Impatiently waiting for your Dirac video ; You master of all clarification, explanation, and clear things up to bottom end , Thanks for what you are doing.
I have a question! In around 32:27 (i think) you talk about how the Field now becomes the generalised coordinate. You that our 'q' is a generalised coordinate for just 1 point in space, but 'Phi' is the generalised coordinate over all of spacetime! So my question is: 'Phi' is expressed as a function of cartesian (or minkowski) coordinates, t,x,y,z. So how would this work if we wanted to express 'phi' in another set of coordinates, for example spherical polar coordinates?
Good question! There is one generalized coordinate for each point in space. “X” and “T” become labels which identify each of these generalized coordinates. The word “coordinate” is being used in two different way, actually. You can transform the labels of phi to any “coordinate system” as a way of renaming the “generalized coordinate” phi(x,t). THEN…each phi(x,t) becomes an operator during “second quantization.”
very nice -- I would like to request you one thing -- please do the derivation for Dirac eqn in both metric signature. I don't know where I can find a derivation of Dirac eqn in (-,+,+,+) signature.
Wow this is so clear to understand now. Thank you so much
Impatiently waiting for your Dirac video ; You master of all clarification, explanation, and clear things up to bottom end , Thanks for what you are doing.
This is gonna help me so much when i learn QED, thanks!
I have a question! In around 32:27 (i think) you talk about how the Field now becomes the generalised coordinate. You that our 'q' is a generalised coordinate for just 1 point in space, but 'Phi' is the generalised coordinate over all of spacetime!
So my question is: 'Phi' is expressed as a function of cartesian (or minkowski) coordinates, t,x,y,z. So how would this work if we wanted to express 'phi' in another set of coordinates, for example spherical polar coordinates?
Good question! There is one generalized coordinate for each point in space. “X” and “T” become labels which identify each of these generalized coordinates. The word “coordinate” is being used in two different way, actually. You can transform the labels of phi to any “coordinate system” as a way of renaming the “generalized coordinate” phi(x,t). THEN…each phi(x,t) becomes an operator during “second quantization.”
very nice -- I would like to request you one thing -- please do the derivation for Dirac eqn in both metric signature. I don't know where I can find a derivation of Dirac eqn in (-,+,+,+) signature.
Simply take any derivation for the +--- convention and slap an i on every gamma matrix
One derivation has +m one has -m?
NIce catch! Can you tell which one is wrong? :) (answer: the first one) I’ll fix it next lecture! THank you sir!
@@XylyXylyX yes! The other is correct for the + spacetime metric
Noether is almost correct, but the "th" is just a t sound, no "th" sound in German.