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Quantum Field Theory operators

5 operators in the quantum_field_theory category of the live registry. Each is a named formula you can compose inside a state contract or call directly through POST /api/zeq/compute. KO42 is always on; add up to three more per call (total ≤ 4), per the 7-step protocol.

OperatorDescriptionEquation
QFT_COMMUTATIONEqual-time canonical commutation relation for a scalar quantum field and its conjugate momentum.[\hat{\phi}(\vec{x},t), \hat{\pi}(\vec{y},t)] = i\hbar \delta^3(\vec{x} - \vec{y})
QFT_PATH_INTEGRALGenerating functional for a scalar field theory expressed as a path integral over all field configurations.Z[J] = \int \mathcal{D}\phi \; e^{i \int d^4 x \, [\mathcal{L}(\phi) + J \phi]}
QFT_PROPAGATORFeynman propagator for a free scalar field giving the amplitude for particle propagation between spacetime points.\Delta_F(p) = \frac{i}{p^2 - m^2 + i\epsilon}
QFT_SELF_ENERGYOne-loop self-energy integral in scalar QFT contributing to mass renormalization via momentum-space integration.\Sigma(p) = -i \lambda \int \frac{d^4 k}{(2\pi)^4} \frac{1}{k^2 - m^2 + i\epsilon}
QFT_WARD_IDENTITYWard-Takahashi identity relating the vertex function to the inverse propagator, ensuring gauge invariance of QED.q_\mu \Gamma^\mu(p+q, p) = S^{-1}(p+q) - S^{-1}(p)

Compute with one of these​

curl -sS -X POST https://zeqsdk.com/api/zeq/compute \
  -H "Authorization: Bearer $ZEQ_KEY" \
  -H "Content-Type: application/json" \
  -d '{"operators":["QFT_COMMUTATION"],"inputs":{}}'

The response carries the bare physics value, its unit and uncertainty, the generated master equation, and a signed envelope you can verify on any node.

See also​