Discussion Overview
The discussion revolves around the ghost number associated with the field ψ in the context of BRST symmetry, exploring the implications of ghost numbers in the action and the BRST operator. Participants delve into the theoretical aspects of ghost numbers, their conservation, and the role of the BRST operator.
Discussion Character
- Technical explanation
- Conceptual clarification
- Debate/contested
Main Points Raised
- One participant presents the action in BRST symmetry and questions why ψ has a ghost number of -1.
- Another participant asserts that ghost number conservation implies that since the action has ghost number zero and the BRST operator s has ghost number +1, ψ must have ghost number -1.
- A participant expresses confusion about why the s operator has ghost number +1, questioning if it acts as a "charge" of BRST symmetry.
- Another participant suggests that the s operator may function as a "ladder" operator for ghost number.
- It is noted that the s operator represents (anti)commutation with the BRST charge, which carries ghost number +1, thus raising the ghost number by +1 when acting with s.
- A participant mentions that conservation of ghost number is not fundamental and discusses the possibility of using ψ with different ghost numbers, which could break ghost number conservation.
- One participant queries the relationship [Q,Φ] and how it relates to the s operator being a "ladder" operator of ghost number.
- Another participant introduces the ghost number operator N and compares its commutation relations to those of a harmonic oscillator.
- Questions arise about the justification for the commutation relation [N,Q]=+Q and how it leads to the conclusion that the ghost number of s is +1.
- A participant suggests consulting Srednicki's text for further clarification.
- One participant reflects on their understanding, proposing that the full BRST transformation involves a fermionic variable θ with a ghost number of -1, leading to the conclusion that s has ghost number +1.
Areas of Agreement / Disagreement
Participants express varying levels of understanding regarding the ghost number of the s operator and its implications. There is no consensus on the nature of ghost number conservation or the role of the s operator, indicating ongoing debate and exploration of these concepts.
Contextual Notes
Some participants' claims depend on specific interpretations of ghost number conservation and the definitions of operators involved, which remain unresolved in the discussion.