All Questions
Tagged with dof or degrees-of-freedom
473 questions
4
votes
1
answer
66
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Counting number of equations for Rarita-Schwinger field (in Supergravity textbook)
I am reading the book "Supergravity" by Freedman and van Proeyen (2012). On page 96, they are talking about the equation of motion of massless vector-spinor field (the spinor index is ...
- 542
3
votes
1
answer
442
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Degrees of freedom in Gaussian Normal Coordinates in GR
I'm learning about GR and have been wondering about something. At any point, we can define Gaussian Normal Coordinates which are orthonormal and approximately flat (first derivative along all axes is ...
2
votes
0
answers
58
views
Degree of freedom and Grubler formula
I am attempting to apply the Grubler formula (which can be found here: https://learnmech.com/how-to-calculate-degree-of-freedom-of/) to determine the number of degree of freedom, but it does not seem ...
- 197
0
votes
1
answer
758
views
Number of degrees of freedom for a gaseous mixture
I came across the formula to find the number of degrees of freedom in a gaseous mixture which is as follows:
$$f_\mathrm{mix}
=\frac{\sum n_if_i}{\sum n_i}$$
Now it has been mentioned in this lecture ...
1
vote
2
answers
285
views
What is the independent variable in electromagnetism?
As we know, In a circuit, simple or complex, electric fields created by surface charges move electrons which creates current which creates magnetic field which can be coupled to other lines and induce ...
- 13
5
votes
3
answers
857
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Doubt in Arnold's "Mathematical Methods of Classical Mechanics", Chapter 2
My question is about Arnold's book "Mathematical Methods of Classical Mechanics", chapter 2, section B (pg. 16).
He talks about systems with one degree of freedom, i.e. systems described by $...
- 165
1
vote
1
answer
95
views
Does off-shell graviton in 3+1D still have two degree of freedom?
In general relativity, on-shell spin 2 graviton has 2 degree of freedom in 3+1D due to gauge symmetry, which is because of einstein equation, however, for off-shell graviton, does it still have 2 ...
- 547
1
vote
1
answer
428
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Why is the heat capacity of water $9R$ and not $6R$?
From the equipartition theorem, the relationship between energy and temperature in a substance is $U=\frac{NRT}{2}$ for $N$ quadratic degrees of freedom associated with a particle of that substance. ...
- 21
1
vote
0
answers
110
views
Residual gauge freedom and complete residual gauge fixing in lorenz gauge
What I understand after reading all answers from physics stack exchange related to residual gauge freedom and complete residual gauge fixing are as follows;
The gauge transformation is:
$A'_{\mu}$=$A_{...
1
vote
0
answers
151
views
What are non-propagating fields?
I have read at different places that in 3 spacetime dimensions, there are NO propagating gravitational degrees of freedom. This seems to imply that we have only "non-propagating" degrees of ...
- 542
2
votes
0
answers
63
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$R_\xi$ gauge and degrees of freedom counting
In the standard classical Maxwell theory, we use the following arguments to claim that there are only two propagating degrees of freedom
$A_\mu$ has 4 components
$A_0$ is non-dynamical (-1)
$\...
- 681
0
votes
1
answer
70
views
Elastic collisions and internal degrees of freedom
As I was considering elastic collisions today a question popped into my head. Do elastic collisions imply that there are no internal degrees of freedom in the colliding objects which couple ...
- 183
4
votes
1
answer
204
views
How many independent equations are contained in $R_{rsmn}=0$ in consideration of the Bianchi identity?
In $d$ dimensions, how many independent equations are contained in $R_{rsmn}=0$ in consideration of the Bianchi identity $\nabla_{[a}R_{bc]de}=0$?
This discussion reveals the independent equations ...
- 117
1
vote
1
answer
316
views
Why do systems of $n$ coupled oscillators have $n$ normal modes?
Consider a linear system of $n$ differential equations with constant coefficients corresponding to a physical scenario where I have $n$ coupled oscillators (like $n$ masses attached by springs in ...
- 249
1
vote
2
answers
461
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How does a field $\phi(x,t)$ have infinite degrees of freedom and why are its inputs labels not variables?
Consider a classical Lagrangian $L(q, \dot{q})$, which by definition has a discrete number of degrees of freedom. Now suppose we have a quantum field (or any field) which we denote by $\phi(x,t)$. It ...
- 3,992
1
vote
1
answer
129
views
How to Conceptually Understand Long Wavelength Fluctuations?
I have been trying to conceptually understand long-wavelength fluctuations of degrees of freedom, and I have been reading this (RG) to do so. I understand was it means for a degree of freedom to ...
- 129
2
votes
1
answer
229
views
What do we mean by "Degrees of Freedom" when we Talk about the electromagentic field?
For point-like particles, the term "degree of freedom" seems rather clear: It's the number of independent coordinate functions $q_i(t)$ that we need to specify to completely describe the ...
