Computed Diagram Summary
This planner estimates topology, scaling, and visual structure for a connected interaction sketch.
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Result Details
Schematic Preview
Lines show external and internal connections. Curved lines suggest loop corrections. This preview is schematic, not a full symbolic derivation.
Vertex Progression Chart
Calculator Inputs
Use this page to estimate a connected interaction sketch. The tool checks topology consistency, projects loop structure, and compares relative scaling across vertex order.
Example Data Table
These sample rows show how the topology changes with interaction order and leg structure.
| Scenario | Incoming | Outgoing | Legs/Vertex | Vertices | Internal Lines | Loops | Class |
|---|---|---|---|---|---|---|---|
| Electron scattering tree | 2 | 2 | 3 | 2 | 1 | 0 | Tree level |
| Vacuum polarization sketch | 2 | 2 | 3 | 4 | 4 | 1 | One loop |
| Self energy sketch | 1 | 1 | 3 | 2 | 2 | 1 | One loop |
| Four boson contact | 2 | 2 | 4 | 1 | 0 | 0 | Tree level |
Formula Used
1) External line total
E = Ein + Eout
2) Internal line estimate
I = (kV - E) / 2
Here, k is legs per vertex and V is the number of vertices. The quantity must stay non-negative and even.
3) Loop count for a connected diagram
L = I - V + 1
4) Relative amplitude proxy
A = (Nf/S) × (g × Fv)V × (Fp)I × (Q/M)L + max(D-4,0)
This is a comparison metric. It is not a replacement for a full renormalized matrix-element calculation.
5) Complexity score
C = E + 2V + 3I + 6L + max(D-4,0)
How to Use This Calculator
- Enter the number of incoming and outgoing particles.
- Choose the interaction order using vertices and legs per vertex.
- Set coupling, symmetry, and scaling factors for your model.
- Click Generate Result to compute topology and plotting data.
- Review the status banner before trusting the interpretation.
- Use the schematic preview to inspect the diagram shape quickly.
- Export the current summary using CSV or PDF buttons.
- Adjust vertices to compare how loop count grows with perturbative order.
Frequently Asked Questions
1) What does this generator estimate?
It estimates connected diagram topology from user inputs. You get external lines, internal lines, loop count, a relative amplitude proxy, complexity score, and a schematic visual preview.
2) Does it create exact textbook diagrams?
No. It creates a planning sketch and topology estimate. Exact field-theory diagrams still require explicit particle assignments, conservation laws, propagators, and symbolic amplitude construction.
3) Why can a topology be inconsistent?
A topology becomes inconsistent when the available interaction legs cannot support the chosen external lines, or when the leg balance leaves a non-integer number of internal lines.
4) What does the loop count mean?
Loop count measures closed internal momentum cycles in a connected sketch. Tree level has zero loops. One-loop and higher corrections usually raise complexity and computational cost.
5) How should I choose the coupling constant?
Use a value that matches your model’s perturbative scale. Smaller couplings suppress high-order contributions. Larger values raise the proxy quickly and can signal a weaker perturbative expansion.
6) Why is there an amplitude proxy instead of an amplitude?
A full amplitude needs particle identities, Lorentz structure, spinors, polarization rules, regularization choices, and renormalization details. The proxy is only a comparative scaling indicator.
7) Can I use four-leg or higher interactions?
Yes. Select a larger legs-per-vertex value to model contact interactions or effective operators. The topological formulas adapt immediately to the new interaction structure.
8) What do the CSV and PDF exports include?
They include the current inputs, summary metrics, topology status, and vertex progression data used in the chart. This makes comparison and reporting easier.