Quantum field theory
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Introduction
Welcome! This is a self-learning guide for all readers that want to learn about quantum field theory. You don't have to be an expert to read this guide! It is made for anyone who is curious and wants a challenge.
Quantum field theory (QFT) is our most accurate description of the universe. The Standard Model, a comprehensive quantum field theory, is the backbone of modern physics, and has been tested to extreme precision. Despite this, quantum field theory has a reputation for not being very accessible, in part due to its scary-long Lagrangians and incredibly formidable integrals. So this is an informal self-learning guide to QFT for anyone who is, as Einstein said, passionately curious.
Preface
As far as we know, all matter in the universe is quantum in nature. Quantum mechanics governs the behavior of all matter. At an introductory and intermediate level, the dynamics of quantum systems is typically solved with the famous Schrödinger equation. The predictions of the Schrödinger equation were (and are) indeed enormously successful; for instance, its predictions reproduced the spectrum of the hydrogen atom, and it correctly predicts probabilities of a quantum particle (such as an electron) to be in a particular position at a particular moment in time.
However, relativistic quantum field theory is a far more accurate theory of quantum mechanics. In fact, while we may use approximations like (semi-)classical theory and nonrelativistic or single-particle quantum mechanics, quantum field theory, and specifically the Standard Model, offers the best and most accurate results.
That is to say, any quantum system may be solved for by the Schrödinger equation, but doing the same calculations with quantum field theory offers results with unparalleled precision. Predictions of the magnetic moment of electrons, energy levels of the hydrogen atom, a variety of previously-unknown elementary particles, and the Rydberg constant made through quantum field theory have been experimentally tested and confirmed very well.
These are not meaningless predictions either; our understanding of the emission and absorption of light, subatomic magnetism, and even our standard of time in the definition of a second are based on these predictions. In turn, numerous scientific experiments, material science, laser technology, and electronics depend on applying these predictions, without which they would likely not progress to how they are today.
Quantum field theory is a very rewarding, if difficult, theory to learn. But given its place as the best theory of matter physics ever devised - learning it is worth it.