Calculating trace with slashed item

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The discussion revolves around calculating the trace of the expression Tr q (p + m) q (p + m). The user initially expands the expression but realizes that terms involving odd numbers of gamma matrices yield a trace of zero, as they are not square matrices. They consider treating (p + m) as a covariant vector, which complicates the calculation due to the emergence of numerous terms. The user acknowledges a misunderstanding regarding the nature of p, concluding that the trace can be meaningful. Assistance is sought to clarify the calculation process.
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Homework Statement



I was asked to find Tr [STRIKE]q[/STRIKE] ([STRIKE]p[/STRIKE] + m) [STRIKE]q[/STRIKE] ([STRIKE]p[/STRIKE] + m)

Homework Equations



Tr [STRIKE]p[/STRIKE] [STRIKE]q[/STRIKE] = 4pq

The Attempt at a Solution



If I expand it as Tr ([STRIKE]p[/STRIKE] [STRIKE]q[/STRIKE] [STRIKE]p[/STRIKE] [STRIKE]q[/STRIKE] + m [STRIKE]q[/STRIKE] [STRIKE]p[/STRIKE] [STRIKE]q[/STRIKE] + m [STRIKE]q[/STRIKE] [STRIKE]q[/STRIKE] [STRIKE]p[/STRIKE] + (m^2)([STRIKE]q[/STRIKE])^2 ), although Tr Π(odd number of gamma matrices) = 0, since [STRIKE]q[/STRIKE] [STRIKE]p[/STRIKE] [STRIKE]q[/STRIKE] and similar terms are not square matrices, trace has no meaning. If I treat ([STRIKE]p[/STRIKE] + m) as a covariant vector (adding m to each component of [STRIKE]p[/STRIKE], I can get a scalar*I, but a lot of [STRIKE]q[/STRIKE]_0,1,2,3 [STRIKE]p[/STRIKE]_0,1,2,3 terms will come out and get really messy. Can anyone help me please? Thank you.
 
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I thought [STRIKE]p[/STRIKE] was a vector, but now I realize that it is not. So the trace makes sense.
 
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