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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51 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, ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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1answer
75 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}$...
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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 $4\times 4$ ...
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1answer
142 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 (...
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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 ...
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1answer
345 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 ...
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2answers
679 views

Coupling of two spin half particles

If there are two electrons coupled by interaction having hamiltonian H=A*S1*S2 where S1 and S2 are spin angular momentum operators of two electrons, we know we have four possible eigenstates for the ...
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Must conclusions from relativistic physics hold in non-relativistic physics?

Example: When one studies the spin statistics theorem, one of the phrases that's been repeated a lot was that "the spin statistics theorem was derived from relativistic physics... there's no way to ...
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1answer
269 views

Why two spin-$1$ bosons could not be in a spin $\frac{1}{\sqrt{2}}(|1,0\rangle-|0,1\rangle)$ state?

Consider two boson of spin $1$ without angular momentum. I'm seeing an argument that "because those two particles were bosons, they must be symmetric under the exchange $m_1,m_2$. Thus they could ...
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Spin Dynamics in strong magnetic Field

it is well known, that the spin of spinning particles such as electrons is aligned when placed in a strong magnetic field. In other words one says that the propability of measuring the electrons spin ...
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241 views

Why are particles either bosons or fermions in spatial dimensions $d>2$ (in Wigner classification)

This questions might have been asked several times, but I haven't seen a mathematical point of view, so here it is. Based on Wigner classfication: A particle is a representation, because any theory ...
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1answer
69 views

Is it known if the ground state of an arbitrary electronic many-body problem has antisymmetric spatial part?

For non-interacting electrons, Hund's rule (#1) says that the state with the highest total spin has the lowest total energy. For two independent electrons, it seems then that the electrons should be ...
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Why is the normal argument for fermions/bosons wrong?

If we have a state $\psi(x_1,x_2)$ of two identical particles and an exchange operator $O$ which swaps the particles. Obviously the physics must be the same and hence $O$ can only introduce an ...
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1answer
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What does Baym mean here in his Lecture on Identical Particles?

I'm reading Lectures on Quantum Mechanics by Gordon Baym (1969). In his discussion of 3-identical fermions Baym writes: "One way to make $\Psi(1,2,3)$ [the total wave-function] antisymmetric is to ...
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Weinberg Phys Rev 133, B1318 1964 - Spin Statistics

I have a question regarding Weinberg's derivation of the spin-statistics relation in the paper listed above (here at https://journals.aps.org/pr/abstract/10.1103/PhysRev.133.B1318). In this paper he ...
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27 views

Linear response theory of spin Seebeck effect

I am trying to re-derive the expressions of linear response theory given in the following article: Theory of the Spin Seebeck Effect, Hiroto Adachi, Ken-ichi Uchida, Eiji Saitoh, Sadamichi Maekawa ...
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$(-1)^{2j}$ in the Spin-statistics theorem - Weinberg/Novozhilov/etc

I am attempting to understand Weinberg's formulation of the spin-statistics theorem as presented in his book "The quantum theory of fields: foundations" pages 233-238. I have at my disposal all three ...
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166 views

Hammersley-Clifford theorem and maximal entropy random walk for Ising-like models?

It seems that condensed matter people usually just brute force use Monte-Carlo, but there are some subtle mathematical tools which might be worth considering, for example: 1) Hammersley-Clifford ...
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168 views

Anti-commutator in Quantization of Dirac field

Can anyone explain while calculating $\left \{ \Psi, \Psi^\dagger \right \} $, set of equation 5.4 in david tong notes lead us to $$Σ_s Σ_r [b_p^s u^s(p)e^{ipx} b_q^r†u^r†(q)e^{-iqy}+ b_q^r †u^r†(q)e^{...
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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 ...
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1answer
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 ...
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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 ...
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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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1answer
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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 ...
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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? ...
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Is the oxygen molecule $O_2$ fermion or boson?

I ask something makes me confused. In generating singlet oxygen molecule, I initially thought a light (photon) can excite the ground state oxygen molecule. However, my colleague said that process is ...
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67 views

What is the physical interpretation of $\langle S_i^z S_j^z \rangle$?

Let's say, that we have some spin system with multiple sites. This system is in a quantum state denoted by $|\psi \rangle$. When we compute e.g. $\langle S_1^z \rangle = \langle \psi | S_1^z | \psi \...
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487 views

Calculating expected values $\langle S_x \rangle$ and $\langle S_y \rangle$ in the Heisenberg model

Let's say, that we are considering the basic Heisenberg model with only two spin-particles. So our Hamiltonian can be written as follows: $$ H = \sum_{\langle i,i' \rangle} S^{(x)}_i S^{(x)}_{i'} + S^...
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Spin-statistics theorem [closed]

I am an undergrad physics student I was curious about the validity of the Pauli exclusion principle and found that spin statistics theorem gives the prrof of this principle . What background do I need ...
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1answer
125 views

Do anyons obey the exclusion principle?

In general, if we have two indistinguishable particles in states $\psi_1$ and $\psi_2$, then starting in the combined state $|\psi_1\psi_2\rangle$ and then exchanging them will produce the state $e^{i\...