Interaction between matter and antimatter in Dirac equation

In summary, the time derivative of matter is dependent on the spatial derivative of antimatter, but not the spatial derivative of matter. Likewise, the time derivative of antimatter is dependent on the spatial derivative of matter, but not the spatial derivative of antimatter. This counterintuitive behavior is explained by the Dirac spinor.
  • #1
lagrangman
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TL;DR Summary
Confusing interaction between matter and antimatter in Dirac equation.
I'm new to relativistic quantum mechanics and quantum field theory and was trying to learn about the Dirac equation.

Unfortunately, I got a little stumped by the interaction between matter and antimatter.

It seems like the time derivative of matter is dependent on the spatial derivative of antimatter, but not the spatial derivative of matter. Likewise, the time derivative of antimatter is dependent on the spatial derivative of matter, but not the spatial derivative of antimatter.

To me this means that if there is momentum of matter, then the antimatter field should be changing, which doesn't make sense to me.

I find this counterintuitive and was hoping that someone could explain this to me.
 
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  • #2
lagrangman said:
Summary:: Confusing interaction between matter and antimatter in Dirac equation.

It seems like the time derivative of matter is dependent on the spatial derivative of antimatter, but not the spatial derivative of matter.
What makes you think that?
 
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  • #3
lagrangman said:
Summary:: Confusing interaction between matter and antimatter in Dirac equation.

I'm new to relativistic quantum mechanics and quantum field theory and was trying to learn about the Dirac equation.

Unfortunately, I got a little stumped by the interaction between matter and antimatter.

It seems like the time derivative of matter is dependent on the spatial derivative of antimatter, but not the spatial derivative of matter. Likewise, the time derivative of antimatter is dependent on the spatial derivative of matter, but not the spatial derivative of antimatter.

To me this means that if there is momentum of matter, then the antimatter field should be changing, which doesn't make sense to me.

I find this counterintuitive and was hoping that someone could explain this to me.
You could read this and tell us precisely what you don't understand. A liitle mathematics might help:

https://en.wikipedia.org/wiki/Dirac_spinor
 
  • #4
Isn't the first row of the dirac equation
$$i\frac{\partial \psi_1}{\partial t} = m \psi_1 - i \frac{\partial \psi_4}{\partial x} - i \frac{\partial \psi_4}{\partial y} - i \frac{\partial \psi_3}{\partial z}$$

I was under the impression that ##\psi_1## and ##\psi_2## were matter and ##\psi_3## and ##\psi_4## were antimatter.
 
  • #5
lagrangman said:
Isn't the first row of the dirac equation
$$i\frac{\partial \psi_1}{\partial \t} = m \psi_1 - i \frac{\partial \psi_4}{\partial x} - i \frac{\partial \psi_4}{\partial y} - i \frac{\partial \psi_3}{\partial z}$$

I was under the impression that ##\psi_1## and ##\psi_2## were matter and ##\psi_3## and ##\psi_4## were antimatter.
Not quite. The Dirac spinors for both particles and antiparticles have four components. In the non-relativistic case, the solutions simplify to approximately two-component solutions, but not in general.
 
  • #6
Thanks, very helpful.
 

FAQ: Interaction between matter and antimatter in Dirac equation

1. What is the Dirac equation?

The Dirac equation is a mathematical formula that describes the behavior of particles with spin, such as electrons, in the framework of quantum mechanics. It was developed by physicist Paul Dirac in the 1920s.

2. What is antimatter?

Antimatter is a type of matter that has the opposite properties of normal matter. It is made up of antiparticles, which have the same mass as their corresponding particles, but opposite charge and other quantum numbers.

3. How does the Dirac equation describe the interaction between matter and antimatter?

The Dirac equation includes terms for both matter and antimatter particles, and describes how they interact with each other. It predicts that when a particle and its corresponding antiparticle come into contact, they will annihilate each other and release energy.

4. What are the implications of the interaction between matter and antimatter in the Dirac equation?

One of the implications of the Dirac equation is that it predicts the existence of antimatter particles, which has been confirmed by experiments. It also helps us understand the behavior of particles at the subatomic level, and has applications in fields such as particle physics and quantum computing.

5. Is the interaction between matter and antimatter always destructive?

In most cases, yes. When a particle and its antiparticle come into contact, they will annihilate each other and release energy. However, there are some rare instances where matter and antimatter can coexist without destroying each other, such as in certain types of particle accelerators or in the early universe before the Big Bang.

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