The Euler-Lagrange Equation - Quantum Field Theory
Here's an image of an equation from my whiteboard, with annotations to explain (a bit at least) what each of the symbols means. If you like it, please let me know and I can try to explain a bit more of what's going on.
The Euler-Lagrange Equation
Brief Description
In the calculus of variations, the Euler–Lagrange equation is a second-order partial differential equation whose solutions are the functions for which a given functional is stationary. [1]
Usage
Given a Lagrangian density, find the equations of motion.
Related Fields of Math and Physics
The calculus of variations [1]. Classical field theory [2]. Quantum field theory [3].
Photo Source
Me. I have a Ph.D. in physics and wrote this on my whiteboard.
References and Recommended Reading
[1] https://en.wikipedia.org/wiki/Euler%E2%80%93Lagrange_equation
[2] https://en.wikipedia.org/wiki/Classical_field_theory#Lagrangian_dynamics
[3] https://en.wikipedia.org/wiki/Quantum_field_theory#Lagrangian_formalism
[4] Quantum Field Theory for the Gifted Amateur - Lancaster & Blundell 2014 - Chapter 7 - Examples of Lagrangians or How to Write Down a Theory
Hi :)
I think that it is great idea use steemit for presentation own scientific research. It could be platform for researcher in future.
I have two questions for you:
Q1: Your formula is result of your own research, or it is some well known formula.
Q2: Can you explain your formula by human words ? What results your formula brings.
Hi @zizelevak. This is a well known formula (check out the wikipedia links in the article). I'll try to figure out how to explain it in "plain english" but it might take some time :)
Hi @nonlinearone
I was looking at wikipedia :) I was badly reading your handwriting. I read dL in your formula as dZ.
In your formula is Lagrangian L(t,a,v) = (mv^2)/2 - mah ? I am correct?
Sorry, I have a strange way of writing the "curly L" which is used to represent the "Lagrangian density". You are on the right track for what "L" is but its a bit trickier. On mobile device right now so cant explain fully... may have to do another post :) So glad you are looking into it, makes my day.
See near 1 minute 20 seconds in this video for an example of what a Lagrangian density used by a field theorist looks like https://steemit.com/science/@nonlinearone/physics-out-loud-broken-symmetries-and-the-masses-of-gauge-bosons-by-peter-w-higgs-1964
Nice to see some science here
Thanks! I love equations and would love to make more posts like this one :)
Now that steemit.com is open source, it would be great if someone could make a clone with mathjax!
That's some heavy science you're doing there! I'll have to read it in more detail later when I'm not at work!
Is it NSFW?
I am highly intrigued to see this in work, and more clearly written :D I have a hard time making out what is going on fully, but it definitely tickles my fancy!