
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Relation between dimension of Hilbert space and degree of freedom
According to the answer by joshphysics, in the first example he gave, he mentioned that the state space of 1D free particle is isomorphic to that of 3D. My understanding of this is: both spaces are ...
- 61
3
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3
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Degrees Of Freedom of Spring-mass system
Consider 2 masses $M_1$ and $M_2$ connected with a spring of stiffness $k$, resting on a smooth frictionless surface. Now, each mass has its own 1 DOF along the $x$-axis. And the system has 1 ...
- 343
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1
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Physical degrees of freedom of the Electromagnetic field
As I understand it, the classical source-free electric, $\mathbf{E}$ and magnetic, $\mathbf{B}$ wave equations are solved by solutions for the electric and magnetic fields of the following form: $$\...
- 3,267
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1
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199
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Degree of freedom of a BEC
I would like to know how many degrees of freedom an atomic gas has. What about the Bose-Einstein condensation from that gas?
- 196
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154
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Kinetic energy of electron in Quantum well
I heard that electrons in bulk semiconductor have 3 degree of freedom so they have 3 dimensional kinetic energy component, but Whenever an electron from bulk material captured by a quantum well (where ...
- 21
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259
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Specific heat capacity vs KE gain of particles
To increase the temperature of 1kg of water by 1C you need 4200J of energy. However, the KE gain is only $\frac{3}{2} k_B \Delta T \cdot 6.02\cdot 10^{23} \cdot \frac{1000}{18} = 692.3$J. Where does ...
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A rod is moving in space and an insect is on it. How many degrees of freedom does the insect have?
Is the answer 7? The number of degrees of freedom of a system can be viewed as the minimum number of coordinates required to specify a configuration. Applying this definition, we have:
For a single ...
- 21
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Why does water have 9 degrees of freedom and that too all vibrational?
How does water has 9 degrees of freedom? If it can vibrate about all three atoms then why can't a diatomic molecule also have 2 instead of 1 possible vibrations?
I haven't studied quantum mechanics ...
- 644
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321
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Rolling ball and number of generalized co-ordinates
Consider a sphere constrained to roll on a rough surface.
Book says it requires 5 generalized co-ordinates to specify sphere's configuration: 2 for its centre of mass and 3 for its orientation.
I ...
- 1,034
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201
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Number of degrees of fredom in diatomic molecule model
In the book of Salinas the author says in chapter The Ideal Quantum Gas he says and I quote
The classical models of a gas of diatomic molecules (a rigid rotator in three dimensions, or a rotator ...
user78217
5
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1
answer
3k
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How many degrees of freedom does a spring have?
I'm currently learning about thermodynamics and heat capacities. We were told that the theoretical molar heat capacities of all solids should be $3R$. I was told this is because there are 6 different ...
- 1,288
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656
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Holonomic constraints and degrees of freedom
Wikipedia and other sources define holonomic constraints as a function
$$ f(\vec{r}_1, \ldots, \vec{r}_N, t) \equiv 0, $$
and says the number of degrees of freedom in a system is reduced by the ...
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814
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Number of degrees of freedom for the 2D diatomic molecule
How many degrees of freedom does a diatomic molecule has in two dimension?
- 2,068
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273
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Why is position considered a label in classical field theory?
I am currently researching into classical field theories and have come across the idea of a position being considered a label in field theory, rather than a dynamic variable.
I am not sure why this ...
- 1,720
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If I evaluate degree of freedom and got some number $n$, then how can I know what are those $n$ independent coordinates?
Using $3N-f=d$ we can evaluate the degree of freedom or independent coordinates of a system.
But how can we know which coordinates are actually independent?
(Here $n$ = number of particles, $f$ = ...
- 123
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278
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Noether's theorem, dimension of the group of symmetry and dimension of conserved quantity
I previously asked on Mathematics Stack Exchange about the relation between $\bigwedge^2(\Bbb R^n)$ and $\text{SO}(n)$. See this link to the post. I noticed that they have equal dimensions, that I ...
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71
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Are the degrees of freedom of a system decreased when the system is subjected to a non-holonomic constraint?
Are the degrees of freedom of a system decreased when the system is subjected to a non-holonomic constraint?
I know when a system is subjected to a holonomic constraint then its degrees of freedom ...
