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Questions tagged [degrees-of-freedom]

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Query about working out the Specific heat ratio of a gas

The specific heat ratio for $\rm CO_2$ at room temperature is $1.28$ according to my tables. Since $C_V= \left.\frac{\partial U}{\partial T}\right|_V$ and $C_P=\left.\frac{\partial U}{\partial T}\...
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1answer
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How many degrees of freedom for $\rm N_2O_2$?

From my reading, I have understood examples a diatomic molecule to be $\rm N_2$ or $\rm O_2$, however, the below seems to suggest that $\rm N_2O_2$ is also diatomic. Is this correct and can someone ...
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Why don't asymmetric molecular orbitals and lone pairs in linear molecules lead to an additional degree of rotational freedom?

For example, in CO2, the molecule is linear and thus rotation about the intermolecular axis leads to an identical molecule. But if you consider the pi molecular orbitals, which are radially ...
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1answer
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Is there only one vacuum solution of the Einstein equations?

I am thinking about this: A vacuum solution means vanishing Ricci tensor. The Ricci tensor is a contraction of the Riemann, which itself involves contains second derivatives of the metric. Thus they ...
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How to determine whether a set of coordinates are independent and sufficient to determine the system completely?

In Analytical mechanics, when we formulate our principles, in general, it is assumed that we start with a cartesian coordinate system, and then find some generalised coordinates $q_j$s they are all ...
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4answers
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Question about holonomic constraints

Goldstein says that when a system of $N$ particles is subject to $k$ holonomic constraints, the positions $\mathbf{r}_1, \dots, \mathbf{r}_N$ can be parameterized by $3N - k$ independent coordinates $...
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2answers
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Why the notion of degree of freedom is correct?

The intuitional definition for number of degrees of freedom is following: it is the minimal amount of numbers which allows us to describe the system's configuration correctly. For example, for dot ...
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2answers
125 views

Why doesn't a monoatomic particle have 6 degrees of freedom? [duplicate]

A monatomic particle can move in three directions(X,Y,Z). So the number of degrees of freedom(DOF) for translation is 3. The particle can also rotate on three axes. So the number of DOF for rotaion is ...
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Relation between spin degrees of freedom and the dimensions of Hilbert space

I came across a question which reads "Suppose the spin degree of freedom of two particles (nonzero rest mass and nonzero spin) is described completely by a Hilbert space of dimension twenty one. ...
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2answers
68 views

Duality transformations, such as between a massless scalar field and the Kalb-Ramond field

There is a kind of duality transformations between antisymmetric tensor fields which I learnt from a series of lectures by Gia Dvali on quantum field theory. I have not been able to locate a source ...
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1answer
117 views

How many degrees of freedom in a massless $2$-form field?

Consider the Kalb-Ramond field $B_{\mu\nu}$ which is basically a massless $2$-form field with the Lagrangian $$ \mathcal L = \frac{1}{2}P_{\alpha\mu\nu}P^{\alpha\mu\nu}\,, $$ where $P_{\alpha\mu\nu} \...
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Computing the spin degrees of freedom for a massless particle in $D$ dimensions

According to the paper A Lagrangian formulation of the classical and quantum dynamics of spinning particles, a relativistic spinless particle in $D$ spacetime dimensions can be described by the ...
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2answers
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Degrees of freedom of gas molecules

What is the degrees of freedom of a three dimensional polyatomic molecule when only one vibrational mode is excited?
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A problem on degree of freeedom?

[The problem is roughly] Toy “Supermag” makes it possible to construct, among others, polyhedrons — e.g. tetrahedrons, cubes, and many irregular polyhedrons, where the edges of the ...
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What is degree of freedom in thermodynamics? [duplicate]

I have read a lit bit of degree of freedom in classical mechanics and hope to understand as if the number of variable used to describe a system in the configuration space. But in thermodynamics I read ...
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What is the formal definition of Degree of Freedom? [duplicate]

Is the degree of freedom defined in classical mechanics same as the degree of freedom in thermodynamics? If not what is the formal definition of degree of freedom in thermodynamics?
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2answers
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Why does Maxwell's equations $\partial_{\mu} F^{\mu \nu} = 0$ have 3 independent components (DOF) in $D = 4$?

