- #1
Turbotanten
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If we were to quantize the Dirac field using commutation relations instead of anticommutation relations we would end up with the Hamiltonian, see Peskin and Schroeder
$$
H = \int\frac{d^3p}{(2\pi)^3}E_p
\sum_{s=1}^2
\Big(
a^{s\dagger}_\textbf{p}a^s_\textbf{p}
-b^{s\dagger}_{\textbf{p}}b^s_{\textbf{p}}
\Big). \tag{3.90}
$$
They write that this Hamiltonian is not bounded below. And that by creating more and more particles with ##b^\dagger## we could lower the energy indefinitely.
What do they mean when they say that we could lower the energy indefinitely by creating more and more particles with ##b^\dagger##? Do they mean that we can lower the energy to negative infinity or do they just mean that we can lower the energy indefinitely to get to the ground state of the system?
Also what does it mean for the Hamiltonian to not be bounded below?
$$
H = \int\frac{d^3p}{(2\pi)^3}E_p
\sum_{s=1}^2
\Big(
a^{s\dagger}_\textbf{p}a^s_\textbf{p}
-b^{s\dagger}_{\textbf{p}}b^s_{\textbf{p}}
\Big). \tag{3.90}
$$
They write that this Hamiltonian is not bounded below. And that by creating more and more particles with ##b^\dagger## we could lower the energy indefinitely.
What do they mean when they say that we could lower the energy indefinitely by creating more and more particles with ##b^\dagger##? Do they mean that we can lower the energy to negative infinity or do they just mean that we can lower the energy indefinitely to get to the ground state of the system?
Also what does it mean for the Hamiltonian to not be bounded below?