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Tagged with anticommutator unitarity
4
questions
4
votes
1
answer
145
views
Anticommutation relations for Dirac field at non-equal times
I'm reading this paper by Alfredo Iorio and I have a doubt concerning the anticommutation relations he uses for the Dirac field.
Around eq. (2.25), he wants to find the unitary operator $U$ that ...
- 2,284
1
vote
0
answers
124
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Is there a Stone-von-Neumann theorem-like result for the canonical anti-commutation relations (CAR)?
The canonical commutation relation (CCR)
$$[\phi(x), \pi(y)] = i\hbar\delta(x-y)$$
is kind of the key to basically any bosonic quantum theory. This is due to many different remarkable properties: By ...
- 6,763
0
votes
1
answer
204
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Anti-commutator for annihilation and creation operators: ordering of indices
I'm trying to prove that $\{\tilde a_i,\tilde a_j^{\dagger} \}=\delta_{ij}$, by defining
$\tilde a_i=\sum_j \bar U_{ji}a_j$. U is an unitary matrix and $a_i$ refers to an element of the operator $a$. ...
- 474
0
votes
1
answer
919
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Quantizing the Dirac field using commutation relations leads to an unbounded Hamiltonian?
If we were to quantize the Dirac field using commutation relations instead of anticommutation relations we would end up with the Hamiltonian
$$
H = \int\frac{d^3p}{(2\pi)^3}E_p
\sum_{s=1}^2
...
- 1,135