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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 7 research declarations. Search 10,000 more complete Mathlib declarations.

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Project-declaredLean 4.32.0

Electric Field eq propogator cross magnetic Field Matrix

Electromagnetism.ElectromagneticPotential.IsPlaneWave.electricField_eq_propogator_cross_magneticFieldMatrix

Project documentation

The corresponding magnetic field function from ℝ to Fin d × Fin d → ℝ of a plane wave. -/ noncomputable def magneticFunction {d : ℕ} {𝓕 : FreeSpace} {A : ElectromagneticPotential d} {s : Direction d} (hA : IsPlaneWave 𝓕 A s) : ℝ → Fin d × Fin d → ℝ := Classical.choose hA.2 lemma magneticFieldMatrix_eq_magneticFunction {d : ℕ} {𝓕 : FreeSpace} {A : E...

physicsquantum field theoryrelativity

Source project: Physlib

Person-level attribution pending.

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Project-declaredLean 4.32.0

Electric Field space deriv eq time deriv

Electromagnetism.ElectromagneticPotential.IsPlaneWave.electricField_space_deriv_eq_time_deriv

Project documentation

The corresponding magnetic field function from ℝ to Fin d × Fin d → ℝ of a plane wave. -/ noncomputable def magneticFunction {d : ℕ} {𝓕 : FreeSpace} {A : ElectromagneticPotential d} {s : Direction d} (hA : IsPlaneWave 𝓕 A s) : ℝ → Fin d × Fin d → ℝ := Classical.choose hA.2 lemma magneticFieldMatrix_eq_magneticFunction {d : ℕ} {𝓕 : FreeSpace} {A : E...

physicsquantum field theoryrelativity

Source project: Physlib

Person-level attribution pending.

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Project-declaredLean 4.32.0

Electric Function differentiable

Electromagnetism.ElectromagneticPotential.IsPlaneWave.electricFunction_differentiable

Project documentation

The corresponding magnetic field function from ℝ to Fin d × Fin d → ℝ of a plane wave. -/ noncomputable def magneticFunction {d : ℕ} {𝓕 : FreeSpace} {A : ElectromagneticPotential d} {s : Direction d} (hA : IsPlaneWave 𝓕 A s) : ℝ → Fin d × Fin d → ℝ := Classical.choose hA.2 lemma magneticFieldMatrix_eq_magneticFunction {d : ℕ} {𝓕 : FreeSpace} {A : E...

physicsquantum field theoryrelativity

Source project: Physlib

Person-level attribution pending.

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Project-declaredLean 4.32.0

Magnetic Field Matrix eq propogator cross electric Field

Electromagnetism.ElectromagneticPotential.IsPlaneWave.magneticFieldMatrix_eq_propogator_cross_electricField

Project documentation

The corresponding magnetic field function from ℝ to Fin d × Fin d → ℝ of a plane wave. -/ noncomputable def magneticFunction {d : ℕ} {𝓕 : FreeSpace} {A : ElectromagneticPotential d} {s : Direction d} (hA : IsPlaneWave 𝓕 A s) : ℝ → Fin d × Fin d → ℝ := Classical.choose hA.2 lemma magneticFieldMatrix_eq_magneticFunction {d : ℕ} {𝓕 : FreeSpace} {A : E...

physicsquantum field theoryrelativity

Source project: Physlib

Person-level attribution pending.

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Project-declaredLean 4.32.0

Space deriv electric Field eq magnetic Field Matrix

Electromagnetism.ElectromagneticPotential.IsPlaneWave.space_deriv_electricField_eq_magneticFieldMatrix

Project documentation

The corresponding magnetic field function from ℝ to Fin d × Fin d → ℝ of a plane wave. -/ noncomputable def magneticFunction {d : ℕ} {𝓕 : FreeSpace} {A : ElectromagneticPotential d} {s : Direction d} (hA : IsPlaneWave 𝓕 A s) : ℝ → Fin d × Fin d → ℝ := Classical.choose hA.2 lemma magneticFieldMatrix_eq_magneticFunction {d : ℕ} {𝓕 : FreeSpace} {A : E...

physicsquantum field theoryrelativity

Source project: Physlib

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Project-declaredLean 4.32.0

Space deriv magnetic Field Matrix eq electric Field mul propogator

Electromagnetism.ElectromagneticPotential.IsPlaneWave.space_deriv_magneticFieldMatrix_eq_electricField_mul_propogator

Project documentation

The corresponding magnetic field function from ℝ to Fin d × Fin d → ℝ of a plane wave. -/ noncomputable def magneticFunction {d : ℕ} {𝓕 : FreeSpace} {A : ElectromagneticPotential d} {s : Direction d} (hA : IsPlaneWave 𝓕 A s) : ℝ → Fin d × Fin d → ℝ := Classical.choose hA.2 lemma magneticFieldMatrix_eq_magneticFunction {d : ℕ} {𝓕 : FreeSpace} {A : E...

physicsquantum field theoryrelativity

Source project: Physlib

Person-level attribution pending.

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