# Tagged Questions

Fermions are particles with an intrinsic angular momentum (i.e. spin) equal to a "half integer" number of fundamental units: $\frac{(2n+1)}{2} \hbar$ for integer $n$. Fermions are required to be in a quantum state that is globally anti-symmetric, which leads to the Pauli Exclusion Principle barring ...

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### Is this a good argument against time travel? [closed]

Two fermions in two different points of space cannot be made to exist in the same point of space. It follows then that two fermions in two different times cannot be made to exist in the same time. ...
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### Why must fermions be antisymmetric? [closed]

I have read that fermions cannot exist in the same state simultaneously. I understand why indistinguishable particles with an antisymmetric superposition of states can't exist in the same state ...
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### Path integral for boson vs fermion (soft derivation + use )

I have been looking around for a soft derivation with a bit of detail for boson and fermion path integrals that I could understand. I have a passing knowledge generally of what a path integral is in ...
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### No two identical fermions can have the same quantum state at once?

This is the Pauli Exclusion Principle, but I have a question about it... It states that no two identical fermions can have the same quantum state, but what about different fermions having the same ...
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### Convert Grassmann numbers to real numbers [closed]

We know Grassmann numbers are complex numbers. Hence Grassmann integrals are also complex. How can we convert a Grassmann integral into real one, ie is there any transformation of converting complex ...
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### Is there a phase transition for degenerate matter?

Does electron or neutron degenerate matter undergo a phase transition? Are there any thermodynamic quantities that are discontinuous?
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### Why is Fermi-Dirac type of distribution used in semiconductors?

We assume that distribution of electrons follows Fermi-Dirac distribution / statistics in semiconductor model which will help to find the concentrations of electron and holes and the relationship ...
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### How to evaluate fermion operator in product state?

I have a question concerning the implementation of DMRG for fermion chains. Suppose I have a simple chain H=t\sum_{<i,j>}\sum_{\sigma}c^{\dagger}_{i\sigma}c_{j\sigma}, \end{...
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### Smoothness of the energy levels of a generic Hamiltonian

Let us take an Hamiltonian $H(\xi)$ which depends on a set of parameters $\xi$, and assume that the matrix elements $h_{ij}(\xi)$ of the Hamiltonian are smooth complex functions of the parameters $\xi$...
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### Are Fermi-Dirac-statistics relevant to view the universal system of neutrinos?

Should the energy distribution of neutrinos be affected by Fermi-Dirac statistics? And if so, what would the consequences be? Could this locally cause weak interaction because of the Pauli Exclusion ...
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### Massless bosons but not massless fermions?

I noticed some article on massless Weyl fermions and it got me thinking. I'm wondering if there is any explanation for why bosons (specifically gauge bosons) can be massless (photon and gluon) but we ...
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### What mathematical structure describes superspace and superfields?

In every book related to supersymmetry I have encountered at some point the idea of superspace is introduced. Superspace is presented as a space spanned by 4 "normal" directions and 4 Grassmannian ...
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### Fermionic path integral on the disk - Recovering the vacuum state

I'm trying to get a better feel for the operator to state map in quantum field theory. There is a general claim for 2d theories that doing the path integral on a disk with no operator insertions gives ...
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### Fourier transform of a set of L fermions operators

I have a set of L fermion creation and annihilation operators: $\lbrace{\hat{C}^+_1,...,\hat{C}^+_L\rbrace}$ and $\lbrace{\hat{C}^-_1,...,\hat{C}^-_L\rbrace}$. Every $\hat{C}^+_l,\hat{C}^-_l$ ...
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### Can someone explain the quote “there would be no chemistry if electrons acted as bosons”?

I am reading a book and in a quote it says that if electrons acted as bosons, then all the electrons would occupy the lowest energy state, and there would be no chemistry. What does the author mean ...
When studying the CFT of a complex fermion $\Psi$ we know that if it's periodic, ie if $$\Psi(\sigma_1+2\pi,\sigma_2)=\Psi(\sigma_1,\sigma_2)$$ then there is a doubly degenerate Ramond vacuum which I ...