I've read some of Francis Bitter's Mathematical Aspects of Physics. It's a great starting point for prepared high school students. This book does a pretty good job at describing the process in words mostly. Not as much of the computational and mathematical modelling process. I haven't read The...
I know what you mean, i just feel it would be nice to see a professional physicist show and describe their process of modelling. I actually found a decent book on this topic, https://www.amazon.com/dp/331980068X/?tag=pfamazon01-20. The authors admit that the process of how a scientist goes about...
@christian0710 did you find the book you were looking for? I am also interested in such a book where it shows exactly what the scientist did to go from observation of phenomena, process of experiment, mathematical modelling and constructing theoretical model. This process is very mysterious to...
I was wondering if there is any such textbook which shows how a real physicist actually goes about developing models and or theories to explain experimental observations. I want to see how it is done in practice. Is there such a book? At a level that an undergraduate can understand. It is great...
@mathwonk what do you mean by thinking geometrically? Could you explain somehow? I don't understand how a geometrical picture can be associated to any space higher than 3 dimensions. And how can you get a geometric picture for some algebraic structures? I don't see any geometry in that appendix...
@mathwonk I read in many places about the importance of geometric intuition in advanced mathematics. If you read some articles and interviews with Misha Gromov, or historical articles on Rochlins and Alexandrovs geometric schools, they mention there are different ways of approaching non...
I read this article History of James Clerk Maxwell and it talks about Maxwell and Dirac also at some point. It is said that Maxwell thought geometrically, and also Dirac said he thought of de Sitter Space geometrically. They say their approach to mathematics is geometric. I see this mentioned...
Oh okay, so differential forms are a subset of multilinear forms. And more specifically differential forms are totally antisymmetric multilinear forms. So can we write any Tensor as multilinear form? Why are differential forms much more important to differential geometry than multilinear forms...
Robphy, that is a great analogy with complex numbers. So then from what I understand, a Tensor with a non-zero symmetric part cannot be written in differential forms (because forms are antisymmetric). So from my understanding, you can rewrite the antisymmetric type (0,n) tensor in a differential...
i don’t understand. Could you maybe provide an example.Maybe what the author was trying to say was a linear combination of a symmetric and antisymmetric form of itself?
Warhammer,
I am sure you will find some of the top theoretical physicists in the list of ISI highly cited researchers. Of course this may not include younger physicists but it will give you a list of more established physicists whose research has made impact. I haven't gone through it but you...
Yes differential forms are defined as antisymmetric tensors. I write here the definition 5.4.1 (page 52) in Michio Nakahara's book. " A differential form of order r or an r-form is a totally anti-symmetric tensor of type (0, r ).". Now if we quote also Gravitation by Wheeler, on page 83 they say...
I read in the book Gravitation by Wheeler that "Any tensor can be completely symmetrized or antisymmetrized with an appropriate linear combination of itself and it's transpose (see page 83; also this is an exercise on page 86 Exercise 3.12).
And in Topology, Geometry and Physics by Michio...
Thanks George, I appreciate your feedback. What do you mean by everything can be treated with bundles? Are bundles a kind of unifying mathematical tool? Do any of the books above take the approach to bundles?
Could you provide recommendations for a good modern introductory textbook on differential geometry, geared towards physicists. I know physicists and mathematicians do mathematics differently and I would like to see how it is done by a physicists standard. I have heard Chris Ishams “Modern Diff...