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

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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.

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Project-declaredLean 4.32.0

Pauli Self Adjoint span

PauliMatrix.pauliSelfAdjoint_span

Plain-language statement

The Pauli matrices span all self-adjoint matrices.

physicsquantum field theoryrelativity

Source project: Physlib

Person-level attribution pending.

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Project-declaredLean 4.32.0

Pauli Self Adjoint' span

PauliMatrix.pauliSelfAdjoint'_span

Plain-language statement

The Pauli matrices where σi are negated span all Self-adjoint matrices.

physicsquantum field theoryrelativity

Source project: Physlib

Person-level attribution pending.

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Project-declaredLean 4.32.0

Self Adjoint ext

PauliMatrix.selfAdjoint_ext

Plain-language statement

Two 2×2 self-adjoint matrices are equal if the real traces of each matrix multiplied by each of the Pauli-matrices are equal.

physicsquantum field theoryrelativity

Source project: Physlib

Person-level attribution pending.

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