In relativistic quantum mechanics and quantum field theory, the Bargmann–Wigner equations describe free particles with non-zero mass and arbitrary spin j, an integer for bosons (j = 1, 2, 3...) or half-integer for fermions (j = 1 ⁄ 2, 3 ⁄ 2, 5 ⁄ 2 ...). The solutions to the equations are wavefunctions, mathematically in the form of multi-component spinor fields.