Questions tagged [spin-statistics]
The spin-statistics tag has no usage guidance.
215
questions
0
votes
2
answers
63
views
Topological proof of spin-statistics theorem confusion
I am currently studying the spin-statistics theorem. I have found a section on John Baez's website which presents a "proof" of the spin-statistics theorem. He states the theorem as:
This is ...
1
vote
0
answers
77
views
Covariant Spin Operator for Massless Fermions
I have been reading the paper The Covariant Definition Of Spin in Relativistic QFT by Hilgevoord and De Kerf, in which the authors derive the spin operator in relativistic quantum theories of free ...
- 3,833
0
votes
0
answers
17
views
About symmetric and anti-symmetric states of a nucleus
Ehrenfest and Oppenheimer published a paper Note on the Statistics of Nuclei in which they write:
The "rule" mentioned in paragraph is also stated in the paper. It is:
I am unable to follow ...
- 2,215
0
votes
0
answers
53
views
How is the dimension of the vector space we represent $SO(3)$ on determined when discussing the spin of a particle?
Consider a single particle with Hilbert space $L^2(\mathbb{R}^3) \otimes V_\ell$ where $V$ is a vector space of dimension $2\ell + 1$ equipped with a projective unitary representation of $SO(3)$. ...
- 2,182
1
vote
1
answer
44
views
Anticommutator Relation of Quantized Fermionic Field and Fermi–Dirac statistics: How are these related?
I'm reading the Wikipedia article about Fermionic field and have some troubles to understand the meaning following phrase:
We impose an anticommutator relation (as opposed to a commutation relation ...
- 1,253
1
vote
0
answers
38
views
Anyonic and plektonic dark matter?
The most studied types of dark matter particles include supersymmetric particles, spin particles that are either boson or fermions. I wonder if there are research about dark matter being not particles ...
- 6,327
0
votes
0
answers
27
views
Spin polarization, ferromagnetism, and size of energy gap
I thought large band gap (larger than relevant spin-spin interaction energy scale) necessarily means there is no spin-polarization (ie, not ferromagnetic). I thought the reason is that {only when ...
- 364
1
vote
1
answer
111
views
Angular momentum quantum number $l$ either integer or half integer
I am trying to understand why the angular momentum quantum number $l$ can either be an integer or an half-integer. At least this is stated in the book that I am learning from. It is the book by ...
- 111
3
votes
0
answers
78
views
Time Reversal symmetry, Quaternions, and spin-1/2 systems
When one has a system with no spin and time reversal symmetry, one can conclude that the Hamiltonian entries (in a particular basis, of course) must all be real. Can something be said about the ...
- 403
3
votes
2
answers
150
views
Why are some collections of fermions considered bosons?
I read that He-4 is a boson because the four fermions in it add up to an integer spin—of zero—hence a boson.
Whereas I thought that if the parts are fermions, so is the whole.
Is an electron pair a ...
- 154
2
votes
2
answers
143
views
Do solutions of the Schrödinger equation for multiple particles automatically obey spin-statistics?
Consider the Hamilitonian for a general two-electron system subject to an external potential $V_\mathrm{ext}$ and an interaction potential $V_\mathrm{ee}$. In this case
$$H\psi(x, y) = -\frac{1}{2} \...
1
vote
1
answer
68
views
Can excited high spin states be used as qubits?
What the title says. I was wondering if we can use excited high spin states formed by enhanced intersystem crossing for qubits? like intramolecular quartets formed by a doublet and an intersystem ...
2
votes
2
answers
114
views
Is the spin of a primary field in 2D necessarily integer or half-integer?
The primary field in a 2D CFT is defined by the transformation property
\begin{align}
\phi^{'}(w) = \left(\frac{dw}{dz}\right)^{-h} \left(\frac{d\bar{w}}{d\bar{z}}\right)^{-\bar{h}} \phi(z)
\end{...
- 357
0
votes
0
answers
64
views
Question on Weinberg QFT eq. (5.5.10)
I am reading Weinberg's treatment on Causal Dirac Field. From (5.5.8):
$$
\mathrm{P} a(\mathbf{p}, \sigma) \mathrm{P}^{-1}=\eta^* a(-\mathbf{p}, \sigma)\tag{5.5.8}
$$
where $\mathrm{P} = U(\mathcal{P},...
0
votes
0
answers
26
views
Ensemble of Spins along magnetic field
Say we have $N$ spins. These can be oriented along a B-Field or "antiparalell" to it. Spins along the field give Energy $\epsilon$ and antiparallel to it energy zero. Now for a given energy $...
- 31
8
votes
2
answers
1k
views
Are the inequalities from Bell's Theorem ever actually satisfied?
Following Griffiths's description from Introduction to Quantum Mechanics, Bell's original experiment was based on the EPR-Bohm experiment, where one considers the decay of a neutral pi meson into an ...
- 101
0
votes
1
answer
57
views
Intepreting the total number of magnons excited at temperature $T$
Suppose a system is at thermal equilibrium.
