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Questions tagged [spin-statistics]

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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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45 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
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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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1answer
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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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1answer
54 views

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
43 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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2answers
154 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
108 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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58 views

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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36 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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44 views

Spin Statistics Theorem wikipedia

I have some questions about a terminus in wikis article about the Spin–statistics_theorem: https://en.wikipedia.org/wiki/Spin%E2%80%93statistics_theorem#General_discussion ...so in paragraph "A ...
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1answer
65 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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1answer
111 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
101 views

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
167 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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2answers
264 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
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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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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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1answer
176 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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1answer
116 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
321 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 ...
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2answers
127 views

Difference between Fermions and electrons [closed]

I'm confused between fermions and electrons. For example say I have a system comprises of three electrons and there are three single particle energy level accessible to each of three electrons. What ...
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1answer
66 views

Do half integer spin fields commute or anti-commute with spin integer fields?

What are the fundamental commutation/anti-commutation relations between half integer and integer spin fields? For instance, in QED do we have \begin{equation} [\psi(x),A^{\mu}(y)]=0 \end{equation} or \...
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2answers
170 views

How is spin-state of an electron defined?

An electron possesses ‘spin’ even at absolute zero. But how are the spin-states identified? It couldn’t be in terms of ‘energy’ states because well, the electron does not possess any energy at all.
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1answer
70 views

Do these pair of diagrams need a relative sign due to Fermi statistics?

Consider the following two diagrams involving a loop correction to some process $q \bar q \rightarrow q \bar q \gamma$. In a special case where I assume that the momenta $p_1$ and $p_2$ are identical (...
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1answer
181 views

Density matrix of a mixture of singlets and triplets

I was wondering how to write the density matrix of two spin-$\frac{1}{2}$ in a mixture of singlets and triplets. By definition for a mixture, $$ \hat{\rho}=\sum_{j}w_j\, |\psi_j \rangle\langle \psi_j| ...
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Is there a leptonic analog of stimulated emission (ie suppressed emission)?

The phenomenon of stimulated emission is often explained by the fact that bosons are excitations in fields that are created by operators that are symmetric under exchange of order. The converse of ...
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Theoretical Proof of Pauli's Exclusion Principle

"No theoretical proof of the Pauli's Exclusion Principle can be given as yet and for the present it must be regarded as something empirical added to and regulating the vector atom model." I've found ...
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2answers
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Are protons and neutrons affected by the Pauli Exclusion Principle?

I'm very confused about the Pauli exclusion principle. Wikipedia states it as "two identical fermions cannot occupy the same quantum state in a quantum system". I understand this for electrons that ...
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224 views

Quantum partition function for spins

I am trying to understand the quantum partition function for spins. The quantum partition function is $$ Z=\text{tr}\left( e^{-\beta \hat{H}} \right) $$ where tr is the trace, and $\hat{H}$ is the ...
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3answers
2k views

Why bosons have integer spin and fermions have half-integer ones?

Due the fact that the fermions are the "block particles" and the bosons are the "carriers" I just came out with the question that, why the "block particle" have half-integer spin and the "carriers" ...
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Why a half-integer spin implies “antisymmetry” on the wave function? [duplicate]

I've read that the Pauli's exclusion principle can be explained because the wave function of fermions (half-interger spin) change sign when you permute two arguments and that this makes it impossible ...
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1answer
133 views

Why does a quantum gas lose its “quantum nature” in the limit $(\epsilon-\mu)/k_BT\gg1$?

Mathematically, the Fermi-Dirac (FD) distribution and Bose-Einstein (BE) distribution coincides with the Maxwell-Boltzmann (MB) distribution in the limit $(\epsilon-\mu)/k_BT\gg 1$. Therefore, in this ...
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1answer
224 views

Link between the Grassmann algebra and spinors

What is the exact link between spinors and the Grassmann algebra? I'm pretty sure there's one, based on the following: The Berezin integral in path integrals is done over the Grassmann algebra of $\...
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2answers
501 views

Why are composite fermions either bosons or fermions but not neither?

The question is getting at something subtle and not necessarily obvious to me. It is often claimed that an atom being composed purely of fermions is either a boson or a fermion itself. I interpret ...
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1answer
956 views

How to find the eigenvalue(s) for joint spin operator states?

I have started learning about spin operators and finding their eigenvalues, I have the following question below which will be split into two parts (the first part is needed to solve the second part). ...
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1answer
229 views

Why isn't the anticommutativity of spinors sufficient as “spin-statistics-theorem”?

From the representation theory of the Lorentz algebra, we know that spinors (objects transforming under the $(\frac{1}{2}, 0)$ and $(0,\frac{1}{2})$ representation), are naturally equipped with a ...
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2answers
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Can the necessity of using anti-commutators for Dirac fields and commutator for Klein-Gorden be deduced from the field equations?

We all learned to use the commutator for quantizing the KG field and the anti-commutator for the Dirac field. We are told (which is correct) so that KG-excitations are bosons and Dirac-excitations ...
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178 views

How to measure spin-spin correlation in Heisenberg Model?

How to measure the spin-spin correlation in Heisenberg Model? I use the QMC method, working on 2d case.
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1answer
142 views

Perturbation propagation in the Ising model

Take the 1D Ising model: A chain of spins (each with two neighbours) with spin values up or down. We start off with all spins up and for simplicity we assume an infinite system. At the location $i$ ...
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1answer
1k views

Integral spin and half integral spin

I am reading a book (Laudau and Lifshitz, Vol. 4, page 94) and it derived why spin-0 should obey Bose quantization and spin-1/2 should obey Fermi Quantization. Then it says, all integral spin ...
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1answer
164 views

What underlies super-selection rule in quantum field theory?

Super-selection rule in quantum field theory states that superpositions of two states with different charges do no exist in nature. What does "charge" mean in this context? Is there a deeper ...
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1answer
54 views

Ginibre inequality in Aizenman & Simon paper

In the paper linked below equation (4) is not well justified. After a lot of reasoning I still can't figure out why the need of taking the hamiltonian in the H' form and how should I use Ginibre ...
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156 views

Spin-charge separation and Spin-Statistics relations

Usually, we associate the half-integer spin to fermion, and the integer spin to boson. And there are constraints like the Spin-Statistics relations. However, in Spin–charge separation or the parton-...
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4answers
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Why does the Pauli exclusion principle not apply to bosons?

The Pauli exclusion principle states that two fermions cannot have the same quantum state simultaneously, but why does this not apply to bosons with whole integer spins?