QFT Lecture 8: Introduction to the Lorentz Transformation & Lorentz Invariance

Lecture 8 introduces the concept of Lorentz transformation and teaches you some important aspects, such as understanding the possible values of its determinant and you will learn about the proper orthocronous Lorentz transformations. I will also discuss the concept of Lorentz invariance, which will be key in the next lecture, when we discuss the covariance of the Dirac equation.

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My name is Nick Heumann, I am a recently graduated physicist. I love to teach physics, so I decided to give YouTube a try. English is not my first language, but I hope that you can understand me well enough regardless.
▬ Contents of this video ▬▬▬▬▬▬▬▬▬▬
00:00 Discussing 3d Rotations
08:59 Introducing Lorentz Transformations
17:30 Finding the Transpose Lorentz Transformation
25:00 Checking that the Lorentz trafos. are orthogonal
31:30 Finding the infinitesimal transformation
35:25 Introducing Lorentz Invariance
44:09 Finding the determinant of the lorentz transformation
51:00 Explaining the different kind of Lorentz Transformations

[valentinodrachuk]

Thanks a lot for your videos. I'm self learning these things and you are helping me so much. Please don't stop uploading new videos. Your effort is much appreciated 😊

[lowersaxon]

The motivation to formulate the Lorentz matrix in terms of hyperbolic cosh and sinh seems to be it being analogously to ordinary rotation matrices. But the job could be done in terms of gamma and betha also, right? I formulated a Lorentz Tr. in still other terms after playing around a little. My inverse tr. matrix (primed to unprimed) unfortunately has a (positive) huge det far beyond 1 ( bec. a scalar multiplication is involved), but leads to the correct solution of t and x nevertheless. The first way matrix (unprimed to primed) has a det =1. Could you comment why that would be rejected and regarded as a „unproper“ transformation? Why does the det matter so much? I mean „gamma^2 minus (betha*gamma)^2 = 1“ is preserved first way but not backwards, giving the correct result though, to repeat the Q in more technical terms! Vielen Dank im Voraus und sehr ansprechend gemacht - den gewöhnungsbedürftigen Stoff! 55:52

[robertthanasouk]

Thank you Brother Nick. When referring to the delta symbol, you kept saying Dirac delta symbol. I think you meant Kronecker delta symbol.

[jayjain]

This playlist is god sent to save me!! btw what do you mean by one matrix commuting with the other, my professor also keeps saying that, I don't exactly understand what it means. Thank you so much for this amazing videos.

[JoeHynes]

you made my day sir, wish i understood more Spanish so i could watch your other channel

[BinAbedin]

exercise set:
1. (a) write down the rotation matrix in 3D.
(b) show that this matrix is orthogonal.
(c) show that det R (from b) = 1
(d) Derive the infinitesimal rotation generator from it.
2. (a) show that Lorentz transformation is orthogonal.
(b) calculate the infinitesimal Lorentz transformation.
(c) calculate the det. of the Lorentz matrix.
(d) derive the Lorentz invariant quantity and show with an example that it works pretty well.

[haoqinggenius]

Is it correct to contract the second index of eta with the second index of epsilon, like what u did in 34:00 ? As long as we contract one top and one bottom, it doesn't matter which index of eta gets contracted with which index of epsilon? Is that right?

Because we all so used to seeing only 2nd index of the first variable contracting with the first index of the second variable.

[artpegios]

thank you for your videos :D can i ask which book did you used for this topic? tyyy

[massimoacerbis]

Minute 24
Would it be better to use the definition INVERSE instead of TRANSPOSE?

[km]

Thanks a lot for the lectures. In which lecture can I know about the current J mu, conserved charge ? Thank you