- #1

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- Summary:
- Need help in understanding the operator product expansion as shown in Schwartz

I have included here the screen shot of the page I am referring to.

I am unsure of how this non-local Lagrangian of Eqtn(32.68) has been constructed. Have they just integrated the interaction Lagrangian densities over two different sets of points (x & y) ?

If so, then why is there no P_L in there, why just a gamma matrix ?

And in this Eqtn(32.68) have they used the full electroweak theory ?

The paragraph above claims that they have integrated out the W boson ,then got this expression but then why have the written the W propagator in there as well ?

In the next step Eqtn(32.69) I dont get how the expression for the propagator is modified ie where does the DeAlembertian come from ?

From this it seems to me that the thing responsible for converting a non-local Lagrangian to a local one,is simply the position space delta function resulting from the momentum integral of the exponential.

From what I understand, the interaction due to the full electroweak Lagrangian should be non-local while for the lower energy 4 Fermi theory, it should be local. So would the answer have been the same had they used the 4 Fermi theory instead ?

I am unsure of how this non-local Lagrangian of Eqtn(32.68) has been constructed. Have they just integrated the interaction Lagrangian densities over two different sets of points (x & y) ?

If so, then why is there no P_L in there, why just a gamma matrix ?

And in this Eqtn(32.68) have they used the full electroweak theory ?

The paragraph above claims that they have integrated out the W boson ,then got this expression but then why have the written the W propagator in there as well ?

In the next step Eqtn(32.69) I dont get how the expression for the propagator is modified ie where does the DeAlembertian come from ?

From this it seems to me that the thing responsible for converting a non-local Lagrangian to a local one,is simply the position space delta function resulting from the momentum integral of the exponential.

From what I understand, the interaction due to the full electroweak Lagrangian should be non-local while for the lower energy 4 Fermi theory, it should be local. So would the answer have been the same had they used the 4 Fermi theory instead ?