Lorentz–Heaviside units Information & Lorentz–Heaviside units Links at HealthHaven.com

Lorentz–Heaviside units (or Heaviside–Lorentz units) are a system of units (particularly electromagnetic units) within cgs. They are often used in relativistic calculations. They share with CGS-Gaussian units the property that $\scriptstyle \varepsilon_0$ and $\scriptstyle \mu_0$ do not exist (having been incorporated implicitly into the unit system), but differ by factors of $\scriptstyle \sqrt{4\pi}$ in the definitions of the fields and electric charge. They are particularly convenient when performing calculations in spatial dimensions greater than three such as is done in string theory.

Lorentz–Heaviside units, like SI units but unlike Gaussian units, are "rationalized", meaning that there are no factors of $\scriptstyle 4\pi$ that appear explicitly in Maxwell's equations.^[1]^[2] The fact that these units are rationalized partly explains their appeal in quantum field theory: The Lagrangian underlying the theory does not have any factors of $\scriptstyle 4\pi$ in these units.^[1]

Lorentz-Heaviside units may be combined with natural units in which $\scriptstyle \hbar=c=1$ also.

[edit] Maxwell's equations with sources

The equations with sources take the following form:

$\nabla \cdot \mathbf{E} = \rho$

$\nabla \cdot \mathbf{B} = 0$

$\nabla \times \mathbf{E} = -\frac{1}{c} \frac{\partial \mathbf{B}} {\partial t}$

$\nabla \times \mathbf{B} = \frac{1}{c} \frac{ \partial \mathbf{E}} {\partial t} + \frac{1}{c} \mathbf{J}$

where c is the speed of light in a vacuum. Here E is the electric field, B is the magnetic field, $ρ$ is the charge density, and J is the current density.

The charge and fields in Lorentz–Heaviside units are related to the quantities in cgs units by

$q_{LH} \ \stackrel{\mathrm{def}}{=}\ \sqrt{4\pi} q_{cgs}$

$\mathbf{E}_{LH} \ \stackrel{\mathrm{def}}{=}\ { \mathbf{E}_{cgs} \over \sqrt{4\pi} }$

$\mathbf{B}_{LH} \ \stackrel{\mathrm{def}}{=}\ { \mathbf{B}_{cgs} \over \sqrt{4\pi} }$ .

[edit] References

^ ^a ^b Littlejohn, Robert (Fall 2007). "Gaussian, SI and Other Systems of Units in Electromagnetic Theory" (pdf). Physics 221A, University of California, Berkeley lecture notes. http://bohr.physics.berkeley.edu/classes/221/0708/notes/emunits.pdf. Retrieved 2008-05-06.
^ Kowalski, Ludwik, 1986, "A Short History of the SI Units in Electricity," The Physics Teacher 24(2): 97-99. Alternate web link (subscription required)

[edit] External links

Heaviside–Lorentz units

[Littlejohn-0] Littlejohn, Robert (Fall 2007). "Gaussian, SI and Other Systems of Units in Electromagnetic Theory" (pdf). Physics 221A, University of California, Berkeley lecture notes. http://bohr.physics.berkeley.edu/classes/221/0708/notes/emunits.pdf. Retrieved 2008-05-06.

[Kowalski-1] Kowalski, Ludwik, 1986, "A Short History of the SI Units in Electricity," The Physics Teacher 24(2): 97-99. Alternate web link (subscription required)

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