Materiality of elementary particles

David Welsh
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Do elementary particles, e.g. electron, protons, etc, have material substance in the ordinary meaning of substance? If so, what is the substance?
 
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What do you mean by "substance"? Elementary particles carry energy, momentum, and angular momentum. If you define substance as something carrying these properties, they are substance.
 
Protons are not elementary - they are made of quarks.
 
Elementary particles are really quantized fields. They are not composed of some "stuff". A field is something that has some value everywhere. Consider the gravitational and the electromagnetic fields.

I remember a physics professor calling a photon a blob of light -- that's the best macroscopic analogy that I know of.
 
'Material' is probably not an applicable term for sub atomic particles, unless you regard anything which has mass as material.
Before sub atomic particles were discovered it was thought that a single atom of some element was as fundamental as possible, a unit which could not be divided further.
That's still true in the sense that a single atom of (say Uranium for example) is as small an amount of Uranium as there can be.
Although we now know that atoms have component parts, a single atom is still as small as you can go and still have 'Uranium'
The component particles have no Uranium-like properties at all, (and it's the same for every other 'element' of the periodic table.
 
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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