Solving the Dirac Equation | Any Frame (Hard Mode)

In this video, we will show you how to take the rest-frame solution of the Dirac equation and boost it to a general frame of reference.

Contents:
00:00 Introduction
00:20 Boost Matrix
00:44 Tedious Calculation

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[PrettyMuchPhysics]

*Errata:*
03:04 Since the Lorentz group SO(3, 1) is non-compact, there are no *finite-dimensional* unitary representations. In particular, if we only look at rotations, S is unitary, but if we consider boosts, S is not unitary! However, this is no problem when we are dealing with classical Dirac spinors. Only when we consider QFT with the quantum Dirac *field*, we would like unitary transformations. Since the Hilbert space (Fock space) of QFT is infinite-dimensional, this allows for unitary representations of the Lorentz group. (Thanks to James Bates for pointing out the non-unitarity of S)

[Higgsinophysics]

Is "boost" a normally used word in this context? I love it

[jimmyb]

3:04 Careful: S(Λ) is not unitary!! Indeed it's hermitian, but clearly not equal to its own inverse!

[paulhighroller]

Why do you use S(Lambda) to rotate 4-momentum p? According to defenitions, only spinors are rotated with S, not vectors...

[UnforsakenXII]

This particular part in Peskin's book gave me a run for my money the first time. = )

[MohammadAlshahrani]

Good job, by the way what kind of table and software that were used in this footage?

[athleticmanu]

One question: where does that blue boost matrix in 2:12 come from?

[yogeshyadav-mzqx]

plz upload a video on Spherical tensor operators