FeynCalc manual (development version)

PCHN

PCHN[x, i, j] is a chain of Pauli matrices x and is transformed into PauliChain[FCI[x],PauliIndex[i],PauliIndex[j]] by FeynCalcInternal.

See also

Overview, PauliChain, PauliIndex, PauliIndexDelta, PauliChainJoin, PauliChainExpand, PauliChainFactor.

Examples

A standalone Pauli matrix with open Pauli indices

PCHN[CSID[a], i, j]

(σa)ij\left(\sigma ^a\right){}_{ij}

A chain of Pauli matrices with open Pauli indices

PCHN[CSID[a] . CSID[b], i, j]

(σa.σb)ij\left(\sigma ^a.\sigma ^b\right){}_{ij}

A single ξ\xi ^{\dagger} spinor with an open Pauli index

PCHN[PauliXi[-I], i]

(ξ)i\left(\xi ^{\dagger }\right){}_i

A single η\eta ^{\dagger} spinor with an open Pauli index

PCHN[PauliEta[-I], i]

(η)i\left(\eta ^{\dagger }\right){}_i

A single ξ\xi spinor with an open Pauli index

PCHN[i, PauliXi[I]]

(ξ)i(\xi )_i

A single η\eta spinor with an open Pauli index

PCHN[i, PauliEta[I]]

(η)i(\eta )_i

ξ\xi ^{\dagger} spinor contracted with a chain of Pauli matrices

PCHN[CSID[a] . CSID[b], PauliXi[-I], j]

(ξ.σa.σb)j\left(\xi ^{\dagger }.\sigma ^a.\sigma ^b\right){}_j

η\eta ^{\dagger} spinor contracted with a chain of Pauli matrices

PCHN[CSID[a] . CSID[b], PauliEta[-I], j]

(η.σa.σb)j\left(\eta ^{\dagger }.\sigma ^a.\sigma ^b\right){}_j

ξ\xi spinor contracted with a chain of Pauli matrices

PCHN[CSID[a] . CSID[b], i, PauliXi[I]]

(σa.σb.ξ)i\left(\sigma ^a.\sigma ^b.\xi \right){}_i

η\eta spinor contracted with a chain of Pauli matrices

PCHN[CSID[a] . CSID[b], i, PauliEta[I]]

(σa.σb.η)i\left(\sigma ^a.\sigma ^b.\eta \right){}_i