page_title: Static forces and virtual-particle exchange
section_title: Delta function currents
hierarchical_section_title: Static forces and virtual-particle exchange / Selected examples / Electrostatics / Coulomb potential between two current loops embedded in a magnetic field / Currents with angular momentum / Delta function currents
caption_attribution_description: English: Angular momentum 1 and 5
context_page_description: Static force fields are fields, such as a simple electric, magnetic or gravitational fields, that exist without excitations. The most common approximation method that physicists use for scattering calculations can be interpreted as static forces arising from the interactions between two bodies mediated by virtual particles, particles that exist for only a short time determined by the uncertainty principle. The virtual particles, also known as force carriers, are bosons, with different bosons associated with each force.
  The virtual-particle description of static forces is capable of identifying the spatial form of the forces, such as the inverse-square behavior in Newton's law of universal gravitation and in Coulomb's law. It is also able to predict whether the forces are attractive or repulsive for like bodies.
  The path integral formulation is the natural language for describing force carriers. Pions, photons, and gravitons fall into these respective categories.
  There are limits to the validity of the virtual particle picture.
context_section_description: Unlike classical currents, quantum current loops can have various values of the Larmor radius for a given energy. Landau levels, the energy states of a charged particle in the presence of a magnetic field, are multiply degenerate. The current loops correspond to angular momentum states of the charged particle that may have the same energy. Specifically, the charge density is peaked around radii of
  where  is the angular momentum quantum number. When  we recover the classical situation in which the electron orbits the magnetic field at the Larmor radius. If currents of two angular momentum  and  interact, and we assume the charge densities are delta functions at radius , then the interaction energy is
  The interaction energy for  is given in Figure 1 for various values of . The energy for two different values is given in Figure 2.
caption: Figure 2. Interaction energy vs. r for angular momentum states of value one and five.
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