New answers tagged fermions
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Grassmann algebras, spinors, and Fermions
Why is the Grassmann algebra part of the field $(v_1\wedge\cdots\wedge v_n)$
often omitted in physics textbooks when discussing Fermionic theories and is only brought up when the path integral is ...
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Why must Grassmann algebras for Fermionic theories be infinite dimensional?
Ref. 1 does define a $2^N$-dimensional Grassmann algebra $\Lambda_N$ with finitely many anti-commuting generators $\xi^1,\ldots,\xi^N,$ and proceeds to write
We shall usually, though not always, deal ...
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Symmetry of spin states with three electrons
How to understand symmetry if there are more than two particles?
What to do with the statement that the wave function should be antisymmetric if two particles are exchanged?
Is it possible to separate ...
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Symmetry of spin states with three electrons
The Pauli principle says that the wave function of identical fermions must be antisymmetric under the simultaneous interchange of spatial and spin coordinates between any two fermions. This is why in ...
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Symmetry of spin states with three electrons
(2) What to do is: you can't put 3 electrons in the same state (disregarding spin). This is how atoms work: H, He get all required electron(s) in the $^1S$ orbital, but when we get to Li, that shell ...
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Inversion on fermionic operators
The matrix $𝑈_{𝑙𝑚}$ is not translationally invariant, i.e. it is not simply a function of $Δ=𝑙−𝑚$. This is because you pick an origin when you think of inversions.
This is also clear from writing ...
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Time evolution and anti-unitary operators
Ah, I see. It comes down to the fact that $\hat{U}$ is not linear. (It is antilinear, duh!). And it doesn't play well with unitary transformation.
Let's say you define $\hat{U}$ by what it does to ...
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Time evolution and anti-unitary operators
In general if $H$ is symmetric under a unitary or anti-unitary transformation $\hat U$, it implies that if $|\psi(t)\rangle$ is a solution to the Schroedinger equation $i\hbar \frac{d}{dt}|\psi(t)\...
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Spinor components in Dirac Equation are 'coupling'?
I'm not sure what physical intuition you are after about the coupled components of Dirac spinors, which describe a particle and an antiparticle of both spin directions each. The Dirac Equation with ...
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Grassmann Numbers, anticommutation and derivative rules
For what it's worth, OP is apparently considering left derivatives, which means that the derivatives act from left, and that it satisfies the following graded Leibniz rule
$$ \frac{\partial_L}{\...
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