Units

Typical for high-energy physics is the natural unit system, which fixes by convention two universal constants to 1:

File:Hepb img670.gif

where h is Planck's constant and c is the speed of light in vacuum.

Thus, the number of fundamental mechanical units (L = length, M = mass, T = time) is reduced to one: Mass is usually measured in GeV in the natural unit system. The presently adopted SI (the international system of units, also known as MKSA) is related to the natural unit system through the values of three fundamental constants:

File:Hepb img671.gif

where e is the elementary charge.

These relations allow one to calculate the conversion factors between different units.

In spite of the attempted standardization to SI, several other unit systems are in use in electromagnetism: the Gaussian, CGS electrostatic and electromagnetic, and Heaviside-Lorentz system (for details on conversion of the units  Jackson75and the physical quantities , appendix). Electrostatic and electromagnetic units differ only by factors of c.

The parallel use of different unit systems can produce confusion, as physical quantities are defined up to multiplicative constants, which depend on the unit system. For instance, in all unit systems the force File:Hepb img672.gif on a charge q in an electric field  is File:Hepb img673.gif , hence (unit of force) = (unit of charge) File:Hepb img674.gif (unit of field).

However, this does not fix the units of charge and field separately, only their product. One way to fix the unit of charge is to fix by convention the proportionality constant k in Coulomb's law

File:Hepb img675.gif

F is the force between two point charges q1 and q2 separated by a distance r. In Gaussian units k=1, in Heaviside-Lorentz units File:Hepb img676.gif , and in SI units

File:Hepb img677.gif

with File:Hepb img678.gif Fm-1 the permittivity of free space. Strictly speaking, the SI unit C = coulomb is defined not from Coulomb's law, but from Ampère's law for the force between parallel currents, plus the relation File:Hepb img679.gif between the units for charge, current and time.

The fine structure constant is

File:Hepb img680.gif

If one combines natural mechanical units, with File:Hepb img681.gif , and Gaussian electromagnetic units, then electric charge becomes dimensionless. Thus, in these units the elementary charge is

File:Hepb img682.gif

Charge is also dimensionless in ``natural Heaviside-Lorentz units:

File:Hepb img683.gif

but not in natural mechanical units combined with SI electromagnetic units.

Gaussian and Heaviside-Lorentz units are different by factors of File:Hepb img684.gif . Some conversion factors from SI units into Gaussian units (see Jackson75 for more detail) are:

File:Hepb img685.gif

Hybrid unit systems are often used in which, for example, momentum is measured in GeV/c, length in m and magnetic induction (  ) in T = tesla. In these particular units, the elementary charge is

File:Hepb img686.gif

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