In the tradition of V.I. Arnold, Goldstein, and Landau & Lifshitz. The author is really classical mechniacs pilled. Though the book is more focused on the mathematics of it all than the physics.
Fundamental Principles of Classical Mechanics In the same tradition as Lems but more heuristic. It uses physical motivation to build up to formal ideas. Places a greater focus on a local co-ordinate approach. The author emphasises Cartan’s Method of Moving Frames, for pedagogical purposes. This is linked to the historical development of the subject, which I quite like. But notably, the author says Goldstein is the gold standard for the mathematical methods of classical mechanics. So why bother reading this book?
Differential Geometry in Physics—Gabriel Lugo Has coloured figures. La-dee-da. Pre-reqs: Calculus, Linear Algebra and Differential Equations. Assumes the reader has encountered the concepts in classical/quantum mechanics. Aims to: 1) Bridge differential geometry’s historical practical formulation and its abstract modern form. 2) Help physicists who want to strengthen their mathematical ability. The author was shocked that HPE folk and differential geometry folk worked on connections on fiber bundles whilst unaware that they were really working on the same stuff. This was part of the inspiration of this book, meant to rectify the situation. 3) Be readable to those at the boundary of maths/physicists. 4) Serve as background for GR. 5) Add material that is unusual for a textbook, such as solitions on the style of Backlund transform instead of Olver.
Geometry from dynamics: classical and quantum. Looks interesting, certainly a different perspective. Something about dynamics giving rise to geometric structure e.g. Hamiltonian, Lagrangian and Symplectic geometries. Claims geometry is experienced first over dynamics.
Relativity and Cosmology—Thorne & Blandford You know you want it. Emphasises a geometric approach. Takes 1/4-1/2 of a semester to teach. Emphasises historical transformations in the physics of GR. Has practical calculations!
Structure and Interpretation of Classical Mechanics − 2nd Edition. 1) Uses Scheme. Apparently they don’t need to teach it, as students just learn it in a matter of days. 2) Notation is built to make turning equations into programs easy. The author claims this simplifies things as a result. 3) Focuses on motion over deriving equations of motion. 3) Non-linear dynamics is given a lot of time throughout the text. 4) Lots of time spent on phase space perspective. 5) This book has many cool qualitative results.
Concise Treatise on Quantum Mechanics in Phase Space 1) This book focuses on Wigner’s formulation of quantum mechanics. Wigner’s Quasi-Probability distribution function in phase space furnishes a representation of quantum mechanics on equal footing to the Hamiltonian and Path Integral formulation. 2) The author claims this representation more naturally and intuitively connects to the classical limit. 3) The representation is weird. You have simultaneous position and momentum variables 4) The theory was built by two unknown researchers, and faced opposition from established physicists. 5) The author claims this approach shows its worth when calculating the effects of time.
Some interesting books from my reading list.
Analytical Mechanics—Nivaldo A Lems
In the tradition of V.I. Arnold, Goldstein, and Landau & Lifshitz. The author is really classical mechniacs pilled. Though the book is more focused on the mathematics of it all than the physics.
Fundamental Principles of Classical Mechanics
In the same tradition as Lems but more heuristic. It uses physical motivation to build up to formal ideas. Places a greater focus on a local co-ordinate approach. The author emphasises Cartan’s Method of Moving Frames, for pedagogical purposes. This is linked to the historical development of the subject, which I quite like. But notably, the author says Goldstein is the gold standard for the mathematical methods of classical mechanics. So why bother reading this book?
Differential Geometry in Physics—Gabriel Lugo
Has coloured figures. La-dee-da.
Pre-reqs: Calculus, Linear Algebra and Differential Equations. Assumes the reader has encountered the concepts in classical/quantum mechanics.
Aims to:
1) Bridge differential geometry’s historical practical formulation and its abstract modern form.
2) Help physicists who want to strengthen their mathematical ability. The author was shocked that HPE folk and differential geometry folk worked on connections on fiber bundles whilst unaware that they were really working on the same stuff. This was part of the inspiration of this book, meant to rectify the situation.
3) Be readable to those at the boundary of maths/physicists.
4) Serve as background for GR.
5) Add material that is unusual for a textbook, such as solitions on the style of Backlund transform instead of Olver.
Geometry from dynamics: classical and quantum.
Looks interesting, certainly a different perspective.
Something about dynamics giving rise to geometric structure e.g. Hamiltonian, Lagrangian and Symplectic geometries.
Claims geometry is experienced first over dynamics.
Relativity and Cosmology—Thorne & Blandford
You know you want it.
Emphasises a geometric approach.
Takes 1/4-1/2 of a semester to teach.
Emphasises historical transformations in the physics of GR.
Has practical calculations!
Structure and Interpretation of Classical Mechanics − 2nd Edition.
1) Uses Scheme. Apparently they don’t need to teach it, as students just learn it in a matter of days.
2) Notation is built to make turning equations into programs easy. The author claims this simplifies things as a result.
3) Focuses on motion over deriving equations of motion.
3) Non-linear dynamics is given a lot of time throughout the text.
4) Lots of time spent on phase space perspective.
5) This book has many cool qualitative results.
Concise Treatise on Quantum Mechanics in Phase Space
1) This book focuses on Wigner’s formulation of quantum mechanics. Wigner’s Quasi-Probability distribution function in phase space furnishes a representation of quantum mechanics on equal footing to the Hamiltonian and Path Integral formulation.
2) The author claims this representation more naturally and intuitively connects to the classical limit.
3) The representation is weird. You have simultaneous position and momentum variables
4) The theory was built by two unknown researchers, and faced opposition from established physicists.
5) The author claims this approach shows its worth when calculating the effects of time.