- #1
weejee
- 199
- 0
In the lower part of page 200 in his book, Weinberg says that any normal-ordered function of the fields can be expressed as a sum of ordinary products of the fields with c-number coefficients.
I don't quite see this.
A field can be decomposed in terms of parts that contain either only creation operators or only annihilation operators.
[tex] \phi(x) = \phi_{+} (x) + \phi_{-} (x)[/tex]
[tex] \phi^{\dagger}(x) = \phi_{+}^{\dagger} (x) + \phi_{-}^{\dagger} (x)[/tex]
If we consider a function of fields
[tex]F(\phi(x), \phi^{\dagger}(x))[/tex]
and its normal ordered version
[tex]:F(\phi(x), \phi^{\dagger}(x)):[/tex],
the difference between the two seems to involve all of the following quantities.
[tex] \phi_{+} (x), \,\phi_{-} (x),\,\phi_{+}^{\dagger} (x),\, \phi_{-}^{\dagger} (x)[/tex]
However, Weinberg says that we can express it in terms of only
[tex] \phi(x),\, \phi^{\dagger}(x)[/tex].
Is there any simple argument to justify this? My impression is that Weinberg would provide some arguments in the book unless it is too obvious.
I don't quite see this.
A field can be decomposed in terms of parts that contain either only creation operators or only annihilation operators.
[tex] \phi(x) = \phi_{+} (x) + \phi_{-} (x)[/tex]
[tex] \phi^{\dagger}(x) = \phi_{+}^{\dagger} (x) + \phi_{-}^{\dagger} (x)[/tex]
If we consider a function of fields
[tex]F(\phi(x), \phi^{\dagger}(x))[/tex]
and its normal ordered version
[tex]:F(\phi(x), \phi^{\dagger}(x)):[/tex],
the difference between the two seems to involve all of the following quantities.
[tex] \phi_{+} (x), \,\phi_{-} (x),\,\phi_{+}^{\dagger} (x),\, \phi_{-}^{\dagger} (x)[/tex]
However, Weinberg says that we can express it in terms of only
[tex] \phi(x),\, \phi^{\dagger}(x)[/tex].
Is there any simple argument to justify this? My impression is that Weinberg would provide some arguments in the book unless it is too obvious.
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