into the vacuum state by another disturbance. The disturbances are imagined to be due to bodies that interact with the virtual particle’s field. The probability amplitude Using natural units, , the probability amplitude for the creation, propagation, and destruction of a virtual particle is given, in the path integral formulation by where is the Hamiltonian operator, is elapsed time, is the energy change due to the disturbance, is the change in action due to the disturbance, is the field of the virtual particle, the integral is over all paths, and the classical action is given by where is the Lagrangian density. Here, the spacetime metric is given by The path integral often can be converted to the form where is a differential operator with and functions of spacetime. The first term in the argument represents the free particle and the second term represents the disturbance to the field from an external source such as a charge or a mass. The integral can be written (see ) where is the change in the action due to the disturbances and the propagator is the solution of Energy of interaction We assume that there are two point disturbances representing two bodies and that the disturbances are motionless and constant in time. The disturbances can be written where the delta functions are in space, the disturbances are located at and , and the coefficients and are the strengths of the disturbances. If we neglect self-interactions of the disturbances then W becomes which can be written Here is the Fourier transform of Finally, the change in energy due to the static disturbances of the vacuum is If this quantity is negative, the force is attractive. If it is positive, the force is repulsive. Examples of static, motionless, interacting currents are the Yukawa potential, the Coulomb potential in a vacuum, and the Coulomb potential in a simple plasma or electron gas. The expression for the interaction energy can be generalized to the situation in which the point particles are moving, but the motion is slow compared with the speed of light. Examples are the Darwin interaction in a vacuum and in a plasma. Finally, the expression for the interaction energy can be generalized to situations in which the disturbances are not point particles, but are possibly line charges, tubes of charges, or current vortices. Examples include: two line charges embedded in a plasma or electron gas,