The average value of the number of magnons excited in the mode $k$ is given by the Planck distribution:
$\langle{n_{k}}\rangle = \frac{1}{exp(\bar{h}\omega /...
- 867
1
vote
0
answers
59
views
Is there a relationship between spin correlation and entanglement entropy?
Can someone explain whether there is a connection between spin correlation in say a 1D Heisenberg chain and its entanglement entropy? I'd say, albeit naively, that there is just from their concepts. ...
- 11
1
vote
0
answers
55
views
Parity of quantum numbers of combined system of two spin-1 particles
I'm looking at the following problem:
Two identical particles of spin $1$ have centre of mass at rest. The
particles have combined spin $\mathbf{S}$, relative orbital angular
momentum $\mathbf{L}$ ...
2
votes
1
answer
84
views
How do spin operators work? [closed]
I am currently studying statistics and 2D Ising models and noticed in my lecturer's notes the operators, acting in the spin space
The text says that this is identity $2^N\times 2^N$ matrix. I don't ...
- 446
1
vote
0
answers
70
views
Can the "symmetric & antisymmetric" stuff of fermions & bosons be explained by first principles? [duplicate]
Many particle wave-functions to me have a very confusing methodology. I've been taught some procedure for creating wave functions that are symmetric or anti-symmetric upon exchange of coordinates.
I ...
- 2,110
1
vote
0
answers
40
views
Pauli exclusion during an NMR or EPR pulse
If we perform a $\pi/2$-pulse on a pair of spins initally in the singlet state $|S\rangle = \frac{1}{\sqrt{2}}\big(|\uparrow\downarrow\rangle-|\downarrow\uparrow\rangle\big)$, in theory we arrive in ...
- 49
1
vote
2
answers
45
views
Why are composite particles grouped with force carrying particles?
This
Huge confusion with Fermions and Bosons and how they relate to total spin of atom
says a hydrogen atom is a boson.
I'm confused. I thought bosons were force carrying - e.g. a photon, gluon, etc?
- 123
2
votes
2
answers
352
views
Why is the decay channel $H \to \gamma\gamma$ direct evidence that the spin of the Higgs must be different from one?
The title says it all really, I searched this website and came across a post with a question titled Why is the Higgs boson spin 0?. But it doesn't really answer my question in the title.
But this next ...
- 620
2
votes
1
answer
193
views
Does the CPT theorem imply $CP=T$?
Does the CPT theorem imply $CP=T$?
That is, does it imply that the action of Charge Conjugation and Parity inversion on some representation of the Lorentz group, is the same as doing a time reversal?
...
- 994
1
vote
0
answers
59
views
What are the observables of a particle's spin, esp. if it doesn't have an EM charge? Or any charge?
What experiment(s), specifically tell you that a spin-1/2 particle has rotated one full rotation (360°), but is (in some other respect) only 'rotated' by 180°?
Or, conversely, if a spin-2 particle has ...
- 4,269
3
votes
0
answers
141
views
Why is CPT symmetry necessary to prove the spin-statistics theorem?
I was reading the Wikipedia article on the spin-statistics theorem. It has a section going through a "suggestive bogus argument", where they rotate products of fields. To show why it doesn't ...
3
votes
1
answer
134
views
Rampant false definition of orthohelium on the internet? [duplicate]
This is an extension of this question, which has no good answers (in my opinion) and seems to have been mostly ignored.
The correct definition of orthohelium seems to be any state of helium in which ...
- 3,285
0
votes
1
answer
140
views
Spin of Fundamental Particles
Is there any explanation/theorem which justifies that most fundamental particles have spin half or spin one?
Apriori, studying representations of symmetry groups and their connection with spin of ...
- 638
1
vote
2
answers
350
views
If a spin $\frac{1}{2}$ particle flips its sign after a 360° rotation, why don't theorists just say it rotated by 180°?
Usually, when a wave or wave-like object or system goes through a $180^{\circ}$ twist or turn or whatever, we say it is opposite to how it was oriented before, and if it came across its former self ...
- 4,269
2
votes
2
answers
400
views
Klein-Gordon Field Quantization and Bose-Einstein Statistics in Peskin & Schroeder
I am trying to understand how Klein-Gordon particles obey Bose-Einstein statistics from Peskin & Schroeder's QFT textbook (page no. 22). The excerpt is given below:
From this passage it is clear ...
- 2,963
1
vote
1
answer
93
views
Homotopic Paths and Spin-Statistics
I am currently reading Schwartz' book on QFT, Section 12.2 on Spin and statistics. He shows, that in 3D there are only two inequivalent ways to exchange two indistinguishable particles. More formally, ...
- 75
0
votes
0
answers
65
views
How can Momenta Affect Probability if Momenta Cancel Out to form the Probabiltiy Density Function?
How does a probability density function for a wavefunction illustrate energy, momenta, or time-dependence in cases where they cancel out (even with more than one stationary state)?