- 6,980
2
votes
0
answers
90
views
Degrees of Freedom in the Newman-Penrose Formalism
In the Newman-Penrose formalism one encodes the ten degrees of freedom of the Weyl tensor $C_{\alpha\beta\mu\nu}$ in the five complex scalar potentials $\Psi_0$, $\Psi_1$, $\Psi_2$, $\Psi_3$ and $\...
- 4,737
2
votes
1
answer
130
views
Extra degrees of freedom in toy spontaneous symmetry breaking model?
Consider a Lagrangian with a real scalar field $\varphi$ and massless vector field $A_\mu$ with field strength $F_{\mu\nu}$,
$$\mathcal{L} = -\frac{1}{2}\left(\partial\varphi\right)^2 - \frac{1}{4}F_{\...
- 747
0
votes
1
answer
384
views
What are the properties of metric tensor? [duplicate]
It's frequently said that graviton has spin-2, so its wave function should have $5$ independent components. The metric tensor has $n^2=16$ components, but it obeys the following property:
\begin{...
- 935
0
votes
2
answers
217
views
Dynamics: why do physicists include derivatives like $\dot{\theta}$ in the state space for a system like a pendulum?
I come from statistics, so my experience with physics is spotty, especially on some simple stuff. I have been working on some applications related to control theory lately, and was looking at some ...
- 181
2
votes
2
answers
451
views
Why don't we use the "degree of freedom" as a factor in the ideal gas equation?
For an adiabatic process, the ideal gas follows the equation
$$ PV^{\gamma}= constant$$
The equation above implies that the pressure of an ideal gas (under adiabatic process) depends on the "...
- 8,476
0
votes
1
answer
529
views
Proca equation gauge conditions
In massive case without any gauge conditions proca equation can be written as
$\partial_\nu(\partial^\nu A^\mu- \partial^\mu A^\nu)+\left(\frac{mc}{\hbar}\right)^2 A^\mu=0$
Since $A_\mu$ is a $n$-...
- 935
1
vote
0
answers
88
views
How to calculate degrees of freedom?
Background
I am trying to run optimizations on a multilink (car-) suspension. That is each link is defined by two points, one on the vehicles body, one on the wheel mount. There are 5 links in total, ...
- 111
2
votes
1
answer
961
views
Number of Independent Components of Levi-Civita Christoffel Symbol
Can anybody explain why Levi-Civita Christoffel symbol in general $N$ dimensional space have $\frac{N^2(N+1)}{2}$ independent components?
I have read that in $N$-dimensional space, metric tensor has ...
- 23
1
vote
1
answer
161
views
How to know if the vibration system requires one degree of freedom or two? and how to pick the right coordinate to describe the movement?
I want to know a trick that helps me understand oscillatory systems and how to pick the correct general coordinates that describe the movement, I tried everything but I still can't get the solution ...
- 21
0
votes
1
answer
1k
views
Is there a way to calculate the number of degrees of freedom of water?
Say we have liquid water. We are given specific heat of water $C=4.2kJ(kg*K)$, a number of molecules in a mol $N_A=6*10^{23}$. The atomic weight of water is $18g/mol$, and the Boltzmann's constant is $...
0
votes
1
answer
92
views
Does the degree of freedom change with speed for massive particle?
There are 2 degrees of freedom for a photon. But how many are there for massive particles and will this change with speed?
- 29
2
votes
2
answers
737
views
Independent variables in thermodynamics
When we are dealing with a gaseous thermodynamic system, in books it's written that state of the system can be described by only two independent variables from the three $(p,V,T ) $. But it's not ...
- 71
0
votes
0
answers
73
views
How many DOF does this system have?
I saw the problem above and thought it would be fun to solve it using lagrangians. However, in order to do this, one has to know the DOF of the system. And this is where it gets confusing for me. ...
- 334
0
votes
1
answer
160
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State of the art on Modified gravity : going beyond the 2nd order differential equations, diffeomorphism invariance breaking, extra degrees of freedom
I am going to do a state of the art on Modified gravity models. I have found a talk that presents the problematic. In particular, it is said the following things :
Modifying General Relativity
How to ...
user87745
1
vote
1
answer
452
views
What is the degrees of freedom (Lagrange equation) of two connected spool rolling down two inclines?
I'm quite confused as to how to use the Lagrange equation [second type] in a system which features a spool rolling down an incline. I think this particular example is quite representative of what is ...
2
votes
1
answer
411
views
Number of Degrees of Freedom of a Rigid Body System - Proof
Let us define the number of degrees of freedom of a material system as
the number of scalar parameters needed to know the position of each particle of the system with respect to any inertial frame of ...
- 402
5
votes
1
answer
644
views
What is a propagating degree of freedom?
Given a gauge field theory, the various fields involved have (pointwise) degrees of freedom.
For instance, if I consider the gauge theory of gravity in four dimensions, I have a set of tetrads $\{ e_\...
