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

All topics

591 results

Clear filters
Project-declaredLean 4.32.0

Pauli Basis' repr inl 0

PauliMatrix.pauliBasis'_repr_inl_0

Plain-language statement

The component of a self-adjoint matrix in the direction σ0 under the basis formed by the covariant Pauli matrices.

physicsquantum field theoryrelativity

Source project: Physlib

Person-level attribution pending.

View proof record
Project-declaredLean 4.32.0

Pauli Basis' repr inr 0

PauliMatrix.pauliBasis'_repr_inr_0

Plain-language statement

The component of a self-adjoint matrix in the direction -σ1 under the basis formed by the covariant Pauli matrices.

physicsquantum field theoryrelativity

Source project: Physlib

Person-level attribution pending.

View proof record
Project-declaredLean 4.32.0

Pauli Basis' repr inr 1

PauliMatrix.pauliBasis'_repr_inr_1

Plain-language statement

The component of a self-adjoint matrix in the direction -σ2 under the basis formed by the covariant Pauli matrices.

physicsquantum field theoryrelativity

Source project: Physlib

Person-level attribution pending.

View proof record
Project-declaredLean 4.32.0

Pauli Basis' repr inr 2

PauliMatrix.pauliBasis'_repr_inr_2

Plain-language statement

The component of a self-adjoint matrix in the direction -σ3 under the basis formed by the covariant Pauli matrices.

physicsquantum field theoryrelativity

Source project: Physlib

Person-level attribution pending.

View proof record
Project-declaredLean 4.32.0

Pauli Co contr pauli Contr

PauliMatrix.pauliCo_contr_pauliContr

Plain-language statement

The statement that σᵥᵃᵇ σᵛᵃ'ᵇ' = 2 εᵃᵃ' εᵇᵇ'.

physicsquantum field theoryrelativity

Source project: Physlib

Person-level attribution pending.

View proof record