# Is there a field for which neutral particle and antiparticle, can be considered as positive and negative charge?

I apologize, but QFT is not my domain. What I ask is connected with the question Do the fields exist without electric charges? .

By analogy with the electron and proton, that carry the electric charges of the electrostatic field, could a neutron and anti-neutron represent the positive, respectively negative, charges of some field? I am sure that, if the answer is positive, the supposed field is not the gravitational one. In the gravitational field all the charges (masses) are positive.

• Sofia, neutrons are bound states of three quarks and they have no net electrical charge because the quark charges balance out. It's like asking if hydrogen atoms could be the source of some field because they have no net charge either. – John Rennie Dec 11 '14 at 12:02

Additionally, quantumly, one would say "to be charged under some field" means to transform non-trivially under some gauge group. The Standard Model has the electroweak $\mathrm{SU}(2)_R \times \mathrm{U}(1)_Y$ and the strong $\mathrm{SU}(3)$ as gauge groups. The neutron is color-neutral and electrically neutral. A left-handed neutron composed of three left-handed quarks has an overall weak isospin of $\frac{1}{2}$, though, and is thus also overall "charged" under the weak $\mathrm{SU}(2)_L$, a right-handed neutron has weak isospin $0$ (Note that the actual states of a neutron may well be a superposition of the two). Since anti-particles have opposite quantum numbers (transform in the conjugate representations), a anti-neutron has either $-\frac{1}{2}$ or $0$ as the weak isospin of its chiral states. Therefore, you might say the neutron is (or can be) "charged under the weak interaction".
Note that non-vanishing weak isospin $T_3$ also implies non-vanishing hypercharge $Y$, since vanishing electric charge means $T_3 + \frac{Y}{2} = 0$. Yet the boson of the $\mathrm{U}(1)$ combines with one of the three bosons of the $\mathrm{SU}(2)_L$ to form the photon, which couples to electric charge. Non-vanishing hypercharge is, in and of itself, not very interesting.