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Project-declaredLean 4.32.0

Of U1Subgroup smul eq smul

StandardModel.HiggsVec.ofU1Subgroup_smul_eq_smul

Project documentation

The subgroup of gaugeGroup := SU(3) × SU(2) × U(1) which preserves every HiggsVec by the action of StandardModel.HiggsVec.rep is given by SU(3) × ℤ₆ where ℤ₆ is the subgroup of SU(2) × U(1) with elements (α^(-3) * I₂, α) where α is a sixth root of unity. -/ informal_lemma stability_group where deps := [``HiggsVec] tag := "6V2MO" /-! ## A.8...

physicsquantum field theoryrelativity

Source project: Physlib

Person-level attribution pending.

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Project-declaredLean 4.32.0

Rep Gauge Group I tmul basis eq sum

StandardModel.QuarkDoublet.repGaugeGroupI_tmul_basis_eq_sum

Plain-language statement

The action of the full gauge group on a tensor product of basis elements, expanded as a sum over the columns of the SU(3) and SU(2) matrices.

physicsquantum field theoryrelativity

Source project: Physlib

Person-level attribution pending.

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Project-declaredLean 4.32.0

Rep Gauge Group I tmul basis eq sum

StandardModel.UpSinglet.repGaugeGroupI_tmul_basis_eq_sum

Plain-language statement

The action of the full gauge group on a tensor product of basis elements, expanded as a sum over the columns of the SU(3) matrix.

physicsquantum field theoryrelativity

Source project: Physlib

Person-level attribution pending.

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Project-declaredLean 4.32.0

Cross product t

standParam.cross_product_t

Plain-language statement

The top-row of the standard parameterization is the cross product of the conjugate of the up and charm rows.

physicsquantum field theoryrelativity

Source project: Physlib

Person-level attribution pending.

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Project-declaredLean 4.32.0

Stand Param As Matrix unitary

standParamAsMatrix_unitary

Plain-language statement

The standard parameterization forms a unitary matrix.

physicsquantum field theoryrelativity

Source project: Physlib

Person-level attribution pending.

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Project-declaredLean 4.31.0

Stir rbr soundness

StirIOP.stir_rbr_soundness

Plain-language statement

Lemma 5.4: Round-by-round soundness of the STIR IOPP Consider parameters: ι = {ιᵢ}_{i = 0, ..., M} be smooth evaluation domains P : Params ι F containing required protocol parameters - initial degree, folding parameters foldingParamᵢ, embedding φᵢ, repetition parameters repeatParamᵢ hParams : ParamConditions ι P, stating conditions that parame...

cryptographyproof systemscoding theory

Source project: ArkLib

Person-level attribution pending.

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