# What are the fundamental properties of matter?

Say we have a particle, what are the most fundamental properties that distinguishes it from another kind of a particle. What is written in it's identity card?

Spin, electric charge, rest mass, mean lifetime.. what else?

Any intrinsic quantum number, like baryon number, strangeness, charm, beauty. But also which kind of interaction the particle can have, like electromagnetic, weak, strong.

mfb
Mentor
But also which kind of interaction the particle can have, like electromagnetic, weak, strong.
That follows from the quantum numbers (charge, weak hypercharge, color charge, (mass)).

=> mass and all quantum numbers. Where mass follows from its interaction with the Higgs field, so you can replace "mass" by the corresponding interaction strength. Just the Higgs boson itself has its own mass (plus contributions from its self-interaction).

Is there a particle that have exactly same mass, spin and charge value? I guess not. So if we represent (distinguish) each particle with that numbers, can't we gather all other properties in terms of mass, spin and charge? Can we say that some properties are more fundamental?

mfb
Mentor
If you want to create a function like hypercharge(mass,spin,electriccharge)=whatever: While this would be possible, it does not give you anything new. There is not a nice relation between those parameters.

With the exception of massless particles, mass is unique to all particle/antiparticle pair in the usual meaning: A particle with a mass of 511keV is an electron or its antiparticle.
But in quantum field theory, you have more: You have left- and right-handed electrons. You have six different up-quarks, one left/right pair for each color. You have 8 gluons, and there is not even a unique way to define them (you have some freedom). Do you count those as different particles? ;)

If you want to create a function like hypercharge(mass,spin,electriccharge)=whatever: While this would be possible, it does not give you anything new. There is not a nice relation between those parameters.

With the exception of massless particles, mass is unique to all particle/antiparticle pair in the usual meaning: A particle with a mass of 511keV is an electron or its antiparticle.
But in quantum field theory, you have more: You have left- and right-handed electrons. You have six different up-quarks, one left/right pair for each color. You have 8 gluons, and there is not even a unique way to define them (you have some freedom). Do you count those as different particles? ;)

What is the difference between left and right handed electron briefly? Is this like a difference between 1s electron and 2s electron of an atom, or a difference with more severe consequences?

mfb
Mentor
The first one couples to the weak interaction, the second one does not. See Chirality for details.

The first one couples to the weak interaction, the second one does not. See Chirality for details.

Then where is the limit of "calling a particle as a different particle"? For example, if an electron's charge is -1, we call it electron, whereas if the charge is +1, we call positron (or antielectron). We divide matter as particles and antiparticles (different particle). Why we call both left and right handed electrons as "electron" instead dividing particles as left and right handed?

mfb
Mentor
Then where is the limit of "calling a particle as a different particle"?
That is the question, and the answer depends on the scientific field or even the person you ask.

That is the question, and the answer depends on the scientific field or even the person you ask.

I see. It seems like I have to go deeper in particle physics to understand the properties of particles. Thanks for the answers.

Bill_K
You have left- and right-handed electrons. Do you count those as different particles? ;)
No. There is no such thing as a left-handed electron.

No. There is no such thing as a left-handed electron.

? Sure there is, it is just that they always come mixed with right-handed electrons. If electrons were massless there would be no mixing and they would even propagate separately. So in fact above the electroweak scale I see no reason not to think about them as being totally separate.

Bill_K
Chirality is just a projection operator. It does not commute with the Hamiltonian, and consequently its eigenvalues do not represent a property of a free fermion. It does not distinguish two 'kinds' of fermions. Its role in weak interactions is only to make the interaction V - A. It is not really a particle property, but if it were, it would be more correctly a property of the W boson than the fermions.

It makes no sense to describe left-handed fermions and right-handed fermions as separate particles. That would make it sound like I could accumulate a box full of right-handed muons, for example, that fail to participate in the weak interaction and so would never decay.

Yes, if electrons were massless, right-handedness and left-handedness would be conserved, and then we could talk about two kinds of particles. But they are not massless. (Neither are neutrinos.) And high-energy particles look to be 'almost' massless, but again they are not. It is just that for a high-energy particle, chirality projects unequal proportions of the wavefunction.

mfb
Mentor
Please do not remove the context:
But in quantum field theory, you have more: You have left- and right-handed electrons.
As far as I know, QFT separates left- and right-handed parts. Real electrons are always a mixture of both, but that is true for the momentum spectrum as well, for example (there are no electrons with an exact momentum in real life).