Retarded, or Casimir, Long-Range Potentials

Only someone with a short‐range view could fail to be aware of the great importance of long‐range interactions. Indeed, from the late 18th century, when Coulomb discovered that the electrostatic interaction has the same ${\text{1/r}}^2$ force law that Newton had found for the gravitational interaction, until perhaps the 1930s, when the strong and weak interactions began to be understood, long‐range interactions largely were the subject of physics. By long‐range interactions I mean not only those for which the potential behaves as $\text{1/r}$ for all r but those whose potentials behave asymptotically as some power of $\text{1/r.}$ These originate in $\text{1/r}$ potentials and include, for example, the van der Waals ${\text{1/r}}^6$ interaction (as calculated nonrelativistically) between two spherically symmetric atoms at a large separation r, and multipole interactions between charge distributions. Long‐range potentials therefore not only play a vital role in astrophysics via Newton's law of gravitation and a significant role in nuclear physics via Coulomb's law, but determine almost all of atomic, molecular and condensed‐matter physics.