Calculating trace with slashed item

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SUMMARY

The discussion revolves around calculating the trace of the expression Tr q (p + m) q (p + m) using the equation Tr p q = 4pq. The user attempts to expand the expression but encounters difficulties due to the properties of traces involving odd numbers of gamma matrices, which yield zero. The realization that p is not a vector but rather a covariant vector is crucial for understanding the trace's implications in this context.

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  • Understanding of trace operations in linear algebra
  • Familiarity with gamma matrices in quantum field theory
  • Knowledge of covariant vectors and their properties
  • Basic proficiency in mathematical expansions and simplifications
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  • Study the properties of traces involving gamma matrices
  • Learn about covariant vectors and their applications in physics
  • Explore advanced topics in quantum field theory related to trace calculations
  • Review linear algebra concepts, particularly matrix operations and expansions
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Students and researchers in theoretical physics, particularly those focusing on quantum field theory and linear algebra applications in physics.

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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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