Discussion Overview
The discussion revolves around clarifications regarding the S-matrix in quantum field theory, particularly its relation to creation and annihilation operators and their evolution under the interaction Hamiltonian. Participants explore the implications of these operators acting on the vacuum state and the interpretation of the S-matrix in specific contexts.
Discussion Character
- Exploratory
- Technical explanation
- Debate/contested
Main Points Raised
- One participant notes that the creation and annihilation operators at ##\pm\infty## are not the same due to their evolution with the full interaction Hamiltonian, suggesting they have different values over time.
- Another participant expresses confusion about the S-matrix's role in the expression $$=$$, questioning whether this indicates that the S-matrix does nothing in this context.
- There is a discussion about the necessity of terms like ##e^{iHt}## to evolve the operators between different times, raising questions about the use of the S-matrix versus the usual time evolution operator.
- One participant points out that Schwartz mentions the dependence of the operators on ##e^{iHt}## and suggests that the derivation may be elaborated in later chapters, but notes a lack of explanation regarding the absence of the S-matrix in certain contexts.
- A reference to a specific page in Schwartz's text is provided for further clarification on the topic.
Areas of Agreement / Disagreement
Participants express uncertainty regarding the interpretation and application of the S-matrix, with no consensus reached on its implications or the necessity of certain terms in the evolution of operators.
Contextual Notes
Participants reference different texts and interpretations, indicating potential variations in definitions and approaches to the S-matrix and vacuum states, which may affect their understanding of the topic.
