$\DeclareMathOperator\Det{Det}\DeclareMathOperator\Tr{Tr}$In physics literature dealing with quantum field theory, the formula \begin{equation} \Det(I+M) = e^{\Tr \ln(I+M)} \end{equation} appears frequently. Moreover, in the so-called infinitesimal cases, \begin{equation} \ln(I+M) \simeq M \end{equation} is used in analogy with the Taylor series for the usual logarithm.

What is worse, $M$ can be not only unbounded but singular as well, containing $\delta(x-y)$ for example and yielding \begin{equation} \Tr\delta(x-y)=\delta(x-x). \end{equation}

I searched everywhere in order to find relevant materials and make sense of the outrageous formulae, especially the "Mathematical Methods of Modern Physics" series by Reed & Simon. However, I cannot find reference to start with.

Could anyone please help me?

`\operatorname{Det} M`

, which takes care of the spacing automatically, rather than doing it manually with $\text{Det }M$`\text{Det }M`

. I have edited accordingly. More importantly, I think it should be $\operatorname{Det}(I + M)$ (as in the body of your post), not $\operatorname{Det} M$, in your title. $\endgroup$5more comments