The Stack Overflow podcast is back! Listen to an interview with our new CEO.

Questions tagged [degrees-of-freedom]

The tag has no usage guidance.

276 questions
Filter by
Sorted by
Tagged with
27 views

What is the energy associated with the degrees of freedom of a nucleus?

I am following Martin in his book on electronic structure. On page 11 he explains that we discriminate between properties of matter due to the electric ground state, and excited states. He writes ...
29 views

Law of equipartition of energy, shouldn't kinetic energy per molecule by $(3/2)kT/f$

I study that according to the law of equipartition of energy the average kinetic energy associated with each degree of freedom is equal to $(1/2)kT$. But shouldn't it be $\frac{(3/2)kT}{f}$ where $f$ ...
87 views

47 views

Some counting of field degrees of freedom for a classical spin-1/2 Dirac field

A classical real scalar field admits a decomposition $$\phi(x)\sim a_pe^{-ip\cdot x}+a_p^*e^{+ip\cdot x}$$ which tells that at each $x$, there exists a real number i.e., one degree of freedom at each ...
97 views

Einstein solid degree of freedom

I was studying from Schroeder's thermal physics book. When it talks about Einstein solids it says that they have 2 degrees of freedom thus $U=NkT$ However, I thought when we talk about Einstein ...
50 views

Physical degree of freedom and gauge fixing?

I'm confused with the gauge fixing in the Higgs mechanism. So if we have an action like $$S=\int |D\phi|-\frac{1}{4}F^2 -V(\phi) ~ ,\tag{1}$$ then expand around some non-trivial vacuum, then we have ...
46 views

Degeneracy in Landau Levels

A subsection from "Landau Levels" from pg 21 from Lectures on Quantum Hall effect by David Tong. He shows and derives the energy of a charged particle in a planar surface under the action of a ...
79 views

How many degrees of freedom does a spring pendulum have? [closed]

I've been looking at a spring pendulum system, but I'm not sure how many degrees of freedom it has.
38 views

Rigorously define degrees of freedom

I want to understand if there is truly a rigorous definition for the degrees of freedom in a system. Say all of a system's physical states are contained in some set $S$. A seemingly acceptable (and I ...
89 views

Why do we have redundant degrees of freedom?

Preliminaries: Consider the homogenous Maxwell's equations $$\partial_\mu F^{\mu\nu}=0.$$ and $$\partial_{\sigma} F_{\mu \nu}+\partial_{\mu} F_{\nu \sigma}+\partial_{\nu} F_{\sigma \mu}=0$$ Since ...
69 views

How to know the number of constants of a free particle?

Landau-Lifshitz Mechanics says that there are $2s-1$ constants of a system with $s$ degrees of freedom (beginning of the second chapter on Conservation Laws). If this is true, for a single free ...
40 views

Equipartition theorem - concerning the square dependence of energy

So the equipartition theorem states that if the energy dependence is square ($\langle\,E\,\rangle= as^2$ + ...(something not dependent on $s$)) then each variable (degree of freedom) contributes ...
22 views

Degrees of freedom [duplicate]

Consider a system of 10 (say) point particles each at a fixed distance from each other in 3-D space. In this case, the number of degrees of freedom: $3*(number-of-particle)-\binom{10}{2}=3*10-45<0$ ...
52 views

Schwinger-Keldysh formalism

I am studying the Schwinger-Keldysh formalism. Basically, we double the number of degrees of freedom for the upper and lower branches. Let´s consider the case where we have a certain field, coupled ...
121 views

Explicit counting of gauge field degrees of freedom

Consider a connection on a principal $U(1)$-bundle $A_\mu$ over the flat base manifold $M_4$. The action of the theory is described in terms of the curvatures of such connection coupled to some source ...
80 views

Dimensionality of the quantum space of states

I don't understand what is the dimension of the space of the states because it looks different dependently on the base that I choose, for example: If I use the position representation (the base are ...
73 views

Constrained Curve in 3 Dimensions [closed]

I have a particle in a 3D space that moves on a curve of the function $$r(x)=\begin{bmatrix}x \\ x\sin(x) \\ \exp(x^2)\end{bmatrix}$$ I know that there must be 1 degree of freedom left thus $S = 3N-P$...
123 views

Goldstone bosons when SSB potential has two fields

A theory consists of two complex scalar fields $φ_0$ and $φ _1$ with a symmetry-breaking potential $$V(|φ_0|^2 + |φ_1|^2).$$ How many Goldstone particles will there be in the theory?
95 views

Degree of freedom

Here our professor told that the degree of freedom of the system is 2 as we just need 2 angles shown in the figure to completely specify the configuration of the system but this system with a given ...
106 views

Non-relativistic E&M Lagrangian: number of dynamical variables greater than 6

There is an argument I do not understand given in "Introduction to quantum electrodynamics" by Cohen-Tannoudji (page 111 for the French version of the book). We are dealing with the non-relativistic ...
48 views

Field degrees of freedom from equations of motion and higher spin

It is my understanding that we compute the number of degrees of freedom of a quantum field as the number of its components minus the number of non trivial equations we get by taking the divergence of ...
104 views

Why we fill dU/dT value in Cv(specific heat at constant volume) only and why not in Cp?

According to equipartition of energy, the energy ossociated with each degree of freedom is $\frac{K_{b}T}{2}$ for one molecule . For 'x' molecule which has degree of freedom f it's energy is given by ...
73 views

Can kinetic energy broken down into its components ? Even if it is scalar?

I'm confused while reading about degrees of freedom. According to what I read the number of degrees of freedom (DOF) of a monoatomic gas is 3 at low temperature. My question is: is that 1) because the ...
139 views

How is the relationship of the value $kT$ and a degree of freedom derived?

Sources that discuss the derivation of the Maxwell-Boltzmann Statistics end up with two unknown constants ($\alpha$ and $\beta$) through the Lagrange Multipliers, of which $\alpha$ is derived by ...
35 views

57 views

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 ...
165 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 ...
72 views

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. ...
107 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 ...
261 views

27 views

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' ...