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### Do rotational degrees of freedom contribute to temperature?

Recently I have come across a mathematical problem where I was said to calculate the temperature increase of certain mol of N2 gas confined in a room. However, I found that there was only ...
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### Degrees of freedom of a two particle rigid system

We have two particles and the distance between them is fixed, let's suppose we know the coordinates of one particle (2,1) and other particle (x,2). So using distance formula (let's suppose the fixed ...
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### 7/2 versus 9/2 for diatomic heat capacity

Question I calculated the classical heat capacity of a diatomic gas as $C_V = (9/2)Nk_B$, however the accepted value is $C_V = (7/2)Nk_B$. I assumed the classical Hamiltonian of two identical atoms ...
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### Is the energy per degree of freedom $\frac{1}{2}kT$ in relativistic systems?

The equipartition theorem says that the mean energy per degree of freedom is $\frac{1}{2} kT$. Is this result relativistically correct?
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### Extra vibrational mode in linear molecule

When calculating the number of vibrational modes for a molecule, the formulas differ for linear $(n = 3N - 5)$ and non-linear $(n = 3N - 6)$ molecules, where $n$ is number of modes and $N$ is number ...
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### Gibbs phase rule and degrees of freedom at the triple point / triple line

The Gibbs phase rule tells me that at a substance's triple point, where there are 3 phases in equilibrium, there should be 0 degrees of freedom. Based on my understanding, that means there should be 0 ...
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### Should the (On-shell) (2+1)d $N=2$ Chiral Multiplet Contain Two Scalars and Two Majorana Spinors?

In supermultiplets, the bosonic degrees of freedom and the fermionic degrees of freedom need to match in number. The number of degrees of freedom of a field corresponds to the number of independent ...
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### Degrees of freedom of a point mass sliding on a rigid curved wire without friction

I am very new to the subject and am going through Structure and Interpretation of Classical Mechanics. One exercise asks to find the degrees of freedom of a number of systems, one of which is a ...
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### Why does the Dirac equation reduce the fermionic degree of freedom by half

We know that in 4D a Dirac spinor has 4 complex components or 8 real components meaning 8 real off shell degrees of freedom (please correct me if I say something wrong here). When we go on-shell i.e ...
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### Why energy at room temperature $= kT$ and not $(3/2)kT$ [duplicate]

I always see that a room temperature of $T=300\,\text{K}$ corresponds to an energy of $k_BT \approx \frac{1}{40}\,\text{eV}$. But shouldn't it be $\frac{3}{2}k_BT$ since the molecules in the air have ...
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### Holonomic constraints and degrees of freedom?

Can we see that a constraint can decrease the degrees of freedom of a system if and only if it is holonomic. Either way please can you explain why?
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Consider the expectation in the canonical ensemble defined by $$\left\langle x_i\frac{\partial \mathcal{H}}{\partial x_j} \right\rangle=\frac{1}{Z}\int d\Gamma x_i\frac{\partial \mathcal{H}}{\... 1answer 53 views ### Amount of unknown parameters in compressible Euler equations I'm looking at this page for the compressible Euler equations. To me it seems, in the 1-dimensional case, there should be 3 unknowns: density, velocity, and pressure. This is because the energy E ... 1answer 233 views ### Degrees of freedom in double Atwood machine? Why the degree of freedom in double Atwood machine (one block on one side and a pulley with one block in its each side on other side) is 2 and not 1? According to the formula s=3*n-m; where n=... 1answer 816 views ### Number g(T) of relativistic degrees of freedom as a function of temperature T Let us consider the total number of relativistic degrees of freedom g(T) for particle species in our universe:$$g(T)=\left(\sum_Bg_B\right)+\frac{7}{8}\left(\sum_Fg_F\right)$$Where the sums are ... 2answers 912 views ### In counting degrees of freedom of a linear molecule, why is rotation about the axis not counted? I was reading about the equipartition theorem and I got the following quotations from my books: A diatomic molecule like oxygen can rotate about two different axes. But rotation about the axis ... 2answers 2k views ### Definition of generalised coordinates? I think the definition of generalised coordinates is something along the following lines: A set of parameters that discribe the configuration of a system with respect to some refrence ... 1answer 53 views ### Locally accessible dimensions of configuration space I am reading a book called "Structure and Interpretation of Classical Mechanics" by MIT Press.While discussing configuration space and degrees of freedom,the authors remark the following: Strictly ... 2answers 141 views ### What's the degree of freedom of this kind of matrix? We first have a unitary matrix$$\{a_{ij}\}\quad(n\times n)$$I know how to calculate its degree of freedom, which is n^2 if we consider a real variable as one degree of freedom. Now we have a ... 1answer 89 views ### Counting d.o.f. and gauge fixing A_{\mu} and \psi in D-dimensions Setup: Let us assume we are in D-dimensional Minkowski space-time where D=d+1. Consider a free Abelian gauge theory. Then the electromagnetic field will satisfy$$\partial_{\mu}F^{\mu \nu}=0 \...
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While doing some calculation in Statistical Mechanics of blackbody radiation from Huang's Statistical mechanics, I came across with the factor 2 which it says comes from two possible polarizations. ...
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### Quantum vs classical degrees of freedom

It is sometimes stated that any classical underpinnings (rightly non-local) of a general quantum system are unrealistic or unphysical because these require exponentially more information to store what ...
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### Degrees of freedom in Quantum Mechanics

If we look at a particle in classical mechanics, the degrees of freedom increase as its size decreases like the degrees of freedom of an atom is more than that of molecule, and subsequently, the ...
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### Why is molar specific heat at constant volume of a monatomic ideal gas a constant?

