QFT with vanishing vacuum expectation value and perturbation theory

In summary: So perturbative calculations work just the same for theories with vanishing VEVs as for theories with non-vanishing VEVs.
  • #1
The Tortoise-Man
95
5
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?
 
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  • #2
Ad 1: That's of course wrong. The electroweak part of the standard model is perfectly suited for perturbative calculations, and the VEV of the Higgs field is non-zero, which is crucial for the entire phenomenology of the weak interaction, described by a Higgsed local gauge theory.

The same holds true for QCD and effective hadronic models, where we have a gluon as well as a quark condensate, the former being responsible for almost all of the mass of the light hadrons and the latter for the spontaneous breaking of the approximate chiral symmetry of the light-quark sector with the pions as the pseudo-scalar pseudo-Goldstone modes.
 
  • #3
Thank you, so the statement from wikipedia is wrong. Nevertheless are there in general any fundamental advantages to work with field theories with vanishing vacuum expectation values in sense of that only in case of fields with vanishing vev certain calculational techniques are available? Or in other words where exactly for theories with non-vanishing vev arise the characteristic obstructions which we in other case not have?
 
  • #4
I don't know, which "obstructions" you mean. Perturbation theory for scattering processes, i.e., considering a few (usually 2) particles in the initial state and asking for the cross section for all kinds of reactions in the collision needs stable ground state. In the case that the VEV of a field (due to Poincare invariance that's usually a constant expectation value of some scalar field) is non-zero there is nothing special concerning perturbation theory except that in the Feynman rules usually this VEV occurs.
 

Related to QFT with vanishing vacuum expectation value and perturbation theory

1. What is QFT with vanishing vacuum expectation value?

QFT with vanishing vacuum expectation value is a theoretical framework in quantum field theory where the vacuum state has a zero expectation value for all fields. This means that the vacuum state has no inherent energy or particles, and all particles and their interactions are described as excitations of this vacuum state.

2. How does perturbation theory apply to QFT with vanishing vacuum expectation value?

Perturbation theory is a mathematical technique used to calculate approximate solutions to complex problems. In QFT with vanishing vacuum expectation value, perturbation theory is used to calculate the interactions between particles as small deviations from the vacuum state. This allows for the calculation of particle interactions that would otherwise be too complex to solve directly.

3. What are the applications of QFT with vanishing vacuum expectation value?

QFT with vanishing vacuum expectation value has many applications in theoretical physics, including the study of particle physics and the behavior of matter at high energies. It is also used in the development of quantum field theories, which are essential for understanding the fundamental forces of nature.

4. How does QFT with vanishing vacuum expectation value differ from other quantum field theories?

QFT with vanishing vacuum expectation value differs from other quantum field theories in that it assumes a vacuum state with a zero expectation value for all fields. This is in contrast to other theories, such as the Standard Model, which have non-zero vacuum expectation values for certain fields.

5. What are the challenges in studying QFT with vanishing vacuum expectation value?

One of the main challenges in studying QFT with vanishing vacuum expectation value is the complexity of the mathematical calculations involved. Perturbation theory can only provide approximate solutions, and more accurate methods are needed to fully understand the behavior of particles in this framework. Additionally, experimental evidence for QFT with vanishing vacuum expectation value is still limited, making it difficult to validate theoretical predictions.

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