In my physics textbook, while talking about the scope of physics, it mentions the four fundamental forces of nature which are Gravitational force, Electromagnetic force, Strong Nuclear force and Weak Nuclear force, of these the most astonishing one I feel is the weak nuclear force. My book states that it is responsible for $\beta$-decay and other kinds of radioactivity. Now as far as I know:

$\mathbf {Force}$ is an interaction between an object and it's surrounding which causes the object to change it's momentum while the interaction is happening.

Now for gravitational and electromagnetic force I know about their classical model and, as far as I know, there they just are cause change in momentum of the object though one acts through charge and other acts through mass. But for weak nuclear force there is something more to it, it causes the particles on which it acts to change it's properties (like proton turning into neutron and vice versa) which is more than just a change in momentum.

So my questions is:

  • How do physicists account for these properties of weak interaction mathematically?

Thanks in advance.

  • $\begingroup$ Related: physics.stackexchange.com/q/4428/2451 $\endgroup$ – Qmechanic Oct 30 '19 at 15:21
  • 1
    $\begingroup$ See physics.stackexchange.com/q/405411/44126 and links therein for an example of a scattering interaction which is modified by the weak force. In such experiments it's more convenient to discuss "cross sections" for an interaction than bare forces. $\endgroup$ – rob Oct 31 '19 at 2:35
  • $\begingroup$ Feedback to the post (v3): Asking How do physicists account for fundamental forces mathematically? is still too broad. Try to focus on your main subquestion. If the answers do not solve your doubts, submit a new question. Look for duplicates. $\endgroup$ – Qmechanic Oct 31 '19 at 9:40
  • $\begingroup$ @Qmechanic I have now specifically asked for weak interaction can you consider reopening the question. $\endgroup$ – user238497 Oct 31 '19 at 10:17
  • $\begingroup$ Why don't you read up on a book or Wikipedia? Looks like you are inviting a tutorial session. $\endgroup$ – Cosmas Zachos Oct 31 '19 at 18:33

Actually one should single out electromagnetic force as special, since its gauge group $U(1)_{EM}$ is Abelian.

All the other 3 forces are non-Abelian, thus capable of changing an interacting particle's properties (with the understanding that the particle transforms non-trivially with regard to the non-Abelian gauge symmetry). For example, strong force could mutate the color of a quark, and gravity could flip the spin of a fermion.


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