How Can I Understand Euler-Lagrange Equations in Physics?

[NYSportsguy]

I'm taking a Physics class at Stanford U. and I am having difficulty understanding how to mathematically understand or translate the Euler-LaGrange equations of motion in both Classical and Quantum Field Theory.

Any sort of English translation, background or hinting as to what type of math I should study to interpret and understand these equations would be very much of help to me. Thanks.

E-Mail: NYSPortsguy2084@gmail.com

 

[NYSportsguy]

PS- A little background information as to how and why these equations were developed and used for would help too.

 

[NYSportsguy]

Also - Why don't photons in light have mass? I find that hard to believe since they contain kinetic energy and have momentum when traveling in light. I would the since P = M * V, photons would contain mass. Also they knock electrons out of orbit based on then "Photoelectric Effect"...isn't that also proof of mass?

 

[EngageEngage]

photons carry momentum that is determined from relativity relations: E^2 = (pc)^2+(mc^2)^2. The reason that they knock electrons out in the PE effect is because the electrons absorb he energy of the photon and go into an excited state. If this energy is enough to get the electron out of the work function well they can escape from the conductor. I am not sure if this is exactly right

 

[NYSportsguy]

That is right according to books EngageEngage. However I read somewhere that photon particles were "Bosnons" while electrons were called "Fermions". According to a book by Lisa Randall, she said that "Fermions" cannnot combine or occupy space with any other fermions or bosnons at the same time...so then why are photons ("Bosnons") able to br absorbed by "Fermions" ( in this case, electrons)?

 

[HallsofIvy]

That is right according to books EngageEngage.

Yes, that is "right according to books". But that was what you asked.

However I read somewhere that photon particles were "Bosnons" while electrons were called "Fermions". According to a book by Lisa Randall, she said that "Fermions" cannnot combine or occupy space with any other fermions or bosnons at the same time...so then why are photons ("Bosnons") able to br absorbed by "Fermions" ( in this case, electrons)?

("Boson" not "Bosnon"-named for the physician P.W. Bose.)
No, photons do not "occupy the same space" as an electron. The energy of the photon is absorbed by the photon and the photon no longer exists.

 

[NYSportsguy]

Thanks Halls of Ivy. Can someone please explain or give me some background on how to understand Euler-LaGrange equations and where they originated form and what they have to do with quantum and classical physics? I am interested in learning.