Though you may not ...
1
vote
1
answer
53
views
Zee's book on QFT on the spin-1/2 state has $T^2=-1$, why not $T^2=+1$
In Zee's book on QFT, p.103, he showed that the spin-1/2 state has $T^2=-1$ by finding that the $T = UK$ has a matrix $U\propto \sigma_2$ and a complex conjugation $K$.
However, how do we know that we ...
- 553
6
votes
3
answers
970
views
Why can we choose spin-1/2 degrees of freedom to commute?
Edit 2:
The previous title of this question was "Why are qubits bosonic?" Thanks to the answers that have been provided so far, I now realize I asked my question in a sloppy way. The ...
- 7,987
0
votes
0
answers
60
views
Sundarshan's proof of the spin-statistics theorem
The proof starts with the $\rm SU(2)$ symmetric Lagrangian
\begin{equation}
\mathcal L=\sum_{r,s=1}^4\frac{1}{2}K_{rs}^0(\xi_r\dot\xi_s-\dot\xi_r\xi_s)
\end{equation}
where the fields $\xi$ either ...
- 21
3
votes
1
answer
245
views
Why the Minkowski and Euclidean spinors need to be fermions?
Minkowski spinors are the spinor representations of the spin group $Spin(1,d)$ of spacetime rotational symmetry.
Euclidean spinors are the spinor representations of the spin group $Spin(1+d)$ of ...
- 4,206
2
votes
1
answer
162
views
Zwiebach String theory text - Why is the $(R-, R+)$ sector fermionic?
On Page 323 of Zwiebach 2ed, he says the state
$$
(R_-,R_+): |R_a\rangle_L \otimes |R_{\bar b}\rangle_R \otimes |p^+, \vec{p}_T\rangle,
$$
'include the product of two $R$ ground states, they are "...
- 107
0
votes
1
answer
63
views
Are there analogues of the spin-statistics theorem for other quantum numbers?
Just like how spin and statistics are connected by the spin-statistics theorem do the other quantum numbers (isospin etc.) enjoy any such relations?
user300004
1
vote
0
answers
197
views
Relative minus sign Feynman Diagrams from spin statistics
I am having trouble understanding whether there should be a minus sign between the two Feynmann diagrams contributing to second order in $\phi \psi \to \phi \psi $ scattering, in Yukawa theory.
I have ...
- 111
2
votes
1
answer
173
views
Why must systems of identical particles be either totally antisymmetric or totally symmetric? Why can there not exist a mixture?
I am reading chapter 6 of Sakurai's Modern Quantum Mechanics and have come across the 'symmetrization postulate', which tells me that for any given system of identical particles, all states must ...
1
vote
3
answers
418
views
Identicalness and Indistinguishability in quantum mechanics
I've been reading chapter 10.3 'Identical Particles' in Shankar's book on quantum mechanics and also looked through some of other books on this subject and one rather subtle objection started ...
- 57
1
vote
2
answers
123
views
Motivation behind the principle that all electrons are not distinguishable
EDIT: It is usually claimed without providing much motivation that elementary particles of the same kind, e.g. electrons, are not distinguishable in principle: there is no way to distinguish between ...
- 2,002
3
votes
2
answers
745
views
Meson as hadron and boson
In wikipedia page about hadrons the following image appears:
I can understand why the intersection between hadrons and fermions are baryons, as a way to say a baryon is a kind of hadron composed of ...
- 1,108
3
votes
2
answers
610
views
Rotation for spin > 1/2
For single spin 1/2 particle, we can use three Pauli matrices as generators to do rotation on Bloch sphere to get any state we want in the Hilbert space.
However, for spin greater than 1/2, I try to ...
- 473
1
vote
1
answer
102
views
Identical Particles in Quantum Field Theory
In Quantum Field theory by M. Schwarz, the author in the introduction of chapter 12 on Spin Statistics theorem says, while describing identical Particles:
Let $$|s_1p_1n_1,...,s_3p_3n_3\rangle \tag{1}$...
- 129
0
votes
0
answers
86
views
How does the Wigner function differ from quantum distribution functions?
I understand that Wigner functions are quantum-mechanical phase-space distribution functions (quasi-distribution to be more specific). For spin-1/2 particles the Wigner function is a $4\times 4$ ...
- 928
1
vote
1
answer
173
views
'Physical realizability' in the Symmetrization Postulate
I have two questions about the $Symmetrization \ Postulate$:
In a system with $N$ identical particles, physical states aren't arbitrary states in $V^{\otimes n}$. Rather, they're totally symmetric (...
- 483
17
votes
2
answers
532
views
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 ...
- 849
4
votes
1
answer
789
views
What if we used "Schwinger Fermions" to study spin waves?
When studying spin waves excitations in the Heisenberg Hamiltonian people often use Schwinger Bosons representation or Holstein-Primakoff which is a specific case of Schwinger Bosons. This leads you ...
- 381