An alternative method of quantization: the existence of classical fields

Annihilation operators associated with unstable vacua in non-equilibrium thermo-field dynamics

“…(The equation (21) corresponds to (2).) Note that the operators satisfying the condition (21) are called tildian operators that are not necessarily Hermitian.…”

“…Note that L is a superoperator [2], i.e., an operator acting on operators. The expectation value of an observable operator A is given by A t = tr Aρ(t) = tr Ae −iLt ρ(0) = tr e iLt Ae −iLt ρ(0) = tr A(t)ρ(0),…”

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“…The logical next step is to consider linear superoperators 3 S in Liouville space [11]. Ordinary operators A can be promoted to superoperators in several ways.…”

“…For instance, parity is a quantum but not a classical observable. 11 Indeed, the whole phase space can be reconstructed from the observable algebra [15], so that a superoperator preserving this algebra has to preserve phase space.…”

“…Let us momentarily return to the detailed Hamiltonian (11). For E 1 = 0, it describes a flux qubit coupled to a fluctuating charge.…”