On Peskin and Schroeder's QFT book, page 251, the book discussed how things will be changed in $d$ dimensions. For example $g_{\mu \nu}g^{\mu \nu}=d$.
In eq. (7.88), the book gave how Dirac matrices can be manipulated as a set of $d$ matrices:
$$\{\gamma^{\mu} ,\gamma^{\nu}\}=2g^{\mu \nu}, \ \ \ \ \ tr[1]=4 \tag{7.88}$$
How to understand $tr[1]=4$? is this "$1$" identity matrix? why not $tr[1]=d$?
Best Answer
In $d=2N$, and in $d=2N+1$, dimensions the trace of the gamma-matrix space identity matrix is ${\rm tr}({\mathbb I}_{\rm spinors})$ is $2^N$.