Discussion Overview
The discussion focuses on the open string Hamiltonian as presented in Witten's book, particularly addressing the implications of the Virasoro constraint and whether the Hamiltonian is zero. The scope includes theoretical aspects of string theory and Hamiltonian mechanics.
Discussion Character
- Technical explanation
- Debate/contested
Main Points Raised
- One participant presents the open string Hamiltonian and questions its validity under the Virasoro constraint, suggesting it may lead to a zero Hamiltonian.
- Another participant asserts that the Hamiltonian is indeed zero on shell for systems with diffeomorphism invariance, referencing general relativity as a related example.
- Further contributions suggest that any parametrization invariance results in a vanishing Hamiltonian, with a simple point particle offered as an analogy.
- A later post introduces a new topic regarding the Virasoro operators and the mass of the string, indicating a shift in focus from the Hamiltonian discussion.
- Additional references are provided for further reading on the mass of an open string, both classically and quantum mechanically.
Areas of Agreement / Disagreement
Participants express differing views on the implications of the Virasoro constraint on the Hamiltonian, with some asserting it is zero while others provide examples of systems where this holds true. The discussion remains unresolved regarding the broader implications for string theory.
Contextual Notes
The discussion does not resolve the assumptions underlying the Virasoro constraint or the conditions under which the Hamiltonian is considered zero. There may be dependencies on specific definitions and interpretations within string theory.
Who May Find This Useful
Readers interested in string theory, Hamiltonian mechanics, and the implications of diffeomorphism invariance may find this discussion relevant.