- 369
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535
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Degrees of freedom in General Relativity
A way one counts degrees of freedom(i.e. independent entries of the metric tensor ) in General Relativity is this:
one goes to the linearized version, vacuum solution, and he sees that there are two ...
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Residual Gauge Freedom [closed]
How are we still left with one Residual Gauge Freedom in the choice of Electromagnetic Potential after having already exploited the Gauge Freedom once.
As is mentioned in Halzen and Martin Section 6.9....
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668
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In 2D machines, why does higher pair joints deduct 1 degree of freedom?
I have been taught that higher pair joints (e.g. gears, cams, rollers) deduct 1 degree of freedom due to the fact that they still allow two motions
translation along the tangent surface
rotation ...
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816
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No of independent components of Riemann tensor in $D=4$
Using symmetric property between two indices and antisymmetric property between pair of indices we have 21 independent components. Also, using one cyclic sum condition over any three indices we ...
- 305
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2k
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How many degrees of freedom has a particle in a box?
How many degrees of freedom has a particle in a rectangular box? Thing that confuses me is that box bounds the movement of the particle but to me it still seems like particle has 3 degrees of freedom.
...
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Degree of Freedom of an $SU(n)$ Group
I've been thinking about the DOF of the $SU(n)$ group. I first consider the DOF of a unitary matrix. See if I get this right:
Any unitary matrix can be written in the form of $e^{iH}$, where $H$ is a ...
- 1,171
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1
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Reduction of degrees of freedom in hamiltonian mechanics
How can the presence of a constant of motion in a Hamiltonian system reduce the number of degrees of freedom of the system?
The thing I don't understand is: the presence of a constant of motion ...
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998
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What is the meaning of each peak of the frequency spectrum?
I have a system with 3DOF. Its mass, stiffness and damping matrix are respectively:
$$
M =
\begin{bmatrix}
60 & 23.5 & 0\\
23.5 & 15.996 & 0\\
0 & 0 & 3.507
\end{bmatrix}
$$...
- 15
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1
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276
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Why isn't there two Higgs bosons?
As I understand, in the SM Lagrangian the Higgs field, $\phi$ is actually a column vector of two complex scalar fields: $\phi_1+i\phi_2$ and $\phi_3+i\phi_4$. Shouldn't there be a particle ...
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12k
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Why do molecules have $3N-5$ or $3N-6$ degrees of freedom?
In linear molecule, it has $3N-5$ degree of freedom in vibration mode and $3N-6$ in non-linear molecule.
I can get idea about $5$ and $6$ which is related to translation and rotation but I cannot ...
- 13
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1
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What is the degree of freedom of pure rolling motion?
A cylindrical body is pure rolling, what will be the degree of freedom for it? I am confused between 2 and 1 if slipping occurs than it has 2 but in pure rolling there's no slipping so what will it ...
- 11
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468
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Integrals of motion for a free particle
I'm struggling to understand the argument on p. 13 in Landau and Lifshitz that for a system with $N$ degrees of freedom there must be $2N-1$ integrals of motion.
In particular, I can't understand ...
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2
answers
511
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is curvilinear motion really a type of linear motion?
Let us consider any arbitrary curve except a straight line in the Cartesian coordinates. From the perspective of the particle tracing the curve the motion can only be linear. But from the point of ...
- 13
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2k
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Number of degrees of freedom in the Standard Model Lagrangian
Consider a Lagrangian $L$ which depends on a number of fields
$F_1$, $\cdots$, $F_N$ and their (spacetime) derivatives. Each of those fields $F_n$ is valued in $\mathbb{R}^{k_n}$.
Is the Standard ...
- 115
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Degrees of freedom of rolling coin
I gave a mental ability test yesterday in which this question was asked.
A rolling coin on a flat surface has how many degrees of freedom?
I read about degrees of freedom but I haven't had much ...
- 123
1
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1
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516
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How is no-conspiracy theory compatible with determinism? [closed]
Bell's theorem states that any physical theory that incorporates local realism and the no-conspiracy assumption cannot reproduce all the predictions of quantum mechanical theory.
Hence, we cannot ...
- 141
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What causes the universe to manifest a given value upon measurement in super-deterministic theory? [closed]
Bell's inequalities show that we have to give up freedom or local realism. If we give up freedom, we have super-determinism, if we give up local realism, we have free-will.
In super-deterministic ...
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