Boson field

In quantum field theory, a bosonic field is a quantum field whose quanta are bosons; that is, they obey Bose–Einstein statistics. Bosonic fields obey canonical commutation relations, as distinct from the canonical anticommutation relations obeyed by fermionic fields.

Examples include scalar fields, describing spin-0 particles such as the Higgs boson, and gauge fields, describing spin-1 particles such as the photon.

Free (non-interacting) bosonic fields obey canonical commutation relations. Those relations also hold for interacting bosonic fields in the interaction picture, where the fields evolve in time as if free and the effects of the interaction are encoded in the evolution of the states. It is these commutation relations that imply Bose–Einstein statistics for the field quanta.

Examples of bosonic fields include scalar fields, gauge fields, and symmetric 2-tensor fields, which are characterized by their covariance under Lorentz transformations and have spins 0, 1 and 2, respectively. Physical examples, in the same order, are the Higgs field, the photon field, and the graviton field. 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, one of the most successful theories in physics. Quantization of gravity, on the other hand, is a long-standing problem that has led to development of theories such as string theory and loop quantum gravity.

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