On 08/04/2011 08:21 AM, cschwan wrote:
Hello!I would like to know if sympy can be used for Quantum Field Theory calculations. In particular, I would like to compute traces of dirac matrices and contract them with four-vectors. For example, the following holds true (latex notation): Tr ( \gamma^\mu \gamma^\alpha \gamma^\nu \gamma^\beta ) p_\alpha n_ \beta = 4 ( p^\mu n^\nu + n^\mu p^\nu - g^{\mu \nu} p \cdot n ) I am using the following clifford identity to calculate the right hand side: \gamma^\mu \gamma^\nu + \gamma^\nu \gamma^\mu = 2 g^{\mu \nu} \cdot 1 The \gamma^\mu are elements of a clifford algebra and at the same time are lorentz vectors, g^{\mu \nu} is the metric tensor. Since the \gamma^\mu are represented by 4x4 matrices, I can take the trace of them. Because of the identity above and Tr (1) = 4 I can show that Tr ( \gamma^\mu \gamma^\nu ) = 4 g^{\mu \nu} By repeatedly applying the clifford identity I can derive identities for traces with than two gamma matrices. Does somebody know if this is possible with sympy? When I looked into sympy's documentation I noticed there are already modules for tensors and geometric algebra, but I did not find anything to work out the traces.
Try looking in Doran & Lasenby, "Geometric Algebra for Physicists", Chapter 8 - Quantum Theory and Spinors. That might show how geometric algebra could be used to calculate what you want. I don't know enough quantum mechanics to know for sure. My interest in geometric algebra is the gauge theory of gravity. -- You received this message because you are subscribed to the Google Groups "sympy" group. To post to this group, send email to [email protected]. To unsubscribe from this group, send email to [email protected]. For more options, visit this group at http://groups.google.com/group/sympy?hl=en.
