The Infinity of the Smallest Particle

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when the smallest particle is cut in half over and over again infinitely times, it will never disappear... since I used the word infinite, right?
 
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How do you cut something that has no dimensions?
 
AnthonyFB said:
when the smallest particle is cut in half over and over again infinitely times, it will never disappear... since I used the word infinite, right?

The particle will decay at some randomly determined time. You can't cut it in half.
 
Decay can't necessarily be in the context of "cutting" either, yes it is a split at a vertex but the the two objects combined aren't necessarily the same size as the "un-split" particle because size is irrelevant. Particles have no size they are dimensionless. Quantum characteristics of particles in terms of mass or other quantities can essentially be "split" into the properties of the product particles.
 
Toponium is a hadron which is the bound state of a valance top quark and a valance antitop quark. Oversimplified presentations often state that top quarks don't form hadrons, because they decay to bottom quarks extremely rapidly after they are created, leaving no time to form a hadron. And, the vast majority of the time, this is true. But, the lifetime of a top quark is only an average lifetime. Sometimes it decays faster and sometimes it decays slower. In the highly improbable case that...
I'm following this paper by Kitaev on SL(2,R) representations and I'm having a problem in the normalization of the continuous eigenfunctions (eqs. (67)-(70)), which satisfy \langle f_s | f_{s'} \rangle = \int_{0}^{1} \frac{2}{(1-u)^2} f_s(u)^* f_{s'}(u) \, du. \tag{67} The singular contribution of the integral arises at the endpoint u=1 of the integral, and in the limit u \to 1, the function f_s(u) takes on the form f_s(u) \approx a_s (1-u)^{1/2 + i s} + a_s^* (1-u)^{1/2 - i s}. \tag{70}...

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