Requirements on Quantum Field Theory to be correct physical theory?

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SUMMARY

The discussion centers on the five essential requirements for a Hamiltonian in Quantum Field Theory (QFT) to be considered a valid physical theory. These requirements include: 1) Unitarity, necessitating the Hamiltonian to be a Hermitian operator; 2) Cluster decomposition, which relates to microcausality and locality; 3) Poincaré invariance, ensuring the Hamiltonian remains invariant under Poincaré transformations; 4) Stability, requiring the Hamiltonian to be bounded; and 5) Renormalizability, which restricts the form of the interaction Hamiltonian. Participants seek comprehensive resources that outline these requirements clearly, with a recommendation for Weinberg's "Quantum Field Theory" volumes I and II.

PREREQUISITES
  • Understanding of Hermitian operators in quantum mechanics
  • Familiarity with microcausality and locality concepts
  • Knowledge of Poincaré transformations in physics
  • Basic principles of renormalization in quantum field theory
NEXT STEPS
  • Study the concept of Unitarity in quantum mechanics
  • Research Cluster decomposition and its implications in QFT
  • Explore Poincaré invariance and its role in physical theories
  • Read about Renormalization techniques in Quantum Field Theory
USEFUL FOR

Physicists, graduate students in theoretical physics, and researchers interested in the foundational aspects of Quantum Field Theory and its requirements for a valid physical framework.

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In some class notes I found those conditions interpreted as a "five requirements on Hamiltonian of physical system":

1. Unitarity -> Hamiltonian has to be hermitian operator
2. Claster decomposition (microcausality and locality) -> (? missing part)
3. Poincare invariance -> Hamiltonian invariance under Poincare transformations
4. Stability -> Hamiltonian has to be under bounded
5. Renormalizability -> Form of interaction Hamiltonian is restricted (?)

Those notes are very concise and not so reader friendly (and some parts missing), so I search in books for further explanations, but I can't find those requirements in any book structured like this in one place.

Anyone know some book or text with this topic ("requirements for qft to be correct phisical theory" or something like that) ?

Thanks
 
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I am not sure but I would recommend to check Weinberg, QFT I-II
 

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