# Reference recommendation： QFT in arbitary dimensions $D=1+d$

When I self-study the QFT, I found that many results in textbook heavily rely on the dimension $1+3$. For example, I heard "In 3+1 dim, Majorana fermion cannot have well-defined handedness. But in dim= $2 \mod 8$ we can have Majorana-Weyl spinors." I think the spin-statistic theorem and representation of Lorentz group and Poincare group in $d+1$ may be different. Furthermore, like superficial degree of divergence, renormalization should also be totally different in other dimension. So I want to know whether there exist some monographs, papers, review or lecture notes which cover topics "QFT in arbitrary dimension"?

• Majorana spinors in higher dimensions are also discussed in 309890. Spin-statistics is essentially independent of $d$, and so are the representations of the P. group (the case $d=2$ is special). Renormalisation for arbitrary $d$ is discussed in almost every book that discusses renormalisation around $d=4$. – AccidentalFourierTransform Apr 23 '17 at 20:45
• @AccidentalFourierTransform I heard that the representation of $SO(1,d)$ is similar to $SO(1+d)$. $1+d$ is even or odd belongs to different simple Lie group. And I also heard that the spinor representation may be different $\mod 4$. – user153663 Apr 23 '17 at 20:55
• @AccidentalFourierTransform In the connected component, the representation of Lorentz group may be considered in $4$ different cases. What's about when I take $P$, $T$ into consideration. – user153663 Apr 23 '17 at 20:57