What is the relation between the Dirac equation and QED?

In summary, there are pros and cons to learning Dirac's equation. The pros are that it is mathematically equivalent to modern QED and that it has some merit. However, there are also cons, such as the fact that it is flawed in its conception and that it does not work in the relativistic regime of collisions.
  • #1
thaiqi
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Hello, everyone.
Need I understand Dirac equation if I plan to learn QED?
 
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  • #2
Yes, but you can (and in my opinion should) start right away with the field-theoretical formulation. There's no merit to learn the awfully complicated formulation of QED in terms of Dirac's "hole theory", which is mathematically equivalent to modern QED but flawed in its conception. You start as if relativistic "quantum mechanics" would make sense only to find out that it doesn't, because in the relativistic regime of collisions the particle number is not conserved but particles can be destroyed and created in accordance with the conservation laws (energy, momentum, angular momentum, various charges). That's why the natural way to describe relativistic quantum theory is quantum field theory.

My favorite introductory textbook is

M. D. Schwartz, Quantum field theory and the Standard
Model, Cambridge University Press, Cambridge, New York
(2014).
 
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  • #3
vanhees71 said:
Yes, but you can (and in my opinion should) start right away with the field-theoretical formulation. There's no merit to learn the awfully complicated formulation of QED in terms of Dirac's "hole theory", which is mathematically equivalent to modern QED but flawed in its conception. You start as if relativistic "quantum mechanics" would make sense only to find out that it doesn't, because in the relativistic regime of collisions the particle number is not conserved but particles can be destroyed and created in accordance with the conservation laws (energy, momentum, angular momentum, various charges). That's why the natural way to describe relativistic quantum theory is quantum field theory.

My favorite introductory textbook is

M. D. Schwartz, Quantum field theory and the Standard
Model, Cambridge University Press, Cambridge, New York
(2014).
Thanks. I have Cohen's Photons and Atoms at hand.
Are there any suggestions for how to learn Dirac's equation?
 
Last edited:
  • #4
thaiqi said:
Thanks. I have Cohen's Photons and Atoms at hand.
Are there any suggestions for how to learn Dirac's equation?
Albert Messiah's old book on Quantum Mechanics is my favorite.
 
  • #5
vanhees71 said:
Yes, but you can (and in my opinion should) start right away with the field-theoretical formulation. There's no merit to learn the awfully complicated formulation of QED in terms of Dirac's "hole theory", which is mathematically equivalent to modern QED but flawed in its conception. You start as if relativistic "quantum mechanics" would make sense only to find out that it doesn't, because in the relativistic regime of collisions the particle number is not conserved but particles can be destroyed and created in accordance with the conservation laws (energy, momentum, angular momentum, various charges). That's why the natural way to describe relativistic quantum theory is quantum field theory.

My favorite introductory textbook is

M. D. Schwartz, Quantum field theory and the Standard
Model, Cambridge University Press, Cambridge, New York
(2014).
Is group theory the best viable option to advance modern physics?
 
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  • #6
glschmitt said:
Is group theory the best viable option to advance modern physics?
This question is not answerable. People can of course give their opinions, but they're just that: opinions.
 
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Yes, I agree. Group Theory is vital for advancement of modern theory.
 
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  • #8
glschmitt said:
Yes, I agree. Group Theory is vital for advancement of modern theory.
You're not agreeing with me. You're just illustrating what I said: that the question is unanswerable. Your statement is just your opinion. That's not an answer; this is a physics forum, not a philosophy forum.
 
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1. What is the Dirac equation and how is it related to QED?

The Dirac equation is a relativistic wave equation that describes the behavior of fermions, such as electrons, in quantum mechanics. It is related to QED (Quantum Electrodynamics) because it provides a mathematical framework for understanding the behavior of particles and their interactions with electromagnetic fields.

2. How does the Dirac equation incorporate special relativity?

The Dirac equation incorporates special relativity by using four-component spinors to describe the wave function of particles. This allows for the inclusion of time and space in the equation, as well as the concept of spin, which is necessary for understanding the behavior of fermions.

3. What is the role of the Dirac equation in QED calculations?

The Dirac equation is a fundamental part of QED calculations, as it allows for the prediction of the behavior of particles in electromagnetic fields. It is used to calculate the scattering amplitudes of particles, which are then used to make predictions about the interactions between particles and electromagnetic fields.

4. How does the Dirac equation account for the behavior of antiparticles?

The Dirac equation accounts for the behavior of antiparticles by incorporating the concept of negative energy solutions. This allows for the prediction of the behavior of particles and their corresponding antiparticles, which is essential in understanding the behavior of particles in QED.

5. Are there any limitations to the Dirac equation in the context of QED?

While the Dirac equation is a powerful tool in understanding the behavior of particles in QED, it is not a complete theory on its own. It does not account for the strong and weak nuclear forces, which are described by other equations and theories. Additionally, it does not fully account for the effects of quantum fluctuations in high-energy interactions.

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