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Source-pinned research

Research proof index

Search theorem names, mathematical ideas, modules, topics, projects, and role-labelled researchers. Open a result for its complete indexed Lean declaration and source record.

This index contains 3 research declarations. Search 10,000 more complete Mathlib declarations.

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Project-declaredLean 4.32.0

Canonical Momentum eq

Electromagnetism.ElectromagneticPotential.canonicalMomentum_eq

Project documentation

The canonical momentum associated with the lagrangian of an electromagnetic potential and a Lorentz current density. -/ noncomputable def canonicalMomentum (𝓕 : FreeSpace) (A : ElectromagneticPotential d) (J : LorentzCurrentDensity d) : SpaceTime d → Lorentz.Vector d := fun x => gradient (fun (v : Lorentz.Vector d) => lagrangian 𝓕 ⟨fun x => A x + x (Sum...

physicsquantum field theoryrelativity

Source project: Physlib

Person-level attribution pending.

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Project-declaredLean 4.32.0

Canonical Momentum eq electric Field

Electromagnetism.ElectromagneticPotential.canonicalMomentum_eq_electricField

Project documentation

The canonical momentum associated with the lagrangian of an electromagnetic potential and a Lorentz current density. -/ noncomputable def canonicalMomentum (𝓕 : FreeSpace) (A : ElectromagneticPotential d) (J : LorentzCurrentDensity d) : SpaceTime d → Lorentz.Vector d := fun x => gradient (fun (v : Lorentz.Vector d) => lagrangian 𝓕 ⟨fun x => A x + x (Sum...

physicsquantum field theoryrelativity

Source project: Physlib

Person-level attribution pending.

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Project-declaredLean 4.32.0

Canonical Momentum eq gradient kinetic Term

Electromagnetism.ElectromagneticPotential.canonicalMomentum_eq_gradient_kineticTerm

Project documentation

The canonical momentum associated with the lagrangian of an electromagnetic potential and a Lorentz current density. -/ noncomputable def canonicalMomentum (𝓕 : FreeSpace) (A : ElectromagneticPotential d) (J : LorentzCurrentDensity d) : SpaceTime d → Lorentz.Vector d := fun x => gradient (fun (v : Lorentz.Vector d) => lagrangian 𝓕 ⟨fun x => A x + x (Sum...

physicsquantum field theoryrelativity

Source project: Physlib

Person-level attribution pending.

View proof record