It has recently been shown that there exists a class of stable gapless spin
liquids in 3+1 dimensions described by higher rank tensor U(1) gauge fields,
giving rise to an emergent tensor electromagnetism. The tensor gauge field of
these theories couples naturally to subdimensional particles (such as
fractons), which are restricted by gauge invariance to move only along
lower-dimensional subspaces of the system. We here work out some of the basic
generalized electromagnetic properties of subdimensional particles coupled to
tensor electromagnetism, such as generalized electrostatic fields, potential
formulations, Lorentz forces, Maxwell equations, and Biot-Savart laws. Some
concepts from conventional electromagnetism will carry over directly, while
others require significant modification.Comment: 14+4 page
