Introduction

In today’s article, we will be attempting to understand Quantum Field Theory (QFT).

Quantum Physics or Quantum Mechanics is a fundamental theory that provides descriptions of the physical properties of nature at the scale of atomic and subatomic particles. Meaning, Quantum physics is the study of extremely small particles like atoms, protons, electrons, etc., and even subatomic or elementary particles like gluons, Higgs boson, photons, quarks, etc. Initially, I thought quantum mechanics and quantum field theory meant the same thing, but quantum field theory is a part of quantum mechanics that combines the elements of special and general relativity to explain the behavior and interactions at a subatomic level.

The Origins of Quantum Mechanics

Quantum Mechanics began with scientists like Einstein, Planck, etc., observing the particle-wave duality of light, which states that light exhibits properties of both waves and particles. With the help of Bohr and Heisenberg, they further extended their understanding to matter itself, discovering that even subatomic particles attain this kind of particle-wave duality.

From this emerges Erwin Schrödinger’s The Schrödinger Equation, a wave function that:

  • Describes how matter waves change over time
  • Helps us predict analytically and precisely the probability of the evolution of quantum systems

However, macrophysics didn’t cooperate with microphysics. It’s been long known that Erwin Schrödinger’s quantum mechanics model never worked out with Einstein’s general and special relativity. Relativity wants events to be continuous and deterministic, meaning that every cause matches up with a specific local effect, whereas quantum mechanics produces events that are discontinuous and probabilistic rather than definite outcomes.

Take for example quantum jump or leap: it is the quantum phenomenon where an electron or an atom can abruptly transition from one discrete energy state to another when it interacts with photons of light. The abrupt transition states that the electron moves to a different energy state without having to move through space or, in other words, has a discontinuous trajectory. Overall, in the microscopic realm, there is uncertainty, chaos, fluctuations, and entanglements, all of which go against Einstein’s gentle, smooth, and deterministic model of the curved spacetime continuum.

The Conflict Between Quantum Mechanics and Relativity

This contradiction left English theoretical physicist Paul Dirac curious if he could find a way to combine these two equations.

Dirac started with Einstein’s relativity equation and attempted to unify it with the spin - an intrinsic property of all elementary particles - of a quantum object. He was stuck in a tangent of messy mathematics until he stumbled upon a new idea of including anti-spin into his equations. This led all that messy mathematics to simplify into a single beautiful equation known as the Dirac equation, which successfully predicted the motion of electrons at any speed, even whilst present in other fields like an electromagnetic field, compared to Schrödinger’s equation that was confined to only describing the possible positions of electrons with no internal properties.

The Discovery of Antimatter

When solving his equation, Dirac encountered two solutions:

  1. A positive solution, representing matter.
  2. A negative solution, implying the existence of antimatter.

Initially confused, Dirac later proposed the Dirac Sea analogy:

  • Imagine an infinite “sea” of electrons filling all negative energy states.
  • Removing an electron leaves a hole, which behaves like a positron (the antimatter counterpart of an electron).

Although the Dirac sea doesn’t exist, these holes act as a visualization of what is now called antimatter. It is said that during the Big Bang, the universe released equal amounts of matter and antimatter, but why matter is more abundant remains an open question.

What is Quantum Field Theory (QFT)?

Quantum Field Theory (QFT) is a theory that describes all elementary particles and their antiparticle counterparts as excitations or vibrations in their respective fundamental fields that exist throughout the universe.

Meaning:

  • Every elementary particle has a field, like the electromagnetic field for a proton, but in this case, it is for every elementary particle, where the particle itself is an oscillation or peak in the field.
  • By representing particles as fields, Dirac’s equation worked better in predicting the evolution and interactions of quantum systems than Schrödinger’s equation.
  • This concept is known as the Second Quantization, whereas Schrödinger’s equation is the First Quantization.

Feynman’s Path Integral Formulation

Physicist Richard Feynman extended QFT using the Path Integral Formulation, which states that:

  • A quantum system can and will take all of the possible paths before and after measurement.
  • However, the most extreme paths cancel out, leaving only a few interactions that we experience daily.

Conclusion

Quantum Field Theory is one of the most successful theories ever proposed, mainly due to:

  • Its predictive power about quantum systems.
  • Its ability to unify relativity with quantum mechanics.
  • Its profound implications, suggesting even more remarkable discoveries in the future.