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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 1,861 to 1,866 of 2,569 results.

Project-declaredLean 4.32.0

Of Clifford Algebra ι single

PauliMatrix.ofCliffordAlgebra_ι_single

Mathematical statement

The generators of the Clifford algebra correspond to the elements σ.

physicsquantum field theoryrelativity

Source project: Physlib

Person-level attribution pending.

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Project-declaredLean 4.32.0

Pauli Basis' decomp

PauliMatrix.pauliBasis'_decomp

Mathematical statement

The decomposition of a self-adjoint matrix into the Pauli matrices (where σi are negated).

physicsquantum field theoryrelativity

Source project: Physlib

Person-level attribution pending.

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Project-declaredLean 4.32.0

Pauli Basis' repr inl 0

PauliMatrix.pauliBasis'_repr_inl_0

Mathematical 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.

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Project-declaredLean 4.32.0

Pauli Basis' repr inr 0

PauliMatrix.pauliBasis'_repr_inr_0

Mathematical 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.

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Project-declaredLean 4.32.0

Pauli Basis' repr inr 1

PauliMatrix.pauliBasis'_repr_inr_1

Mathematical 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.

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Project-declaredLean 4.32.0

Pauli Basis' repr inr 2

PauliMatrix.pauliBasis'_repr_inr_2

Mathematical 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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