Source-pinned research
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 research declarations. Search 10,000 more complete Mathlib declarations.
2569 results
SUSY.N1.deltaContr₂_metric
Plain-language statement
The contr_metric law (two-module): contracting the inner M/N legs of deltaCap b ⊗ deltaCap b' yields deltaCap₂ b' b.
Source project: Physlib
Person-level attribution pending.
SUSY.N1.deltaContr₂_unit
Plain-language statement
The snake identity (two-module, contr_unit law): contracting x ∈ M into the M-leg of deltaCap₂ b' b ∈ N ⊗ M returns x.
Source project: Physlib
Person-level attribution pending.
SUSY.N1.repr_conjChiralCovector
Plain-language statement
Component formula for the holomorphic covector conjugate: the ![I] basis component of conjChiralCovector t is the complex conjugate of the ![I] component of t.
Source project: Physlib
Person-level attribution pending.
SUSY.N1.toField_conjScalar
Plain-language statement
For scalar tensors, toField of the normalized tensor conjugate is the complex conjugate of toField.
Source project: Physlib
Person-level attribution pending.
Sᵥₙ_eq_trace_cfc
Plain-language statement
Entanglement of Formation of bipartite systems. It is the convex roof extension of the von Neumann entropy of one of the subsystems (here chosen to be the left one, but see Entropy.Sᵥₙ_of_partial_eq). The function Sᵥₙ ∘ traceRight ∘ pure is phase-invariant because pure maps phase-equivalent kets to the same mixed state, so it descends to `KetUpToPha...
Source project: quantumInfo
Person-level attribution pending.
Sᵥₙ_ofClassical
Plain-language statement
Entanglement of Formation of bipartite systems. It is the convex roof extension of the von Neumann entropy of one of the subsystems (here chosen to be the left one, but see Entropy.Sᵥₙ_of_partial_eq). The function Sᵥₙ ∘ traceRight ∘ pure is phase-invariant because pure maps phase-equivalent kets to the same mixed state, so it descends to `KetUpToPha...
Source project: quantumInfo
Person-level attribution pending.