- 16.7k
2
votes
1
answer
229
views
The effect of the non-existense of longitudinal polarisation mode of the photon on equipartition theorem
Massless vector bosons like photons only have 2 independent polarisation degrees, unlike massive vector bosons. For a spin 1 boson with mass $\mu$ and with $k^λ = (ω, 0, 0, k)$ the longitudinal mode ...
- 1,610
0
votes
1
answer
899
views
Degrees of freedom for Constrained Motion
I'm starting to learn about Degrees of freedom, and the idea of 'constrained motion' seems strange to me, surely any particle with a predefined path is 'constrained' in its motion, We also had ...
- 283
0
votes
1
answer
1k
views
How much degree of freedom of a rigid body in $N$-dimensional space?
Well I have the answer it is
$\frac{N(N+1)}{2}$ but what the procedure to derive it .
I tried this.
1).I have $N$ number of translation freedom.
To calculate the number of rotational freedom I tried ...
- 41
4
votes
2
answers
519
views
How many independent equations are contained in the Bianchi identity?
In consideration of the various symmetries of the Riemann curvature tensor, how many independent equations are contained in the Bianchi identity $R_{rsmn|t}+R_{rsnt|m}+R_{rstm|n}=0$ ?
Symmetries of ...
- 117
3
votes
2
answers
373
views
How many field components are there in vector-spinor field?
I am trying to find out the degrees of freedom of the vector-spinor field ($s=3/2$). The degrees of freedom are given by $N=\frac{1}{2}\left(N_{F}-N_{C}\right)$ for this spin where $N_F$ is the number ...
- 310
1
vote
1
answer
223
views
Why does the Lorenz gauge $\partial_\mu A^\mu=0$ eliminate the spin-0 part of $A^\mu$?
Schwartz' QFT textbook states on page 116 that:
Since $\partial_\mu A^\mu=0$ is a Lorentz-invariant condition, it has to remove a complete representation, which with one degree of freedom can only be ...
- 2,678
4
votes
1
answer
453
views
Why are $p$ and $q$ independent variables in Hamiltonian formalism?
Let's say we have $(q, \dot{q})$ as the generalised coordinate and generalised velocity. If we have a Lagrangian given by
$$L=Aq\dot{q}+Bq$$
where $A$ and $B$ are constants that give the right units ...
- 4,276
1
vote
3
answers
210
views
Why should degrees of freedom be independent?
To define the position of a system of $N$ particles in space, it is necessary to specify $N$ radius vectors, i.e. $3N$ co-ordinates. The number of independent quantities which must be specified in ...
- 88
0
votes
1
answer
39
views
Is $n=1$ (degrees of freedom) for monatomic?
In $PV=nRT$, $n$ is degrees of freedom. While in $PV=Nk_BT$, N is number of moles in a molecule. So value of $n$ is $3$, $5$ and $6$ for monatomic, diatomic and polyatomic respectively. But in the ...
- 17
3
votes
2
answers
658
views
Why there are so many spinor components in higher dimensions if the number of degrees of freedom is only 2?
In the book of Freedman & van Proeyen on Supergravity a table (3.2) can be found which shows for dimensions from 2-11 the number of components of Majorana spinors.
For instance in 4 dimensions we ...
- 10.2k
1
vote
1
answer
183
views
How many real degrees of freedom do Euclidean spinors have in 3D Euclidean space?
For the Euclidean case, we have that spinors transform under the $\mathbf{2}$ representation of (the double cover of) $SO(3,\mathbb{R})$. It would seem to me that since vectors live in $\mathbf{3}$, ...
- 1,142
3
votes
4
answers
2k
views
Why is there a $1/2$ in the definition of energy per degree of freedom $E=(1/2)kT$?
I was looking for an authoritative definition of Boltzmann's Constant. That led me to this discussion on NIST's site: Kelvin: Thermodynamic Temperature
Thus, internal energy and temperature are ...
- 2,052
1
vote
3
answers
155
views
Do angular equivalents of linear equations in physics reveal extra information?
First of all, This question is completely based on intuition and some concepts of mathematics. I have been thinking about this now for 5 months and haven't figured it out yet. I am beginner in physics ...
- 493
2
votes
2
answers
220
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"One-parameter" gauge transformation
In my advanced classical physics course, it was stated that the electromagnetic field strength tensor $F_{\mu\nu} = \partial_{\nu}A_{\mu} - \partial_{\mu}A_{\nu}$ is invariant under "one-...
- 234
1
vote
0
answers
263
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The role of the Weyl-tensor in gravitation
In his book "Road to Reality" section 19.7 Roger Penrose asks the question:
What is the appropiate analogue of the Maxwell field tensor $F_{ab}$ describing the gravitational degrees of ...
- 10.2k
4
votes
1
answer
112
views
Do physical systems have intrinsic degrees of freedom that are independent of its representation?
Considering just the Newtonian case, suppose we have a system described by $n$ canonical position-momentum pairs, $(p_1,q_1),\dots,(p_n,q_n)$, and a Hamiltonian $H$. If we "scrubbed" all the ...
- 111