Operation with tensor quantities in quantum field theory

[illuminates]

I would like to know where one may operate with tensor quantities in quantum field theory: Minkowski tensors, spinors, effective lagrangians (for example sigma models or models with four quark interaction), gamma matrices, Grassmann algebra, Lie algebra, fermion determinants and et cetera.
I know little about

• REDUCE
  • Homepage: http://www.reduce-algebra.com/
• FORM
  • Homepage: http://www.nikhef.nl/~form/
• GiNaC (is based on C++)
  • Homepage: http://www.ginac.de/
• sympy (is based on Python)
  • Homepage: http://www.sympy.org/en/index.html
• FERMAT
  • Homepage: http://home.bway.net/lewis/

And I heard about HEPMath, FORM, TRACER, FormCalc, FeynCalc, Redberry. And there is Maple, but I didn't see how it can be used in quantum field theory. What is the best programme for analytical operation in quantum field theory?

 

[highflyyer]

I know that high energy phenomenologists find FeynCalc to be particularly appealing. My standard model course had problems where we had to use FeynCalc, but that might just be the case in my physics department.