One model, every verdict
Compare supported model diagnostics across gauge-equivalent boundary descriptions and identify which results remain unchanged in that comparison.
Control names are kept as they appear in the application. Start with a reference, change one input at a time, and retain the assumptions with your result.
What this tool is for
Use this to avoid mistaking a convenient description of a model for an observable property of the theory. A group or spectrum read at a fixed symmetric point can move under an equivalent boundary description. The dossier recomputes its diagnostics to show which quantities survive that change and which questions cannot be answered by the available calculation.
First steps
- Start from the model in SU(N) builder.
- Select another member of its displayed equivalence class.
- Read the theory, frame and declined tags with their explanations.
- Run the separate separation test to ask whether an invariant diagnostic distinguishes different classes.
Controls and inputs
| Control | Meaning | Try this |
|---|---|---|
| Shared builder model | Defines the equivalence class and diagnostics being examined. | Begin with a model having more than one displayed class member. |
| Class-member selection | Changes the boundary description within the displayed equivalence class. | Compare the same row before and after changing member. |
| Separation test | Asks whether the measured invariant distinguishes the different tested classes. | Run it after understanding why a row is invariant within one class. |
Reading the results
| Result | Meaning |
|---|---|
| Theory / frame / declined tags | Summarize invariance, dependence on the chosen description, or a reason the calculation cannot supply a verdict. |
| Symmetric-point and vacuum diagnostics | Show why the point at which a property is evaluated matters to its interpretation. |
| Separation results | An invariant may be shared by several different classes and therefore fail to identify a theory uniquely. |
Invariance across the tested equivalent descriptions and ability to distinguish different theories are separate properties. The tags report the performed comparison; they should not be extended into an untested classification theorem.
Worked example
Test a tempting model label
- Choose a model with several equivalent boundary descriptions.
- Record its apparent group and one vacuum diagnostic.
- Select another class member and compare the same rows.
- Read the separation test before using an invariant as a unique model identifier.
What to expect: A quantity can be invariant without uniquely identifying the theory, and a useful coordinate label can still depend on the chosen frame.
Scope and limitations
- The conclusions cover the displayed diagnostics and equivalence comparison.
- A numerical comparison is not automatically a proof over every possible model.
- A declined row should retain its stated reason; it is not a zero or a successful test.
If something is unclear
A label changes even though the selected descriptions are equivalent.
Check whether the row is evaluated at a fixed symmetric point and tagged as frame-dependent.
An invariant fails to separate two classes.
Use another diagnostic; invariance alone does not imply completeness as a classifier.
Terms used here
Sources and attribution
Current instrument guide. Archived editions retain their own scope.
Back to top