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Results tagged with grassmann-numbers
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user 80810
0
votes
1
answer
149
views
What is the content of an occupied QFT fermionic state?
A simple non-interacting quantum field is constructed by analogy to a harmonic oscillator, with $\hat{x}$ & $\hat{p}$ replaced by operator-valued distributions $\hat{\phi}(r)$ & $\hat{\pi}(r)$, and wi …
- 990
6
votes
1
answer
596
views
What's the ground state wave-functional of a fermion?
The vacuum state, free field wave-functional of a scalar field $\hat\phi(x)$ in the Schrödinger representation of quantum field theory is
$$\begin{array}{cl}
\Psi_0[\phi] &= C\prod_k e^{-\omega(k)\fr …
- 990
9
votes
1
answer
346
views
What's the space of eigenvalues/field configurations for a fermion?
In the Schrödinger picture of quantum field theory, the field eigenstates of a real scalar field $\hat\phi(\mathbf x)$ with $\mathbf x \in\mathbb R^3$ are the states $\hat\phi(\mathbf x)|\phi\rangle=\ …
- 990