Posted: Mar 09, 2017 8:52 pm
More rigorously, the creation and annihilation operators for particles in Hilbert space are, in the most general case, complex-valued operators of the form x+iy and x-iy (they are complex conjugates of each other). So, if x+iy is the creation operator for a particle, then x-iy is the creation operator for an antiparticle. (They are also the annihilation operators for the vice-versa entities).
However, if y=0, then the creation and annihilation operators are identical (and real), and the resulting particles become their own antiparticles.
The spin-statistics theorem, which divides particles into fermions and bosons on the basis of their spin angular momentum quantum numbers, implies that bosons are particles for which y=0 above.
However, if y=0, then the creation and annihilation operators are identical (and real), and the resulting particles become their own antiparticles.
The spin-statistics theorem, which divides particles into fermions and bosons on the basis of their spin angular momentum quantum numbers, implies that bosons are particles for which y=0 above.