Quantum Field Theory and the Standard Model


Quantum field theory (QFT) unifies Einstein's special relativity with quantum mechanics. QFT is the foundation of what physicists refer to as the Standard Model (SM), which is the theoretical framework that describes all known particles and their interactions except gravity. A word of caution on QFT. It is one of the most difficult subjects in science.
Quantum mechanics (QM) is based on three things:
1- Physical observable are operators
2- the Uncertainty principle
3- Commutation relations.


However, QM cannot describe particle reactions at relativistic high energy. That is why it is referred to as non-relativistic quantum mechanics (NRQM). Relativity states that:
E = mc2......(equation 1)

This equation relates energy to mass. This means that with high enough energy that is proportional to the particle's mass, then by equation 1, we can "create" the particle. Due to conservation laws, we need twice the particle's energy, so that we can create the particle and its antiparticle. So, in high energy reactions:
1- Particle number is not fixed
2- Types of particles present are not fixed.



The two facts are in direct conflict with NRQM. In NRQM, the dynamics of the system are described by the Schrodinger equation. In relativistic quantum mechanics (RQM), the dynamics of the system are described by the Dirac equation. In QM, we dealt with the coordinates and momenta as quantized variables. This process is called "first quantization". However, in QFT, we make the transition to "second quantization", where we quantize "fields" which have an infinite number of degrees of freedom. The transition from first to second quantization, that is from QM to QFT, we make the transition from three degrees of freedom, to an infinite number of degrees of freedom, described by the field. QFT consists of electromagnetic, weak and strong interactions. Electromagnetic and weak interactions were unified under one interaction, the Electro Weak (EW) interaction. Electromagnetic interactions are referred to as Quantum Electrodynamics (QED), and the strong interactions are referred to as Quantum Chromodynamics (QCD).


QFT or SM is the most successful theory in physics. The Higgs particle found in 2012 is one of the best confirmations of the SM. There are theories beyond the SM, such as Supersymmetry, Supergravity, and Superstring theories. However, none of the particles predicted by these theories have been found. My bet is that the next new particle that will be found at the Large Hadron Collider (LHC) will be a supersymmetric particle. Only time can tell.

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