Quantum Field Theory operators

5 operators in the quantum_field_theory category of the live registry. Compose them in a contract or call POST /api/zeq/compute — KO42 is always on, plus up to three more per call.

How it computes: dedicated closed-form solver solveQR — real equations over CODATA-2018 constants; where an operator needs a series/matrix/field a scalar cannot express, it refuses honestly. See the solvers.

Operator	Description	Equation
`QFT_COMMUTATION`	Equal-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_INTEGRAL`	Generating 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_PROPAGATOR`	Feynman 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_ENERGY`	One-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_IDENTITY`	Ward-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 one — a real call

Ask the operator which inputs it needs (the honesty contract refuses empty inputs rather than inventing them):

curl -sS -X POST https://zeqsdk.com/api/zeq/operator-spec \
  -H "Content-Type: application/json" \
  -d '{"operator":"QFT_COMMUTATION"}'

Compute one — a real call​

See also​

Compute one — a real call

See also