- #1

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I encountered the following problem:

The timeordering for fermionic fields (here Dirac field) is defined to be (Peskin; Maggiore, ...):

[tex]

T \Psi(x)\bar{\Psi}(y)= \Psi(x)\bar{\Psi}(y) \ldots x^0>y^0

[/tex]

[tex]

= -\bar{\Psi}(y)\Psi(x) \ldots y^0>x^0

[/tex]

where [tex]\Psi(x)[/tex] is a Dirac spinor and [tex]\bar{\Psi}(y) = \Psi(y)^\dagger \gamma^0[/tex] it's Dirac adjoint so that

[tex]

S(x-y) = \langle 0|T{ \Psi(x)\bar{\Psi}(y)}|0 \rangle

[/tex]

is the Feynman propagator wich is a 4x4 matrix.

But there is my problem: while it is clear that [tex]\Psi(x)\bar{\Psi}(y)}[/tex] is a 4x4 matrix, [tex]\bar{\Psi}(y)\Psi(x)[/tex] is a scalar.

I would be glad for an explanation.

Thanks.

Tommy