thanks everyone 

@Christopher2222 It can be done within the physics package then. He said the following on November 29, 2007, so I have been waiting for more than 5 years. @ecterrab

Re: the physics package

Commented by: ecterrab 5466 

November 29 2007

Hi Could you be more explicit on the computation you want to do? Generally speaking, with Physics in Maple 11 you can operate with tensors in flat spacetime, that can also be quantum operators, anti or non commutative variables etc. The algebra of Dirac matrices and a representation for them, as well as for Pauli matrices, come with the package, Traces of expressions involving products of these objects are also computed and the algebraic perturbative expansion underlying a sequence of Feynman diagrams is also computed using the Physics:-FeynmanDiagrams command. Besides that, Fundiff performs functional differentiation and, you know, you can perform functional integration in terms of Functional differentiation provided that we are interested in the perturbative expansion of the object. I used Physics for a number of QFT computations and in fact the precursor of this package is called QFT. Having said that, many things are still to be done, like returning the actual Feynman graphs, not the analytical expression behind them, providing complete representations for spinors of different types, making the package handle curved spaces, supersymmetry notation, and other etc. The package is evolving into that direction. So if you could make more explicit what is the computation you have in hands, depending on what you post it may be possible to do some or all of it already in Maple 11. Edgardo S. Cheb-Terrab Research Fellow, Maplesoft Editor for Computer Algebra, Computer Physics Communications

Thank you very much for your answer. It worked.