Requirements on Quantum Field Theory to be correct physical theory?

Chapter 2 and 4. There he is discussing the requirements for a quantum field theory to be a correct physical theory. In summary, the five requirements on the Hamiltonian of a physical system are: unitarity, cluster decomposition, Poincare invariance, stability, and renormalizability. These conditions ensure that the Hamiltonian is hermitian, invariant under Poincare transformations, under bounded, and has a restricted form of interaction. These requirements can be found in Weinberg's QFT I-II, specifically in Chapters 2 and 4.
  • #1
multipole
2
0
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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  • #2
I am not sure but I would recommend to check Weinberg, QFT I-II
 

1. What is Quantum Field Theory (QFT)?

Quantum Field Theory is a theoretical framework in physics that combines the principles of quantum mechanics and special relativity to describe the behavior of elementary particles and their interactions.

2. What are the key requirements for QFT to be considered a correct physical theory?

There are several key requirements for QFT to be considered a correct physical theory, including the principles of locality, causality, and unitarity. It must also be able to accurately describe and predict observable phenomena and be consistent with experimental data.

3. How does QFT relate to other theories in physics?

QFT is a more comprehensive and fundamental theory than classical mechanics or special relativity. It provides a framework for understanding and unifying other theories in physics, such as quantum electrodynamics and the standard model of particle physics.

4. What challenges are associated with developing a correct QFT?

One of the major challenges in developing a correct QFT is the issue of renormalization, which involves dealing with infinite quantities that arise in calculations. Another challenge is the theoretical and experimental verification of the theory, as it requires highly advanced technology and complex experiments.

5. How does QFT impact our understanding of the universe?

QFT has greatly impacted our understanding of the universe by providing a deeper understanding of the fundamental building blocks of matter, as well as the fundamental forces that govern their interactions. It has also led to the development of advanced technologies, such as quantum computing, that have the potential to revolutionize many aspects of our lives.

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