- #1
thaiqi
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Hello, everyone.
Need I understand Dirac equation if I plan to learn QED?
Need I understand Dirac equation if I plan to learn QED?
Thanks. I have Cohen's Photons and Atoms at hand.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).
Albert Messiah's old book on Quantum Mechanics is my favorite.thaiqi said:Thanks. I have Cohen's Photons and Atoms at hand.
Are there any suggestions for how to learn Dirac's equation?
Is group theory the best viable option to advance modern physics?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).
This question is not answerable. People can of course give their opinions, but they're just that: opinions.glschmitt said:Is group theory the best viable option to advance modern physics?
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.glschmitt said:Yes, I agree. Group Theory is vital for advancement of modern theory.
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.
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.
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.
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.
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.