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## Hot answers tagged trace

3

I quite like your characterization of the partial trace! I think you perceive a conflict with the Wikipedia definition because you are only taking part of the latter: given an operator $T\in L(V\otimes W)$, the requirement that its partial trace obey $$\text{Tr}_W(T)\in L(V)$$ simply says that the partial trace over $W$ be an operator on $V$, but that ...

2

The oscillatory part is nothing but Thomas-Fermi approximation or more riguresly, this is a version (someone should correct me if I am wrong) Weyl's formula Regrading on how to obtain the WKB from the trace formula: You can read the 2 papers by Berry and Tabor on how they derived a trace formula (like that of Gutzwiller) but to the case of integrable ...

2

You should write the indices on the gamma matrices. So your expression is actually \begin{align} \text{tr}[\gamma^\mu(\gamma^\alpha k_\alpha + \gamma^\beta p_\beta + \gamma^\delta q_\delta + m) \gamma_\mu(\gamma^\rho k_\rho + \gamma^\sigma p_\sigma + m) ]. \end{align} Then you use the trace technology to evaluate the traces. For example, the $m^2$ term has ...

1

The source you linked to looks for the divergent part of the integral in a high energy limit ($m \to 0$). If you want to compute the whole thing, here's how you would do it. Focus on just one of the two traces: 1) "Rationalize" all the propagators by doing something like $$\frac{1}{\gamma^\mu k_\mu - m} = \frac{\gamma^\mu k_\mu + m}{k^2 - m^2}$$ ...

1

OP's algebraic manipulations are formally correct. But the formal calculation could be wrong for many reasons. For instance: If the summation $\sum_n$ in $\Theta$ is not convergent. If one is not allowed to change order of summation $\sum_n$ and integration $\int_{0}^{\infty}\!dt$. If the Sokhotsky distribution formula is applied to a singular ...

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