Discussion Overview
The discussion revolves around the analytic continuation to Euclidean space in the context of gauge fields and the implications for maintaining a compact gauge group. Participants explore the relationship between the continuation of gauge fields and the properties of gauge transformations, particularly in the transition from Minkowski to Euclidean space.
Discussion Character
- Exploratory
- Technical explanation
- Conceptual clarification
Main Points Raised
- One participant notes the necessity of continuing the gauge field when transitioning to Euclidean space to maintain the compactness of the gauge group.
- Another participant suggests that this requirement is related to keeping the representation of the gauge transformation unitary and finite dimensional.
- A request for sources or methods to demonstrate this relationship is made, indicating a desire for further clarification or evidence.
- It is mentioned that transitioning from Minkowski space to Euclidean space involves substituting the proper orthochronous Lorentz group with O(4), which affects the nature of four-vectors and the gauge group.
Areas of Agreement / Disagreement
Participants express varying levels of understanding and seek clarification on specific aspects, indicating that the discussion remains unresolved with multiple viewpoints on the implications of the analytic continuation.
Contextual Notes
There are references to specific texts and authors that may address the topic, but no consensus on a definitive source or explanation is reached. The discussion highlights the complexity of the relationship between gauge fields and their transformations in different spacetime signatures.
Who May Find This Useful
This discussion may be of interest to graduate students and researchers in theoretical physics, particularly those studying quantum field theory and gauge theories.