Physlib.QFT.QED.AnomalyCancellation.LowDim.One

The Pure U(1) case with 1 fermion

We show that in this case the charge must be zero.

1 declaration

theorem

The only linear ACC solution for a pure $U(1)$ theory with $n=1$ is $S = 0$

Consider a pure $U(1)$ gauge theory with $n=1$ Weyl fermion carrying a rational charge $x_1$ . If $S = (x_1)$ is a solution to the linear anomaly cancellation condition (the gravitational anomaly), which requires $\sum_{i=1}^1 x_i = 0$ , then the solution $S$ is the zero vector, meaning $x_1 = 0$ .

Physlib.QFT.QED.AnomalyCancellation.LowDim.One

The Pure U(1) case with 1 fermion

The only linear ACC solution for a pure U(1)U(1)U(1) theory with n=1n=1n=1 is S=0S = 0S=0

The only linear ACC solution for a pure $U(1)$ theory with $n=1$ is $S = 0$