Questions tagged [spin-statistics]
229 questions
73
votes
3 answers
Idea of Covering Group
$SU(2)$ is the covering group of $SO(3)$. What does it mean and does it have a physical consequence?
I heard that this fact is related to the description of bosons and fermions. But how does it follow from the fact that $SU(2)$ is the double cover…
SRS
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27
votes
1 answer
A reading list to build up to the spin statistics theorem
Wikipedia's article on the spin-statistics theorem sums it up thusly:
In quantum mechanics, the spin-statistics theorem relates the spin of a particle to the particle statistics it obeys. The spin of a particle is its intrinsic angular momentum…
Niel de Beaudrap
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22
votes
2 answers
Are protons and neutrons affected by the Pauli Exclusion Principle?
I'm very confused about the Pauli exclusion principle. Wikipedia states it as "two identical fermions cannot occupy the same quantum state in a quantum system". I understand this for electrons that for each energy level in an atom there are two…
shA3245699
- 335
21
votes
2 answers
Does a non-relativistic proof of spin-statistics theorem exist?
There are lots of questions here related to the spin-statistics theorem, though none of them answer this question directly.
I had the notion that one can only prove the theorem on relativistic grounds and for example the Wikipedia page on the…
A. Jahin
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20
votes
2 answers
What is the reason why anyons escape spin-statistic theorem?
I'm wondering about the exact reason why anyons escape the spin-statistic theorem (SST), see e.g. http://en.wikipedia.org/wiki/Spin–statistics_theorem.
I've read somewhere (the wikipedia page is sufficient I believe to understand this point, to be…
FraSchelle
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20
votes
1 answer
What is the spin-statistics theorem in higher dimensions?
In $d = 3+1$ dimensions, the spin-statistics theorem states that fermionic particles have half-integer spin and bosonic particles have integer spin, in a well-behaved relativistic quantum field theory. We also know that in $d = 2 + 1$ dimensions,…
knzhou
- 107,105
19
votes
2 answers
Braiding statistics of anyons from a Non-Abelian Chern-Simon theory
Given a 2+1D Abelian K matrix Chern-Simon theory (with multiplet of internal gauge field $a_I$) partition function:
$$
Z=\exp\left[i\int\big( \frac{1}{4\pi} K_{IJ} a_I \wedge d a_J + a \wedge * j(\ell_m)+ a \wedge * j(\ell_n)\big)\right]
$$
with…
wonderich
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19
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1 answer
What causes Paulis Exclusion Principle?
Currently I'm taking an astrophysics class and has now come across electron degeneracy. As far as I understand, the reason why white dwarfs and such, does not collapse, is due to this, meaning that the electrons are so close together in the core,…
Denver Dang
- 2,587
16
votes
5 answers
What are distinguishable and indistinguishable particles in statistical mechanics?
What are distinguishable and indistinguishable particles in statistical mechanics? While learning different distributions in statistical mechanics I came across this doubt; Maxwell-Boltzmann distribution is used for solving distinguishable particle…
Eka
- 1,057
16
votes
5 answers
Is there a reason why the spin of particles is integer or half integer instead of, say, even and odd?
It seems to me that we could change all the current spin values of particles by multiplying them by two. Then we could describe Bosons as even spin particles and Fermions as odd spin particles. Is there some consequence or reason why we can't simply…
Kainui
- 309
14
votes
5 answers
Theoretical Proof of Pauli's Exclusion Principle
"No theoretical proof of the Pauli's Exclusion Principle can be given as yet and for the present it must be regarded as something empirical added to and regulating the vector atom model."
I've found it in Atomic & Nuclear Physics by N. Subrahmanyam…
Deepayan Turja
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14
votes
2 answers
Time reversal symmetry and T^2 = -1
I'm a mathematician interested in abstract QFT. I'm trying to undersand why, under certain (all?) circumstances, we must have $T^2 = -1$ rather than $T^2 = +1$, where $T$ is the time reversal operator. I understand from the Wikipedia article that…
Kevin Walker
- 303
13
votes
1 answer
What feature of QFT requires the C in the CPT theorem?
Classical tensor field theories have a PT theorem, so what changes in a QFT to require charge conjugation to be a part of the theorem? Charge conjugation seems a bit unrelated to space-time, but is an integral part of the theorem.
I have a suspicion…
lazcisco
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13
votes
2 answers
Irrelevance of parastatistics for space dimension > 2
Consider a system of $n$ undistinguishable particles moving in $d$-dimensional Euclidean space $E^d$. The configuration space is $M=((E^d)^n \setminus \Delta)/S_n$ where $\Delta$ is the diagonal (subspace where at least 2 particles have coincidental…
Squark
13
votes
1 answer
Can the CPT theorem be valid if Lorentz invariance is only spontaneously broken?
Earlier, I asked here whether one can have spontaneous breaking of the Lorentz symmetry and was shown a Lorentz invariant term that can drive the vacuum to not be Lorentz invariant. How relaxed are the assumptions in the CPT theorem? Can one have…
dbrane
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