![]() Later on, you’ll employ the latter in constructing Yang-Mills theories.Įlectrodynamics: The $\mathbf E$ and $\mathbf B$ fields are the earliest real-life examples of (classical, not quantum!) fields, and so a detailed knowledge of their systematics is necessary for understanding their quantized dynamics. It’s not terribly difficult, and you’ll see what initially daunting objects like $i\bar\psi_a\gamma^\mu_(n)$. Tensor Calculus: This has the added benefit of being a key prerequisite to general relativity too. Being able to resolve all the paradoxes under the Sun is not a must, but is nonetheless a good measure of one’s SR background. Knowing about Lorentz transformations, covariance and electromagnetism on a relativistic footing is essential. Special Relativity: As I mentioned, QFT operates in Minkowski space, on a relativistic footing. Don’t worry about knowing about the Dirac equation or the problems QM faces when extrapolating to the relativistic regime: all sources provide background on them. Quantum Mechanics, at an intermediate level - say, a mastery of all the topics mentioned in Griffiths’ at the level of Sakurai, and especially the harmonic oscillator via ladder operators, angular momentum, scattering and time-dependent perturbation theory (much of QFT is working with perturbative series even virtual particles can be seen at the level of ordinary quantum mechanics!). I can’t guarantee you’ll appreciate the depth and complexity of QFT, but you will get a reasonable understanding of how fields work.ĭisclaimer: all of the prerequisites listed below each have their own prerequisites, and so on, I have deliberately suppressed these to avoid a stack overflow. It looks just like a harmonic oscillator in the x coordinate but with a shifted equilibrium position, and a frequency \omega = eB/m.Interestingly however, you could technically start learning QFT with the minimal knowledge of quantum mechanics up to the quantum harmonic oscillator, and - wait for it - a system of infinite blocks connected by springs in a lattice. ![]()
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