Discussion Overview
The discussion revolves around the assumption in S matrix theory that interacting particles can be considered free at time \( t = \pm \infty \). Participants explore the implications of this assumption, particularly in the context of the \( \phi^4 \) theory and quantum electrodynamics (QED), questioning the validity of treating particles as free when they are still interacting with the vacuum state.
Discussion Character
- Exploratory
- Technical explanation
- Debate/contested
Main Points Raised
- One participant questions why the interaction term in \( \phi^4 \) theory would vanish at large distances from the experiment, particularly in the context of electron-positron collisions.
- Another participant suggests that the interaction with the vacuum is treated separately and does not affect the collision process, implying that the free electron's properties are distinct from the interactions occurring during the collision.
- A participant raises a point about the difference in operators used to create particles in the two theories, noting that while the particles may be treated as identical at \( \pm \infty \), the operators evolve differently due to the differing vacuum states.
- Links to Haag's theorem are provided, with one participant asserting its irrelevance in practical applications (FAPP) and recommending further reading on the conceptual framework of quantum field theory.
- Another participant emphasizes the fundamental nature of the issue regarding the description of processes in relativistic quantum theory, suggesting that observable quantities pertain only to free particles.
Areas of Agreement / Disagreement
Participants express differing views on the treatment of vacuum interactions and the implications for the S matrix theory. There is no consensus on the validity of the assumption that particles are free at infinity, and the discussion remains unresolved.
Contextual Notes
Participants highlight the complexity of the assumptions involved in the treatment of particles at infinity, including the dependence on definitions of vacuum states and the implications of Haag's theorem, which remain unresolved in the discussion.