Bosonic field

Of the last two, only the photon field can be quantized using the conventional methods of canonical or path integral quantization.

In a non-relativistic many-body theory, the spin and the statistical properties of the quanta are not directly related.

In fact, the commutation or anti-commutation relations are assumed based on whether the theory one intends to study corresponds to particles obeying Bose–Einstein or Fermi–Dirac statistics.

In this context the spin remains an internal quantum number that is only phenomenologically related to the statistical properties of the quanta.

Such non-relativistic fields are not as fundamental as their relativistic counterparts: they provide a convenient 're-packaging' of the many-body wave function describing the state of the system, whereas the relativistic fields described above are a necessary consequence of the consistent union of relativity and quantum mechanics.