Creation and annihilation operators in particle physics

In summary, the conversation discusses the concept of quantization of the energy of a harmonic oscillator in particle physics and how it manifests physically. It is mentioned that quantum field theory has an infinite number of harmonic oscillators at each spacetime point, making it difficult to view the process as simple quantization. The conversation also addresses the issue of heavier particles in particle accelerators and how the quantized harmonic oscillator model can still be adjusted to accommodate them.
  • #1
Sophrosyne
128
21
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.

Thanks in advance.
 
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  • #2
Sophrosyne said:
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.
 
  • #3
Vanadium 50 said:
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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  • #4
Sophrosyne said:
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".
 
  • #5
Sophrosyne said:
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.
 
  • #6
Sophrosyne said:
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.
 
  • #7
PeterDonis said:
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.
 

FAQ: Creation and annihilation operators in particle physics

1. What are creation and annihilation operators in particle physics?

Creation and annihilation operators are mathematical operators used in quantum field theory to describe the creation and destruction of particles. They are used to represent the creation and annihilation of a particle at a specific location and time.

2. How do creation and annihilation operators work?

Creation and annihilation operators are represented by symbols, such as a^+ and a, respectively. When applied to a quantum state, the creation operator adds a particle to the system, while the annihilation operator removes a particle from the system. These operators follow certain mathematical rules, known as commutation relations, which allow for the calculation of particle interactions and probabilities.

3. What is the significance of creation and annihilation operators in particle physics?

Creation and annihilation operators play a crucial role in quantum field theory, which is the theoretical framework used to describe the behavior of particles at the subatomic level. They allow for the calculation of particle interactions and the prediction of particle properties, leading to a better understanding of the fundamental building blocks of the universe.

4. How are creation and annihilation operators related to each other?

Creation and annihilation operators are related to each other through their commutation relations. These relations dictate how the two operators behave when applied to a quantum state. For example, the commutation relation between the creation and annihilation operators for a specific type of particle determines the probability of finding that particle at a certain location and time.

5. Can creation and annihilation operators be observed in experiments?

Creation and annihilation operators are mathematical tools used in theoretical calculations, and as such, they cannot be directly observed in experiments. However, the predictions made using these operators have been experimentally verified, providing strong evidence for their existence and importance in describing particle interactions.

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