I thought specific heat varies depending on the substance. Why is it always $(3/2) R$?
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### Are there diffrent understandings of dimensions?

If people are talking about 4 or higher dimensions they are always pictured as space dimensions. But if you have have a look at the simplest definition of a mathematical dimension it only needs to be ...
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### Variation of the metric with respect to the metric

For a variation of the metric $g^{\mu\nu}$ with respect to $g^{\alpha\beta}$ you might expect the result (at least I did): \frac{\delta g^{\mu\nu}}{\delta g^{\alpha\beta}}= \delta^\...
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### $E=kT$ or $\frac32kT$?

Basically, which is the correct formula for thermal energy, and is this the same as kinetic energy? My notes are pretty conflicting on this topic, and I'm getting pretty confused.
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### Explicit Symmetry Breaking: Where do the additional d.o.f. come from?

Massless vector bosons have only two independent degrees of freedom, while massive ones have three. In spontaneous symmetry breaking, the massless vector belonging to the broken group becomes massive ...
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### What does degrees of freedom mean in the context of vibrations?

If you have an $N$ degrees of freedom system what does this mean? What is the difference between a 1 and a 2 degrees of freedom system?
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### Is the ground state of a QFT always a pure state? And excited states are mixed?

I am studying entanglement entropy. It's fullfilled for any local quantum system that the entanglement entropy of a region $A$ in a highly mixed state is extensvie,  S_A \sim \frac{\text{Vol}(A)}{\...
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### Integrals of Motion for s Degrees of Freedom

From Landau & Lifshitz, Classical Mechanics, the number of integrals of independent integrals of motion for a system of $s$ degrees of freedom is $2s-1$. I am considering a spherical pendulum in ...
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### Graviton polarization in higher dimensions

It's not difficult to see that the graviton in $D$ spacetime dimensions has $(D-3)D/2$ polarizations. In $D=4$ there are two $\epsilon^{\pm}_{\mu\nu}$. What I find curious is that in $D=4$ I can ...
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### Independent components in a 4-vector representing massless fields

In Ryder Page141, it is written "the electromagnetic field, like any massless field, possesses only two independent components, but is covariantly described by a 4-vector $A_{\mu}$". Why are there ...
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### General relativity: gauge fixing

In his lectures professor Hamber said that the metric tensor is not unique, just like the 4 vector potential is not unique for a unique field in electrodynamics. Since the metric tensor is symmetric, ...
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### Degrees of Freedom for an Asymmetric top

How many degrees of freedom does an asymmetric top have if it is rotating about a fixed point?What are the generalised coordinates used then?
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### Counting the number of propagating degrees of freedom in Lorenz Gauge Electrodynamics

How do I definitively show that there are only two propagating degrees of freedom in the Lorenz Gauge $\partial_\mu A^\mu=0$ in classical electrodynamics. I need an clear argument that involves the ...
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### How do I find the generalized coordinates in a certain system?

I'm learning about constraints and I know the following: If there are $N$ particles in 3 dimensional space, I have $3N$ degrees of freedom. If I have $n_b$ holonomic constraints and I switch over to ...
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### How are degrees of freedom and energy related in classical theory?

How are degrees of freedom and energy related in classical theory? How do we come to know that each quadratic degree of freedom classically contributes a factor of $\frac{k_{B}T}{2}$.
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### How many physical degrees of freedom does the $\mathrm{SU(N)}$ Yang-Mills theory have?

The $\mathrm{U(1)}$ QED case has two physical degrees of freedom, which is easy to understand because the free electromagnetic field must be transverse to the direction of propagation. But what are ...
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### What are “local degrees of freedom in gravity”, and why do they lead to fixed energy densities?

I am reading Jan de Boer's review of the AdS/CFT correspondence and I quote from end of page 1, where he is talking about equivalence of $(d+1)$-dimensional gravity to $d$-dimensional field theory “...
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### Gauge fixing of an arbitrary field

How to count the number of degrees of freedom of an arbitrary field (vector or tensor)? In other words, what is the mathematical procedure of gauge fixing?
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### Degrees of freedom of the photon in $d=n$

It is well known that in ordinary $4$ dimension, the photon has on shell only two physical degrees of freedom. Physically this means its elicity is either $\lambda=+1$ or $\lambda=-1$ but cannot ...