# Questions tagged [spin-statistics]

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### Topological proof of spin-statistics theorem confusion

I am currently studying the spin-statistics theorem. I have found a section on John Baez's website which presents a "proof" of the spin-statistics theorem. He states the theorem as: This is ...
1 vote
77 views

### Covariant Spin Operator for Massless Fermions

I have been reading the paper The Covariant Definition Of Spin in Relativistic QFT by Hilgevoord and De Kerf, in which the authors derive the spin operator in relativistic quantum theories of free ...
17 views

### About symmetric and anti-symmetric states of a nucleus

Ehrenfest and Oppenheimer published a paper Note on the Statistics of Nuclei in which they write: The "rule" mentioned in paragraph is also stated in the paper. It is: I am unable to follow ...
53 views

### How is the dimension of the vector space we represent $SO(3)$ on determined when discussing the spin of a particle?

Consider a single particle with Hilbert space $L^2(\mathbb{R}^3) \otimes V_\ell$ where $V$ is a vector space of dimension $2\ell + 1$ equipped with a projective unitary representation of $SO(3)$. ...
1 vote
44 views

### Anticommutator Relation of Quantized Fermionic Field and Fermi–Dirac statistics: How are these related?

I'm reading the Wikipedia article about Fermionic field and have some troubles to understand the meaning following phrase: We impose an anticommutator relation (as opposed to a commutation relation ...
1 vote
38 views

### Anyonic and plektonic dark matter?

The most studied types of dark matter particles include supersymmetric particles, spin particles that are either boson or fermions. I wonder if there are research about dark matter being not particles ...
27 views

### Spin polarization, ferromagnetism, and size of energy gap

I thought large band gap (larger than relevant spin-spin interaction energy scale) necessarily means there is no spin-polarization (ie, not ferromagnetic). I thought the reason is that {only when ...
1 vote
111 views

### Angular momentum quantum number $l$ either integer or half integer

I am trying to understand why the angular momentum quantum number $l$ can either be an integer or an half-integer. At least this is stated in the book that I am learning from. It is the book by ...
78 views

### Time Reversal symmetry, Quaternions, and spin-1/2 systems

When one has a system with no spin and time reversal symmetry, one can conclude that the Hamiltonian entries (in a particular basis, of course) must all be real. Can something be said about the ...
150 views

### Why are some collections of fermions considered bosons?

I read that He-4 is a boson because the four fermions in it add up to an integer spin—of zero—hence a boson. Whereas I thought that if the parts are fermions, so is the whole. Is an electron pair a ...
143 views