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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 2,569 curated research declarations and 119,070 complete package declarations. Search 10,000 more complete Mathlib declarations.

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Showing 961 to 966 of 2,569 results.

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

Person-level attribution pending.

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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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Project-declaredLean 4.32.0

Time deriv electric Field eq magnetic Field Matrix

Electromagnetism.ElectromagneticPotential.IsPlaneWave.time_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

Person-level attribution pending.

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Project-declaredLean 4.32.0

Kinetic Term add time mul const

Electromagnetism.ElectromagneticPotential.kineticTerm_add_time_mul_const

Project documentation

The kinetic energy from an electromagnetic potential. -/ noncomputable def kineticTerm {d} (𝓕 : FreeSpace) (A : ElectromagneticPotential d) : SpaceTime d → ℝ := fun x => - 1/(4 * 𝓕.μ₀) * {η' d | μ μ' ⊗ η' d | ν ν' ⊗ A.toFieldStrength x | μ ν ⊗ A.toFieldStrength x | μ' ν'}ᵀ.toField /-! ### A.1. Lorentz invariance of the kinetic term We show that the kine...

physicsquantum field theoryrelativity

Source project: Physlib

Person-level attribution pending.

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Project-declaredLean 4.32.0

Kinetic Term eq electric Matrix magnetic Field Matrix time space

Electromagnetism.ElectromagneticPotential.kineticTerm_eq_electricMatrix_magneticFieldMatrix_time_space

Project documentation

The kinetic energy from an electromagnetic potential. -/ noncomputable def kineticTerm {d} (𝓕 : FreeSpace) (A : ElectromagneticPotential d) : SpaceTime d → ℝ := fun x => - 1/(4 * 𝓕.μ₀) * {η' d | μ μ' ⊗ η' d | ν ν' ⊗ A.toFieldStrength x | μ ν ⊗ A.toFieldStrength x | μ' ν'}ᵀ.toField /-! ### A.1. Lorentz invariance of the kinetic term We show that the kine...

physicsquantum field theoryrelativity

Source project: Physlib

Person-level attribution pending.

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Project-declaredLean 4.32.0

Kinetic Term eq sum

Electromagnetism.ElectromagneticPotential.kineticTerm_eq_sum

Project documentation

The kinetic energy from an electromagnetic potential. -/ noncomputable def kineticTerm {d} (𝓕 : FreeSpace) (A : ElectromagneticPotential d) : SpaceTime d → ℝ := fun x => - 1/(4 * 𝓕.μ₀) * {η' d | μ μ' ⊗ η' d | ν ν' ⊗ A.toFieldStrength x | μ ν ⊗ A.toFieldStrength x | μ' ν'}ᵀ.toField /-! ### A.1. Lorentz invariance of the kinetic term We show that the kine...

physicsquantum field theoryrelativity

Source project: Physlib

Person-level attribution pending.

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