Are there any good physics books with a more mathematical approach?

[Keen]

Hi.

I am not sure whether to put this topic in physics or mathematics, since it's kind of both.

I used to take physics courses back when I was an undergraduate student and unfortunately I didn't like them much. Mainly because of how the mathematical models were treated 'poorly'. By that I mean that we lacked rigorous definitions and I wasn't even sure of for instance how regular the functions that we employed were.

I once stumbled upon a book whose name I have unfortunately forgotten, but I remember it was about special relativity and it was really written for people with my mindset. To give you an example, it defined a material point as a couple (gamma, m) with gamma an infinitely differentiable curve in a Minkowsky space and m a positive real number.

I know that physics is supposed to represent real world and I don't mind that. I just think that as soon as physicists use mathematical representations, they should define their objects well... mathematically.

I wanted to ask if you know of other books which take this kind of formal approach to physics?

I am mainly interested in classical and relativistic mechanics, electromagnetism and thermodynamics. Again I don't mind references to experiments and physical explanations: it's physics after all, but I would just like that all the formal mathematical part is treated "correctly".

[studiot]

Here is the first page of

 

Mathematical Foundations of the Quantum Theory.

 

Is this the sort of thing you want?

 

[fiveworlds]

Are there any good physics books with a more mathematical approach?

 

 

A physics workbook?? I found them great for studying. :)

[ajb]

I wanted to ask if you know of other books which take this kind of formal approach to physics?

I quite like Mathematical Physics by Geroch. He introduces mathematical structures using category theory in a gradual way. He does then as examples discuss some applications of these structures in physics, but really the book is a nice introduction to category theory.

 

Another book I quite like is Mathematical Physics by Hassani. He covers a large amount of material from differential geometry to operator algebras. Not mathematically the best book, but it has a lot of basic notions all in one place.

 

If you want to know more about geometry and topology, then you could try Geometry, Topology and Physics by Nakahara. The book may leave you mathematically dissatisfied, but it does give you the basics and shows how they are useful in physics.

 

I am mainly interested in classical and relativistic mechanics, electromagnetism and thermodynamics.

More specifically...

 

For mechanics I suggest Arnold's book Mathematical Methods of Classical Mechanics, and Foundations of Mechanics by Abraham + Marsden.

 

For special relativity you could try The Geometry of Minkowski Spacetime by Naber (I do not actually know this book, just that it exists!)

 

If you want general relativity, then I suggest Advanced General Relativity by Stewart and General Relativity by Wald.

 

Electromagnetism, I am not sure what to advice. The modern approach is based on the geometry of fibre bundles and any book on quantum field theory should mention this.

 

Thermodynamics I am also not sure what to recommend. Maybe if you are interested, there are good mathematical texts on statistical mechanics such as the books by Bratteli and Robinson.

 

The warning I will give here with all the books I have suggested is that they are aimed at graduate level.

[seriously disabled]

Physics is a very very difficult subject, especially topics such as quantum mechanics, relativity, quantum field theory, thermodynamics, quantum statistical mechanics, particle physics, supersymmetry, quantum gravity, string/M-theory etc.

 

You need to work extremely extremely hard to become really good in physics but considering that the payment for all those years of effort is not good I don't think it's really worth it to study physics.

[Bill Angel]

Physics is a very very difficult subject, especially topics such as quantum mechanics, relativity, quantum field theory, thermodynamics, quantum statistical mechanics, particle physics, supersymmetry, quantum gravity, string/M-theory etc.

 

You need to work extremely extremely hard to become really good in physics but considering that the payment for all those years of effort is not good I don't think it's really worth it to study physics.

An excellent book came out in 2011 : Quantum Man, Richard Feynman's life in Science, by Lawrence M Krauss.

The author goes to great lengths to explain the value of Feynman's contributions to the scientific community. While his contributions are not necessarily easy to grasp, making the effort to read the book is still I think worthwhile.

[hoponpop]

I like Feynman's stuff for that.

 

I liked his statistical mechanics lectures:

 

ISBN-13: 978-0201360769

 

And his statistical thermodynamics thing (can't find that anymore).

 

Probably pretty low level to a lot of people on here, but hey...

[Sensei]

I know that physics is supposed to represent real world and I don't mind that.

Then watch the real particles in the real particle detectors, like in this video:

http://www.scienceforums.net/topic/92471-the-limits-of-physics/#entry894800

Watch them by naked eye, not just numbers on white table, for more healthy approach..

 

f.e. alpha decay

Isotope with nuclear spin=0, before decay has mass [math]m_{src}[/math], and is at rest, p=0.

after decay newly made nucleus (with rest-mass [math]m_{dst}[/math]) has 2 protons less Z'=Z-2, has 2 neutrons less N'=N-2, and Baryon Number smaller 4 units, A'=A-4.

Emitted alpha takes 2 protons, 2 neutrons.

Decay energy (see my signature how to calculate it), is split accordingly to their masses.

Energy prior decay is [math]E=m_{src}*c^2[/math]

Energy after decay is the same,

[math]E=m_{dst}*c^2*\gamma_1 + m_{alpha}*c^2*\gamma_2[/math]

Momentum prior decay is 0.

Momentums of new products is where you can show your math skills..

 

I just think that as soon as physicists use mathematical representations, they should define their objects well... mathematically.

Are not they defined mathematically enough?

Charge of particle -1e = -1.602176565*10^-19 C, or 0e = 0 C, or +1e = 1.602176565*10^-19 C,

Kinetic energy of particle [math]m_0*c^2*\gamma-m_0*c^2\approx\frac{1}{2}*m_0*v^2[/math] for v<<c

Rest-mass of particle measured by mass spectrometer.

And observation how charged particle reacts for acceleration (more massive particle accelerates differently than lighter particle).

And particle spin, measured in other device.

 

ps. I think that students should go exactly reverse direction: experiments more than mathematics..

Edited December 11, 2015 by Sensei