Questions tagged [spin-statistics]

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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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Bosonic Fock space

Given the single particle Hilbert space $H$ with basis $(|e_\alpha\rangle)_\alpha$, consider the free Fock space $$\mathcal{F}(H)=\bigoplus_{n\ge 0} H^{\otimes n}.$$ According to experimental facts, ...
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'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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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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118 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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How will we know whether the interacting $\phi^4$ theory eigenstates are bosonic states/symmetric?

For the free scalar field $\phi$, the commutation relation $[\phi(x),\pi(y)]=i\delta(\vec{x}-\vec{y})$ leads to the bosonic commutation relation $[a_p,a_q^\dagger]=\delta(\vec{p}-\vec{q})$. From there,...
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PCT Theorem and PCT, spin and statistics, and all that book

I am reading through PCT, spin and statistics, and all that, and trying to understand the construction on page 15 specifically equation (1-26) and the calculations that follows, what I can't see is ...
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51 views

Lorentz Binary Group actions in Spin Statistic theorem: $D[-1] = (-1)^{2j}$ in Novozhilov

In Novozhilov's book "Introduction to Elementary Particle Field Theory" there is a reproduction of Weinberg's S-matrix covariant proof of the Spin Statistics Theorem. I've referenced this in ...
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Antisymmetric under exchange of spins means invariant under rotation of spins?

How can I prove that this is true? I'm trying to build a BCS ground state wavefunction that is invariant under rotation of spins. The way that I wrote it is: $$u_{k}^{2}+u_{k}v_{k}\left ( c_{k,+1}^{\...
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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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126 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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34 views

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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164 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
64 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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406 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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56 views

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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1answer
46 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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22 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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137 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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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
71 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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128 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
58 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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67 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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364 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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66 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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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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69 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 Grassmann fields “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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39 views

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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238 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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185 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
98 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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251 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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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 ...