And how can we generalize this to the statement that it has $D-1$ independent components in dimension $D$? I know that $F_{\mu \nu}$ has six independent components (because of antisymmetry), how do ...
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1answer
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Kelvin and kinetic theory of gases

I know that the degree of freedom increase by 2 when the temperature is high and decrease by 2 when the temperature is low. A dumb question here, what temperature is considered as 'high temperature' ...
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Are singularities' behaviour really unpredictable?

If a real/true singularity existed our models and theories would become useless to predict what would happen in that singularity. For example if naked singularities really existed, we could not ...
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43 views

Notion of 'functional degrees of freedom' for the metric function in GR?

I have read through the numerous questions on 'degrees of freedom' in the metric tensor, and won't list them all here. However none of them address my question on 'functional' degrees of freedom in ...
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1answer
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Why is $4=3\oplus 1$? What are propagating modes? Etc

In Schwartz's QFT book, he said that the vector representation of the Lorentz group, $V_\mu$ that is four-dimensional, is the direct sum of two irreducible representations of $SO(3)$: a spin-0 ...
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3answers
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Why does gauge invariance in electrodynamics mean that there are redundant degrees of freedom? [closed]

It is possible to choose different gauges in electrodynamics. I am familiar with two of them: Coulomb gauge and Lorenz gauge. Let us stick to the Coulomb gauge. It sets $$\nabla\cdot\vec{A}=0.$$ The ...
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1answer
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Degrees of freedom in General Relativity and well-posedness of the EFE

I would like to understand what are the degrees of freedom in GR. I have read a few previous posts already, but none of them really help me. Below, I will try to write down the entangled web of ...
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1answer
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Counting degrees of freedom in the Higgs mechanism for different gauges

I am wondering how to count the degrees of freedom (dof) for a massive gauge field in different gauges. I've been reading some other answers, but haven't found a solution yet. I am looking at the ...
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2answers
68 views

Degrees of freedom for diatomic molecules [duplicate]

I have a doubt in understanding about the degrees of freedom (dof) ......as I have learned dof is nothing but the necessary parameters to specify the location and configuration of a system.....if that'...
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1answer
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Angular momentum conservation reduces degree of freedom

In 2 dimention dynamics, if angular momentum is conserved: mr^2(theta dot)=constant, does that mean degree of freedom is reduced from 2 to 1? I think it should since r and theta(although theta dot ...
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2answers
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Why does the lowered Riemann tensor only have 20 independent components for the Schwarzschild metric?

I have seen quite a bit online about how there are only 20 independent components for the (lowered) Riemann tensor $R_{abcd}$ for the Schwarzschild metric. I've been told this follows from the ...
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2answers
359 views

Number of degrees of freedom of a photon

I am learning Quantum Field Theory. There they have shown that, for the four vector $A$, even though it has 4 components, it only has 2 degrees of freedom because the other 2 corresponds to gauge ...
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1answer
256 views

2 Extra Degree of Freedom in Linear Triatomic Molecules?

Ok, there is a bit problem in understanding Degree of Freedom of Linear Molecules specially of Triatomic Linear Molecules. See, the DOF in general is given as $f=3N-k$. Here, N=Number of atoms in a ...
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1answer
110 views

How does the graph of molar heat capacity point towards quantization of motion?

In the graph below, if we consider that the jumps are stepwise for a molecule, even then, how does it point toward quantization of vibrational and rotational motion? The thing it implies is that (...
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2answers
268 views

Degree of freedom in Lagrange's formalism

Degrees of freedom $=3K-N$ where $K$ is number of particles and $N$ is number of constraints. How to find the number of degrees of freedom for a rigid body which has both translation and rotation, ...
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2answers
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Why does $H_2$ have $C_V$=$7/2 R$ at high temperatures, while the total number of degrees of freedom is 6?

The two hydrogen atoms have 6 degrees of freedom in total. Of them, $3$ contribute to translation, $2 $contribute to rotation and $1$ contribute to the vibration. I know that the vibrations motion is ...
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Number and nature of independent variables to descibe a thermodynamic system

In a thermodynamic system which has n ways of doing work, we have in total n+1 vaiables or degrees of freedom to know about the system. However, how many of the n+1 have to be intensive or extensive ...
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Classical theory fails to explain quantization of motions?

I understand everything written here. But the last point, I cannot get, at all. How does it point towards Quantization of the two motions, since the energy change is not sudden, but gradual? And if ...
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1answer
109 views

Number of d.o.f. in massless and massive Maxwell field?

