# Questions tagged [spin-statistics]

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### 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 ...
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### 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 ...
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### 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 ...
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### 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, ...
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### 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 ...
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### 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 ...
831 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 ...
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### Polchinski's notes on CPT and Spin-Statistics

On Polchinski's website for Physics 221B, QFT, Winter 2015, there is a link that is supposed to contain notes on CPT and Spin-Statistics, but the link is dead. Does anybody have these notes, and if so ...
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### How to work out the multiplicity of Uranium Hexafluoride?

Consider the uranium atom which itself has a multiplicity of 5 since it has 4 unpaired electrons, each with half a spin, and so the total spin S =2 and so 2S+1 is 5. I am trying to work out the ...
22 views

### Defining an auxiliary vector for a gluon polarization sum?

I am trying to understand the derivation of the "auxiliary 4-vector" defined for a gluon polarization spin sum in order to use it in a symbolic matrix element calculator (defined for ...
49 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 ...
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### 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 ...
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### 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 "...
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### 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?
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### 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 ...
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### Exchange symmetry between mixed species

I am reading Weinberg Vol.1 chapter 4, in section 4.1 page 171 last paragraph he says that for interchanges of particles to different species can be taken to be symmetric for any two bosons or one ...
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### 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 ...
160 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 ...
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### 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 ...
400 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 ...
382 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 ...
75 views

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### Spin and Statistics: Feynman rules for any spin I - Weinberg 1964

I am trying to understand the spin statistics theorem through the point of view of Weinberg's "The Quantum theory of Fields," (QToF) in which he cites a series of papers he published in 1964-1969 ...
127 views

### Can the correspondence between irreps of $SU(N)$ and Young diagrams be interpreted as particle permutations only for the fundamental representation?

The decomposition of the $N$-fold tensor product of an irreducible representation of $\mathfrak{su}(N)$ can be conveniently found using Young diagrams and some combination rules. If the irreducible ...
236 views

### Why does spin determine particle statistics?

I understand that "spin" refers to the intrinsic angular momentum of a particle, which relates to the magnetic moment of a particle. I mostly follow the "Background" section of the spin-statistics ...
45 views

### Spin structure, Intersection form and 2D TQFT

I am reading this (page 20) and watching this Anton Kaputins' talk (33:24). Here, he tried to explain how to define a spin structure on a lattice in a closed oriented (1+1)-D manifold $M$ (or at ...
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### Rotating three (or $n$) times to come back to itself

Hello I'm a quantum mechanics newbie. I learned about spinors, and how they are different from vectors because unlike vectors, rotating them once does not give the original spinor, but the negative ...
108 views

### Why are twistors commuting?

In his book, Srednicki introduces the notion of twistor in chapter 50. It is described as a simply commuting spinor, as opposed to anti-commuting. How do we know that this object is simply commuting? ...