Bosonic field

In quantum field theory, bosonic fields are quantum fields whose quanta are bosons; that is, they obey Bose-Einstein statistics.

By definition, free (non-interacting) bosonic fields obey canonical commutation relations. Those relations also hold in the interaction picture, where the fields evolve in time as if free. It is these commutation relations that imply Bose-Einstein statistics for the field quanta.

As implied by the Spin-statistics theorem, quantization of local, relativistic quantum field theories in 3+1 dimensions may lead to either bosonic or fermionic fields, i.e., fields obeying commutation or anti-commutation relations, according to whether they have integral or half integral spin, respectively. In this sense, bosonic fields are one of the two theoretically possible types of quantum field, namely those with integral spin. In lower dimensions, e.g. 2+1, one may have other types of fields, known as anyons, that obey fractional statistics.

Examples of bosonic fields include scalar fields, vector fields, and tensor fields, as characterized by their properties under Lorentz transformations (or equivalentely by their spin, 0,1 and 2, respectively). Physical examples, in the same order, are: the Higgs field, the photon field and the graviton field. While the first one remains to be observed, it is widely believed to exist. Of the last two, only the photon field can be quantized using the conventional methods of canonical or path integral quantization. This has led to the theory of quantum electrodynamics, arguably the most successful theory in Physics. Quantization of gravity, on the other hand, is a long standing problem that has led to theories such as string theory.

See also