Questions tagged [spin-statistics]

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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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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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58 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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393 views

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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Fermionic vanishing VEV in conflict with spin-statistics proof?

I have what is hopefully a quick question. In Streater and Wightman's 1980 book PCT, Spin and Statistics and all that, they provide a proof of the PCT and Spin-statistics theorem by comparing vacuum ...
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41 views

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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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 ...
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1answer
183 views

$(-1)^{2j}$ 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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118 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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60 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
64 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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104 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
57 views

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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1answer
63 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? ...
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202 views

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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2answers
64 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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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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28 views

Quantum numbers of a particle system

I have a problem to understand the solution of an exercise. The statement is the following: Find the possible values of isospin, parity, charge conjugation, G-parity and totoal angular momentum J, up ...
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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
53 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\...
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Commutation relations in QFT [duplicate]

So I have just started learning QFT. So you take a classical field and turn the degrees of freedom into operators. All fine, just like normal quantum. However I am confused about the commutation ...
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How are anticommuting fields ($\eta \chi = -\chi \eta$) “forced upon us” by representation theory of $SO(d-1,1)$?

I would like to know if anticommuting fields (which physicists use as fermions) emerge naturally from the spin representation theory of $SO(d-1,1)$. Is the fact that spinor fields anticommute a ...
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Typo on 'PCT, Spin and Statistics, and All That'

On page 163, formula (4-76) says $$ (Ψ_{10},…Ψ_0)=… $$ but it should say $$ (Ψ_{10},…Ψ_{10})=… $$ right?
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Legal values of quantum field can take? $\mathbb{R}$, $\mathbb{C}$, $\mathbb{H}$, ..?

Main issue: What are the legal and possible values of the quantum field can take? Clarify by examples: (1) For example, for the spin-0 Klein Gordon field $\phi$, we may choose it to be: real $\...
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1answer
141 views

Constructing singlet state in second quantization formalism

I am trying to understand the second quantization formalism. Let's say we have a system of fermions (e.g. electrons) with spin in an array of quantum dots. The creation and annihilation operators $c^{\...
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2answers
153 views

CPT transformation for bilinears

In the page 5 of the document 'CPT Symmetry and Its Violation' by Ralf Lehnert (https://core.ac.uk/download/pdf/80103866.pdf), appears a discussion about how the spin-statistics theorem applies to the ...
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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....
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Why are Spin 1/2 particles invariant to $4\pi$ rotation loops while Spin 1 particles are invariant to $2\pi$ loops?

Why do Spin 1/2 particles when turning them by 360 deg get a phase factor of -1 and a loop of 720 deg leads to the identity while for spin 1 particles a loop of 360 deg gives already the identity?
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Is the spin-statistics theorem true for antifermions?

The spin-statistics theorem says that having a system of identical fermions, the total wavefunction is antisymmetric with respect to exchange of any two fermions. My question is, does this hold for ...
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Particle statistics in fractal dimensions? [closed]

We know that fermions and bosons are the only two (indistinguishable) particle statistics for $d\geq 3$, and that anyons are for $d=2.$ What if the space were a fractal? Like the Sierpinski gasket, ...
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Spin statistics from the fundamental group of $SO(D)$

I read the answer to this question and am very intrigued by its simple and elegant explanation of the emergence of anyon, boson & fermion statistics. @Trimok basically says: In a space-time ...
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1answer
71 views

Identical Spin Fermions in the same orbital state: Finding total spin

Say we have two identical spin 3/2 particles in the same orbital state. What are the possible total spin? I know that there is a simple formula for adding angular momenta, but this breaks down when ...
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208 views

Intuition behind Pauli’s Principle

While reading about electronic structure of multi-electron atoms, Pauli’s Principle comes out to be a very important feature. But it feels very vague as little explanation is given about it. I mean ...
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3answers
152 views

Can we say that bosons attract each other?

We know that bosons donot follow Pauli exclusion principle, thus they can occupy the same state. But is it equivalent to say that bosons attract each other?
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A possibility of the theoretical derivation of Pauli's Exclusion Principle [duplicate]

Pauli's exclusion principle tells us (in an informal language) that each and every electron in an atom is unique. When I searched for a derivation , I got nil everywhere (even the wiki site says only ...
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43 views

Is Quantum spin greater than $1$ possible? [duplicate]

I know that fermions have a spin of half of and bosons have a spin of 1 but at many places I have seen that their is written that spin for a boson can be 0,1,2.... Is there any physical meaning of ...
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94 views

Entropy without thermodynamic limit

I am reading K. Huang Statistical Mechanics (2Ed , Wiley, 1987) Chapter 14 Ising Model. The paragraph of title Absence of Spontaneous Magnetization in One Dimension bothers me. Problem discussed is ...
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152 views

Ising 2d Using Montecarlo Metropolis (Markov chain method)

I'm doing as a personal training the 2d Square lattice Ising model. I decided to go with metropolis Monte Carlo method using Markov chain. I'm not into this methods, but I'm just using them as a tool (...
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1answer
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Spin statistical theorem in curved spacetime

In Wikipedia https://en.wikipedia.org/wiki/Spin%E2%80%93statistics_theorem?wprov=sfti1 It states that “The proof requires the following assumptions: The theory has a Lorentz-invariant ...
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Mathematical proof that Fermions are half-integer spin particles, and half-integer spin particles are Fermions [duplicate]

See: Why must fermions be antisymmetric? What causes the Pauli exclusion principle (and why does spin 1/2 = fermion)? It was said that all fermions were half integer spin particles and all half ...
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1answer
181 views

Apparent discrepancy between partition function from density matrix and partition function from counting microstates in finite level system

Consider a quantum two-level system indexed by states $|l\rangle = |0\rangle,|1\rangle$ and energies $\epsilon_l$, where $\epsilon_0 = 0$,$\epsilon_1 = \epsilon$. I throw in 2 bosons into the system ...
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424 views

Boson or Fermion

How do you deduce that an atom is a fermion or a boson? Do you determine it from the number of neutrons because "electrons and protons cancel out each other in a neutral atom"? What does this have to ...
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1answer
87 views

How do you know $W$ and $Z$ bosons are really bosons and not fermions?

It has been always said that $W$ an $Z$ bosons are bosons and not fermions but is there any experimental trial that prove that? Has anyone put two of them in the same quantum state or studies have ...
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154 views

1D Ising Model in B-Field Partition Function (2 Spins)

I have a one-dimensional system of two Spins ( $\sigma_1$, $\sigma_2$) in a magnetic field B with energy: \begin{equation} E = -J \sigma_1 \sigma_2 -B (\sigma_1 + \sigma_2) \end{equation} each $\sigma$...
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263 views

Information from four point correlation functions in Ising model

For a one-dimensional classical Ising model with the Hamiltonian $$H=-J \sum_{i}\sigma_{i} \, \sigma_{i+1}$$ where $\sigma=\left\{+1,-1\right\}$ one can calculate two point correlation for the spins $$...
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154 views

Why are spins initially coherent after 90 degree pulse in NMR?

In NMR we apply a 90 degree radio frequency pulse to the sample. This causes magnetization vector to fall into transverse plane. Then the relaxation of initial phase coherence occurs. Why are the ...
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1answer
414 views

Why must fermion fields anticommute and bosons commute?

Fermion fields must satisfy anticommutation relation. But why? I know that unless they anti-commute the Pauli exclusion principle cannot be satisfied. But is there some other deeper/fundamental ...