Quantum field theory (QFT)
Dirac(left) and Feynman (right) have made huge contributions to quantum field theory.
Theory of fundamental interactions
QFT is a theory framework inclusive of the fundamental interactions below:
- Electromagnetic interaction: described in quantum electrodynamics (QED).
- Strong interaction: described in quantum chromodynamics (QCD).
- Weak interaction: described in electroweak theory with electromagnetic interaction, which is the first unified theory.
Yet there is an exception here:
- gravitational interaction: described in general relativity.
- Electromagnetic interaction: described in quantum electrodynamics (QED).
- Strong interaction: described in quantum chromodynamics (QCD).
- Weak interaction: described in electroweak theory with electromagnetic interaction, which is the first unified theory.
Yet there is an exception here:
- gravitational interaction: described in general relativity.
Dirac equation
In QFT, Dirac equation describes spin 1/2 massless particle,just like electron:
where γ is Dirac matrices, μ=0,1,2,3. Dirac equation has important meaning such as below:
1. Positron: Dirac equation predicts the existence of positrons,so the equation is considered as the origin of antiparticles.
2. CPT-symmetry: An antiparticle is seen as a normal particle in time slip circumstances(time reversal transformation).
3. Dirac spinor: It's useful for showing the connection between particles and antiparticles.
4. QFT: Dirac equation combine special relativity with quantum mechanics. Therefore, it can be seen as the origin of QFT.
1. Positron: Dirac equation predicts the existence of positrons,so the equation is considered as the origin of antiparticles.
2. CPT-symmetry: An antiparticle is seen as a normal particle in time slip circumstances(time reversal transformation).
3. Dirac spinor: It's useful for showing the connection between particles and antiparticles.
4. QFT: Dirac equation combine special relativity with quantum mechanics. Therefore, it can be seen as the origin of QFT.
Feynman diagram
To describes the behavior of particles, Feynman diagram is a useful way to realize that.It is also a tool of perturbation theory. There are plenty of rules such as below:
However, if the diagram being closed loops,it means the divergence of energy. To manage this problem, it needs a way called "renormalization".
Renormalization
To manage the problem of divergence, "regularization" is the first step to do it. And "renormalization" is an overall technique. In QFT, renormalization is one significant technique especially in QED.
Anomaly
Anomaly implies the failure symmetry of the action of a theory. The way to cancel the anomaly in gauge theory is that constrain the fermion content of the SM. Further techniques including axion, Chern-Simons theory, and GS mechanism. These are also important way in string theory.