Consider the Maxwell kinetic Lagrangian $$L_{kin}=-\frac{1}{4}(F_{\mu\nu})^2$$ where the field strength is $F_{\mu\nu}=\partial_\mu A_\nu-\partial_\nu A_\mu$. A vector quantity can contain at most 4 ...
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Proof of no. of degrees of freedom for $N$-atom molecule [duplicate]

How can we say that the no. of degrees of freedom for a $N$-atom molecule is $3N$? How to $\mathbb{prove}$ it? I have heard people saying that for each atom, there are 3-independent variables to ...
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The ultimate (SUSY) degrees of freedom and how to test them: particles, strings or something else?

I have been thinking about these question and if I should post it, because I want it to fit the rules of these site. Let's see if I managed it: Are the ultimate degrees of freedom of the subatomic ...
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1answer
78 views

Equipartition of energy and degrees of freedom in Diatomic gas [duplicate]

Suppose we have a gas of $N$ diatomic molecules (ex $O_2$) with one-molecule hamiltonian being: $$\mathcal{H} = \frac{\vec{p}_1^2}{2m}+\frac{\vec{p}_2^2}{2m} + V(r_{rel}) $$ Where $r_{rel}$ is the ...
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Infinite-dimensional Hilbert spaces in QM vs. finite-dimensional Hilbert spaces in quantum gravity?

It seems to me that there are fairly good reasons to assume that quantum theories need to rely in their formulation on infinite-dimensional spaces (cf. Why do we need infinite-dimensional Hilbert ...
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2answers
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Degrees of freedom of a constrained vector

I have to handle with this lagrangian of a real vector $\chi^\mu$ $$ \mathcal{L} = -\frac{1}{4}F_{\mu\nu}^2 + B^\mu \square \chi_\mu + C\, \partial_\mu \chi^\mu + \mathcal{L}_{int} $$ where $B^\mu$ ...
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2answers
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Actual Degree of Freedom of Diatomic Molecule

Ok, I have 2 very different values for degree of freedom(DOF) of diatomic molecules arising due to the difference in the vibrational DOF of the diatomic molecules. According to this DOF wiki page:- ...
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What does “degrees of freedom ” mean in classical mechanics?

The definition I come up with is 3M - N ...where N is the number of constraints. I assume M is the number of distinct points. In what context is it used ? According to Wiki it says "an ...
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202 views

Calculation of number of degrees of freedom of a rigid body

I was reading a paper called Exact calculation of the number of degrees of freedom of a rigid body constituted by n particles where a method is suggested on how to calculate the degrees of freedom of ...
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3answers
303 views

Variation of degrees of freedom with temperature

I read in my friend's thermodynamics notes that polyatomic molecules have a different degree of freedom at high temperatures (viz. non-linear triatomic molecules have 9 dof but only 7 are accessible ...
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1answer
135 views

Understanding the degrees of freedom counting argument for complex amplitudes in quantum mechanics

In these lecture notes, Scott Aaronson gives three arguments for why complex Hilbert spaces are more natural than real ones for formulating quantum mechanics. I don't understand his second argument, ...
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Dimensions and complex vector space

I am getting rather confused by the dimensions of the Hilbert space in which a state $\psi$ lives, and with regards to the distinction between the Hilbert space and projective Hilbert Space. Consider ...
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1answer
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Equations of motion

Say, I have a system at rest. I was wondering - how many equations of motion can the system have (without redundancy)? Well, I thought that equating the forces along 2 or 3 different axes would give 3 ...
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1answer
266 views

How many degrees of freedom does an electromagnetic field have? How to correctly count them?

How many independent degrees of freedom does a most general classical electromagnetic field have in presence of sources? What is the correct way to count them? In terms of the components of the ...
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Is the description of the gravitational field as a vector field and a tensor field compatible?

By electric or magnetic fields we mean the vector fields $\vec{E}(\vec{r},t)$ and $\vec{B}(\vec{r},t)$ respectively. But a gravitational field in Newtonian theory is a vector field that $\vec{g}(\vec{...
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1answer
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Degree of freedom and specific heat concept link with radiation

I was reading the black body radiation and there the total energy of the black body radiation is $E=\sigma T^4$ and so specific heat is $C_v = 4 \sigma T^3$ so it is proportional to $T^3$. I read ...