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The Tortoise-Man

- 95

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In This wikipedia article is said:

"If the quantum field theory can be accurately described through perturbation theory, then the properties of the vacuum are analogous to the properties of the ground state of a quantum mechanical harmonic oscillator, or more accurately, the ground state of a measurement problem. In this case the vacuum expectation value (VEV) of any field operator vanishes. For quantum field theories in which perturbation theory breaks down at low energies (for example, Quantum chromodynamics or the BCS theory of superconductivity) field operators may have non-vanishing vacuum expectation values called condensates."

Question 1: Why if perturbation theory is applicable on a quantum field theory, then necessary the VEV of every field operator in this theory must vanish? Can it be directly proved?

Question 2: Can this also be "reversed" and used as a criterion when a QTF is approachable by techniques from perturbation theory? Namely if and only if all VEVs of every field operator in this theory vanish?

Meta question: Can it be summarized that that's exactly THE reason that whenever it is possible the field theories with vanishing VEV's are preferred BECAUSE these allow to use techniques from PT?

"If the quantum field theory can be accurately described through perturbation theory, then the properties of the vacuum are analogous to the properties of the ground state of a quantum mechanical harmonic oscillator, or more accurately, the ground state of a measurement problem. In this case the vacuum expectation value (VEV) of any field operator vanishes. For quantum field theories in which perturbation theory breaks down at low energies (for example, Quantum chromodynamics or the BCS theory of superconductivity) field operators may have non-vanishing vacuum expectation values called condensates."

Question 1: Why if perturbation theory is applicable on a quantum field theory, then necessary the VEV of every field operator in this theory must vanish? Can it be directly proved?

Question 2: Can this also be "reversed" and used as a criterion when a QTF is approachable by techniques from perturbation theory? Namely if and only if all VEVs of every field operator in this theory vanish?

Meta question: Can it be summarized that that's exactly THE reason that whenever it is possible the field theories with vanishing VEV's are preferred BECAUSE these allow to use techniques from PT?

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