Cgs or SI in quantum field theory?

[nomadreid]

I have an acquaintance who maintains that in quantum field theory, primarily the cgs system is used. OK, I know it's not really important, but I was under the impression that everyone had switched to SI. (My book on quantum field theory has very few actual quantities with units outside of GeV, so I couldn't check it there.) So, for example, if one had a text that covered both astronomical distances and nuclear distances, and one wished to use a single base unit (instead of having everything from light years down to femtometers), would one typically choose meters or centimeters?

 

[Demystifier]

People in QFT usually use a simplified SI with ##\hbar=c=\epsilon_0=\mu_0=1##.

 

[vanhees71]

In my opinion in theoretical physics one should use the Heaviside-Lorentz system of units, i.e., rationalized Gaussian cgs units, because it reflects the fundamental structure of electrodynamics, i.e., electric and magnetic field components have the same dimension. You can also simplify your life a lot by introducing on top "natural units", where ##\hbar=c=1##. Then you have only one base unit left. In HEP usually one uses GeV for energies, masses and momenta. For distances and times a handy unit is fm. Then you only need the conversion factor ##\hbar c=0.197 \; \text{GeV} \; \text{fm}## to convert GeV to 1/fm and vice vs.

Of course, there's no principle objection to use SI units in all of physics, although it's cumbersome and unintuitive in some applications.

 

[nomadreid]

Many thanks, Demystifier and vanhees71. Live and learn... if I understand correctly, both answers are equivalent, with vanhees71 giving a bit more detail.

In the Wiki page on Heaviside-Lorentz, https://en.wikipedia.org/wiki/Lorentz–Heaviside_units, one has examples of many quantities, but not of distance, for which vanhees71 gave the conversion. Although it seems strange to refer to a distance in terms of the reciprocal of an energy, that would nonetheless provide the base unit for all scales that I was looking for. (That is, question nicely answered!) However, I presume that this strangeness is the reason that vanhees71 suggested fm. If, after using fm for referring to small distances, one would then talk of a large distance in the same paragraph, it would seem strange to continue to talk in terms of fm, and so I guess you would not try to keep one unit but rather switch to other units (cm, m, km, ly, etc.) in that case to stay on the intuitive level.

 

[Demystifier]

If one (i) simplifies SI by putting ##\epsilon_0=\mu_0=1## and (ii) rationalizes CGS by moving ##4\pi## from Maxwell equations to their solutions, what differences between SI and CGS still remain?

 

[vanhees71]

In the original Gaussian or Heaviside-Lorentz system, of course you have cm, g and s as base units. Only when you introduce "natural units" by setting the conversion factors ##\hbar## (modified Planck action quantum) and ##c## (vacuum speed of light) to 1, you have only one unit left, which is usually chosen as GeV for masses, energies, and momenta and fm for lengths and times. You then only need the above given conversion factor ##\hbar c=0.197 \text{GeV} \, \text{fm}##.

You can of course also go to Planck units, by also setting Newton's Gravitational constant ##G=1##. Then all quantities are pure numbers ("dimensionless"):

https://en.wikipedia.org/wiki/Planck_units

 

[vanhees71]

If one (i) simplifies SI by putting ##\epsilon_0=\mu_0=1## and (ii) rationalizes CGS by moving ##4\pi## from Maxwell equations to their solutions, what differences between SI and CGS still remain?

You still have the idiosyncratic difference in the units used for electric and magnetic components in the SI. Only if you set in addition ##c=1##, this difference vanishes.