Hi!
The first problem comes from the output of
Tex@PDNP[{1, -NP}][PsiCD1[]]
which is
"\Psi _{1}{}{}_{\text{\c } 1}"
\c is not understood by the LaTeX compiler.
The quickest fix is probably
Tex["\[Cedilla]"] = ",";
Observe that TexAct will choose Prefix or Postfix notation from
the $CovDFormat variable.
I suspect that you actually would like the Tex output to match the
notation you have in this part of the notebook. You can do this
with
$CovDFormat = "Prefix";
FormatTexBasis[PDNP[{1, -NP}], "D "];
FormatTexBasis[PDNP[{2, -NP}], "\\Delta "];
FormatTexBasis[PDNP[{3, -NP}], "\\delta "];
FormatTexBasis[PDNP[{4, -NP}], "\\bar\\delta "];
I can also recommend that you take a look at the SpinFrames
package. With this you can probably make your notebook much
shorter if you want.
I told a little bit about this package in the end of the 20 Years
of xAct webinar
https://youtu.be/k_7s6_ZqV6M?list=PLdIcYTEZ4S8TSEk7YmJMvyECtF-KA1SQ2
https://amoeba.wolfram.com/index.php/s/ZxgjKXtJgALyCw4
Please let me know if you want more information or help.
Regards
Thomas