Same potential?
Compare two SU(7) bulk contents using the full-potential coordinates, and distinguish equal potentials from equal low-order moments.
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 counting different matter descriptions as different one-loop potentials. It also demonstrates a common limitation of approximations: two models can agree on the few coefficients used near a symmetric point while differing elsewhere. The algebraic comparison and the numerical graph are deliberately shown together so you can tell an identity from a visually small difference.
First steps
- Use the shared model as content A and copy it into content B.
- Apply a displayed kernel relation or edit B's multiplicities.
- Read the five-coordinate comparison as well as the curves.
- Load the equal-moment example to see how matching local moments can leave different full potentials.
Controls and inputs
| Control | Meaning | Try this |
|---|---|---|
| Content B: copy, clear and multiplicities | Creates the second input independently of the shared content A. | Copy A first so the initial equality has an obvious cause. |
| Kernel-relation arrows | Rewrite a content using a relation that leaves the potential coordinates unchanged, subject to valid nonnegative counts. | Apply an available arrow and inspect which multiplicities change. |
| Canonical of A | Chooses the canonical representative used by the implemented algebraic reduction. | Compare its content with A while keeping the coordinates in view. |
| Equal-moment example and plot range | Loads a pair with matching selected local moments and lets you compare local and full phase ranges. | Read the small-angle view, then expand to the full range. |
Reading the results
| Result | Meaning |
|---|---|
| Five potential coordinates | The complete identity test for this stated family. Equality has a stronger meaning than agreement at sampled plot points. |
| Two potential curves | A numerical illustration of the algebraic comparison. Use the full range to inspect structure hidden by a local zoom. |
| Moment diagnostics and evidence | Show which selected moments coincide and what the available exact or interval checks establish about the example. |
For the stated potential family, equality of the five coordinates is the algebraic equality criterion. Two overlapping plots alone cannot prove an identity. Matching only the selected local moments is weaker and can leave different global behaviour.
Worked example
Compare exact equality with approximate agreement
- Copy A to B and verify coordinate equality.
- Apply a permitted kernel relation; the content changes while the identity criterion remains satisfied.
- Load the equal-moment example.
- Compare the local and full plots and read the separate full-potential conclusion.
What to expect: A kernel rewrite and a low-order moment match have different logical strength. Use the coordinate or certificate statement, not the apparent thickness of an overlaid curve.
Scope and limitations
- The equality criterion concerns the implemented one-loop potential family and its conventions. It does not prove that all particle spectra, couplings or boundary sectors are identical.
- Numerical agreement at finitely many phase values does not establish an analytic identity.
- A canonical representative of a potential is not automatically a canonical representative of the complete physical theory.
If something is unclear
A relation arrow cannot be used.
Check whether the proposed rewrite would require a negative multiplicity.
The curves look identical but the tool distinguishes them.
Read the exact coordinate comparison and use the full phase range; a plot may hide a small or distant difference.
Terms used here
Sources and attribution
Current instrument guide. Archived editions retain their own scope.
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