Step-by-step mathematical physics from classical to quantum physics

[aalaniz]

Dear folks,

Under the aalaniz blog, I just posted step-by-step notes starting for ODEs and PDEs both linear and nonlinear, of the type you will see in grad physics programs. The notes connect Lagrangian, Hamiltonian and Poisson Bracket methods in classical physics to the various approaches to quantum physics and quantum field theory. You'll see in detail how deeply symmetry methods underlie physics.

The basis of the notes are Lie symmetry methods. You will see that differential equations, abstract algebra, topology all go hand-in-hand towards practical methods for differential equations and mathematical physics.

I got a 36 hour MS in pure math and a PhD in theoretical physics in particles and fields. I've spent ten years dotting i's and crossing t's on techniques I never felt I truly understood. I never felt like an honest PhD as long as math seemed ad hoc and full of tricks. I finally feel honest. The material in the notes should serve as the foundations for grad physics (possibly grad math), but it has been forgotten. Schools now teach each subject in isolation, which is not good.

Give the notes a look. I hope they are useful.

Cheers,

Alex

 

[eljose79]

Dear Alex,

Thank you for sharing your notes on ODEs and PDEs with us. It is clear that you have a deep understanding of the subject and have put in a lot of effort to connect the various approaches in physics. Your use of Lie symmetry methods to explain the connection between differential equations, abstract algebra, and topology is impressive and shows the importance of these concepts in mathematical physics.

It is unfortunate that these foundations have been forgotten in current education systems, where subjects are taught in isolation. Your notes will definitely be useful to those studying graduate physics and mathematics, as well as to those who are trying to deepen their understanding of these subjects.

I believe that understanding the fundamentals is crucial in any field of study. Your dedication to mastering these techniques is admirable and I am sure it will inspire others to do the same. I will definitely take a look at your notes and I am sure they will be a valuable resource for me.

Thank you for sharing your knowledge and expertise with us. Keep up the good work!