All Questions
Tagged with dof or degrees-of-freedom
94 questions with no upvoted or accepted answers
4
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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 ...
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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 ...
- 305
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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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What is the deepest cause of the such high specific heat capacity of water?
Yes, I know about the hydrogen bridges. But I think, it isn't the deepest cause. Anyway, they are only second-order bindings, although quite strong.
I think, somehow should have the water a ...
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3
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115
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How many degrees of freedom does a photon have in 2+1D?
Wigner's classification of particles implies that the internal degrees of freedom of a particle transform under unitary representations of the subgroup of the Lorentz group that leaves its momentum ...
- 820
3
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388
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Entropy - can we express number of microstates as a function parameterized by degrees of freedom?
In some of the answers and comments from this question people contended (not in so many words) that because entropy is parameterized by number of microstates $\Omega$, and the definition of $\Omega$ ...
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3
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177
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Counting supersymmetries in $d=4$ vs in $d=1+1$
Having studied supersymmetry in $d=4$, my understanding is that we count supersymmetries by the number of pair of complex supercharges $$ Q_\alpha^I = \begin{pmatrix} Q_1^I \\ Q_2^I \end{pmatrix}~,~ \...
- 113
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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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73
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RG Flow and Bound State DOF
I have a question regarding how one should view resonance modes in QFT's along the RG-flow, and their effect on $c$. Note that I'm somewhat new to the ideas of RG-flows and CFT's. According to the $...
3
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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 ...
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4
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583
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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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2
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250
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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 ...
- 1,497
2
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42
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Degrees of freedom for a bosonic closed string
I'm a newbie in string theory and I'm trying to get some insights about Polyakov action for the bosonic closed string, although my question isn't uniquely related with string theory: it is about ...
2
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90
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Why does $\rm{H_2 O}$ have 12 degrees of freedom?
I know there will be 3 translational D.O.F. and 3 rotational D.O.F., and it can have 4 vibrational D.O.F. (one potential and one kinetic) for each O-H Bond. But from where does 2 more D.O.F. come from?...
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73
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Equal average energies in translational and rotational degrees of freedom
In, An Introduction to Thermal Physics, Schroeder states
It’s not obvious why a rotational degree of freedom should have exactly the same
average energy as a translational degree of freedom. However, ...
2
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0
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58
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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 ...
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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
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90
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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 $\...
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143
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Understanding the Degrees of freedom of a Ballbot
A Ball Balancing Robot is dynamically stable robot capable of omnidirectional motion. It possesses non-holonomic properties and is a special case of underactuated system, classified as a Shape-...
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491
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Effective degrees of freedom of relativistic gases: Intuition for fermion factor 7/8?
When calculating the number density of a gas of identical massless particles you get the following integral
$$ I_{n,\,\pm} \equiv \int_0^{\infty} \frac{u^2}{e^u\pm1} \,\text{d}u $$
with (+) for ...
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161
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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 ...
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384
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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. ...
- 475
2
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1
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212
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Hadron contribution to effective degrees of freedom in early Universe
In transition from quark-gluon plasma to hadron gas in the early Universe, the value of the effective degrees of freedom $g_{\star}$ decreases abruptly. This seems to me like a sort of decoupling: ...
- 1,154
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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 ...
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0
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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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0
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1k
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What is the degrees of freedom of metric tensor?
As $g_{\mu\nu}$ can be taken to be symmetric, it contains 10 functions of spacetime in 4 dimensions. But, why we call these 10 functions as the degrees of freedom of the metric while they are the ...
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2k
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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 ...
- 2,241
2
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4
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166
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Is Bohr's model one-dimensional?
Purdue university in its article on Bohr's Model explains:
At first glance, the Bohr model looks like a two-dimensional model of the atom because it restricts the motion of the electron to a circular ...
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1
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60
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About Yo-yo motion and forces constraint
The purpose of the Euler-Lagrange equation, is supposed to enable us to describe a system with the fewest possible coordinates, using generalized coordinates instead of traditional ones.
However, in ...
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1
answer
58
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Counting of degrees of freedom in Higher Spin Theories in curved spacetime
In 4d Minkowski, a (bosonic) tensor field with spin $s\in\mathbb{N}_+$ are constrained by Poincaré symmetry, and the physical degrees of freedom can be counted by considering the little group: a spin-$...
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0
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326
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Degrees of freedom in the early universe with MSSM?
As nicely summarized on P4 in On effective degrees of freedom in the early universe here; at high temperatures where all the particles of the Standard Model are present, we have 28 bosonic and 90 ...
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110
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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
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0
answers
151
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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 ...
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0
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88
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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, ...
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1
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452
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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 ...
1
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0
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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 ...
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1
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0
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102
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Representation of Holonomic Constraints by independent generalized coordinates
Say we have a system with N particles described by N position vectors: $\{\vec{r_{i}}\};$ $i=1,...N$
Say we have a holonomic constraint: $$f(\{\vec{r_{i}}\},t)=0 \tag{1}$$
Since we have one holonomic ...
user279008
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0
answers
189
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Are gravitons possible in 2+1 spacetime dimensions?
Spin-1 massless particles are transverse waves, so they need at least three space-time dimensions to exists. As for gravitons, I think they are still not possible in three dimensions, and to reveal ...
1
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1
answer
150
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Properly accounting for indistinguishability of (homonuclear) diatomic molecules in "internal" partition function
I have always liked Schroeder's take on the partition function being a product of translational and internal degrees of freedom:
$$
Z_1 = Z_{\text {trans}} Z_{\text{int}}
$$
where $Z_{\text{int}}$ can ...
- 1,081
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0
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54
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Degrees of freedom in a Kahlerian NLSM
Lagrangian for $d=1$ $\mathcal{N}=4$ SUSY model on a $n$-complex dimensional Kahlerian target space is given as (see p.213, eqn. (10.251) in the Mirror Symmetry book (pdf))
$$\begin{equation}
L= ...
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How do I calculate the bosonic/fermionic degrees of freedom from the helicity content?
After constructing a physical state and discovering the particle content, how can one find the fermionic and bosonic degrees of freedom?
Eg.
Constructing the physical states of an $\mathcal{N} = 2$ ...
user256673
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0
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52
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Wilsonion Renormalization Group in Asymptotically Free Theories
Consider some correlation function computed at some renormalization scale $\mu_0$ in an asymptotically free theory
$$ \langle M(z; \mu_o) \rangle. $$
From what I understand of renormalization-group ...
- 391
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145
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graph relativistic degrees of freedom
I'm trying to graph the relativistic degrees of freedom, which should look like the figure
And I am trying to guide me with this Phys.SE answer: Number $g(T)$ of relativistic degrees of freedom as a ...
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0
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173
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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 ...
- 315
1
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0
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109
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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 ...
- 1,914
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0
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249
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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 ...
- 4,067
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54
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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 ...
- 1,222
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146
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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 ...
- 4,067
1
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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 ...
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