- #1
MathematicalPhysicist
Gold Member
- 4,699
- 371
In Peskin and Schroeder on page 681 they write:
Now, as far as I can tell the generators of ##U(1)## are just exponents, i.e ##e^{2\pi ix}##, so how can they have a zero trace if it's just one number which never vanishes?
Perhaps I am missing something here, can anyone clear this matter to me?
Ah, wait perhaps this contradiction means that you cannot couple gravity to this theory?
...if the gauge group of the theory contains ##U(1)## factors, the theory cannot be consistently coupled to gravity unless each of the ##U(1)## generators is traceless.
Now, as far as I can tell the generators of ##U(1)## are just exponents, i.e ##e^{2\pi ix}##, so how can they have a zero trace if it's just one number which never vanishes?
Perhaps I am missing something here, can anyone clear this matter to me?
Ah, wait perhaps this contradiction means that you cannot couple gravity to this theory?