# Creation and annihilation operators in particle physics

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• Sophrosyne

#### Sophrosyne

I was recently reading about annihilation and creation operators in particle physics using the model of an harmonic oscillator, and then quantizing it. This is fine. I can understand it.

But how does this quantization of the energy of the harmonic oscillator manifest physically? Is it that only the masses of the particles created are quantized, or is it that the combination of the mass and velocity of the resulting particle created are quantized (ie, the total energy)? In other words, given the same oscillator energy level, you could create a very light particle moving away very fast, or you could have a heavier particle moving away very slowly?

Have the observed masses and velocities of elementary particles formed in particle accelerators been seen to follow this rigid quantization? It seems the masses of many of these particles are so much heavier than the quantization of the quantized harmonic oscillator model that it would be very difficult to verify that, especially if the differential velocities are also taken into account.

Have the observed masses and velocities of elementary particles formed in particle accelerators been seen to follow this rigid quantization

Yes. One particle weighs m, two weigh 2m, three weigh 3m, and so on.

Yes. One particle weighs m, two weigh 2m, three weigh 3m, and so on.

But in a particle collider, you can have a collision with, say, a resultant photon, couple of electrons, 3 muons, and a top quark. Is the sum of all those things perfectly quantized too (ie, a photon is 1m, a top quark is...X m, where X is some big integer)? How can you verify this quantization when there is such a massive difference in energy in the creation of a photon from a top quark?

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But how does this quantization of the energy of the harmonic oscillator manifest physically?

The harmonic oscillator is a highly idealized model, useful for learning basic concepts but way too simple for understanding actual experiments. Even at the heuristic level, quantum field theory, which is what you have to use to analyze experiments like the one you describe in post #3, does not just have one harmonic oscillator. It has an infinite number of them at each spacetime point. (And even that leaves out the complications involved with fermions.) So there is no simple way to look at what is going on as "quantization of the energy of the harmonic oscillator".

the masses of many of these particles are so much heavier than the quantization of the quantized harmonic oscillator model

Huh? You can make the quantized energy levels of a harmonic oscillator be as "heavy" as you want by adjusting the mass and spring constant.

But in a particle collider, you can have a collision with, say, a resultant photon, couple of electrons, 3 muons, and a top quark.

Sure, but that isn't the situation described by repeatedly applying a creation operator.

Huh? You can make the quantized energy levels of a harmonic oscillator be as "heavy" as you want by adjusting the mass and spring constant.

I see. Thanks.