Re: Please Help with Dimensional analysis of Gaussian Integrals

ebunn@xxxxxxxxxxxxxxxxxxxxxx skrev:
In article <5fo59kF3dnmltU1@xxxxxxxxxxxxxxxxxx>,
Jay R. Yablon <jyablon@xxxxxxxxxxxx> wrote:

Referring to section I.2, Appendix 1, all of the Gaussian integrals are
very clear to me mathematically, but, of course, we do want to associate
certain physical quantities with these. Particularly, the scalar a and
matrix A in appendix 1 are to be associated with (d/dx)^2 (partial
derivative) and p^2 (square momentum) and so are envisioned to have mass
dimension 2. The variable x throughout is to be associated with a field
psi (scalar) or A^u (vector), and so in each case, are also envisioned
to have mass dimension of 1.

You make a couple of statements here that don't look self-consistent.
If x has mass dimension 1 then (d/dx)^2 has mass dimension -2, not 2.
Conversely, if (d/dx)^2 has mass dimension 2 then x has mass dimension -1.
I don't have Zee's book, so I can't confirm which one of these it is,
but my money's on the second option.

As Ted states, the parameter for the exponential function is always
dimensionless, so in a plane wave of the form exp(ipx), the dimensions
cancel each other out. If we assume c = \hbar = 1, then p = -i(d/dx) has
mass dimension 1 and x has mass dimension -1.



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