1
vote
2answers
78 views

Books that integrate physical reasoning with mathematical reasoning? mathematicians?

As the title says, can anyone help me to find any book that shows how physical reasoning using concepts from classical/quantum mechanics and physics in general can enlighten us about mathematical ...
10
votes
2answers
172 views

Applications of Algebra in Physics

Often I have heard about the link between Algebra (in particular Representations of Groups and Algebras) and some "indefinite" field of Physics. I have a good preparation in Algebra and ...
-1
votes
2answers
126 views

List of Advanced Math Text Books with answers

Can anybody please recommend a list of Advanced Mathematics Books for physics that can be used for self study. Most importantly they must have answers for odd or even problems. I have a big list of ...
0
votes
2answers
29 views

what are some typical systems of equations generating from practical problems?

I want to know some typical forms of system of equations generating from practical problems in engineering/economics/physics,etc. Some examples or research articles would be good. Specifically, I am ...
4
votes
5answers
563 views

What physics book for aspiring theoretical physicist / pure mathematician [closed]

I am a high school student. I want to learn physics on my own, but I am puzzled : Should I read a book which talks about all branches of physics? If yes, recommend a book. Should I read a book which ...
2
votes
3answers
155 views

Learning math for physics

I am very interested in physics and am planning to self studying it. But for this I need to be mature in various areas of math. So I want to know what is the order in which I need to learn the math ...
8
votes
2answers
187 views

Wave-Particle Duality in PDE?

I am reading Arnold's Lectures on Partial Differential Equations. It is definitely a good book, yet sometimes I am a little bit confused. One theme of the first chapter seems to be From the ...
2
votes
0answers
45 views

Filling a infinite colored graph with basis

This is a mathematical question raised from engineering and physics: Is there some established mathematical approach in filling a physical lattice with some colored basis (black and white here)? For ...
1
vote
0answers
76 views

Sources for learning Lie groups and symplectic geometry for Quantum optics

I am asking this question on behalf of my junior who has recently joined in the graduate programme. As suggested by my boss, the student wants to work on quantum optics from a symplectic geometric ...
4
votes
6answers
238 views

Books for studying Mathematical Physics?

Currently I'm doing Advanced Classicial Mechanics courses.I'm finding it hard to understand due to the lack of knowledge in linear algebra, multi variable calculus and other chapters. Can anyone ...
1
vote
0answers
42 views

What's the mathematical formulation for frames for reference?

In this lecture I've come across an interesting formulation of kinematics and reference frames. When I studied kinematics, the idea of what is meant by a 'frame of reference' was never quite fully ...
8
votes
1answer
426 views

Applications of representation theory in physics

The notes of a lecture on basic group and representation theory I attended last semester begin with a bit of motivation for the argument. They give the following examples for applications in physics: ...
5
votes
0answers
82 views

Second law of thermodynamics as a theorem about state space evolution

I once saw a mathematical explanation of the second law of thermodynamics. The statement was something like this: there is a mapping $f$ from the set of thermodynamic states $S$ to itself, and a ...
4
votes
3answers
106 views

What does boson-type realization mean?

I have seen several different contexts the expression "boson-type realization", for instance in the study of algebras growth and realization of affine algebras. To be or not be a boson-type ...
2
votes
3answers
276 views

Thermodynamics for math majors

I'm about to wrap a course in partial differential equations. We've discussed the heat/wave equations and introductory Fourier Analysis. I'd like to do some reading into the field of thermodynamics. ...
1
vote
0answers
34 views

Three body problem with point interactions

I've studied the HVZ theorem for the three body problem interacting with regular potentials. I'd like to extend this result to the three body problem with point interactions (delta potentials). Is ...
1
vote
1answer
105 views

Translation of an article

I need to read this article "On the spectrum of an energy operator for atoms with fixed nuclei in subspaces corresponding to irriducible representations of permutation groups" authors:G.Zhislin, A. ...
1
vote
0answers
27 views

References for three body problems with Fermi statistic

I'm studying the three body problem with two fermions of unitary mass and another different particle. I need references of the HVZ theorem in this case. Is there someone who knows them?
1
vote
1answer
453 views

Can the differentiating and squaring process in the cochlea explain a reported dichotic stimulation experiment?

On this math.stackexchange on url What is Octave Equivalence? in an answer on the related ( octave equivalence ) question is stated: Mathematically, this signifies that the mammalian cochlea ...
2
votes
1answer
191 views

concise review of Maxwell's electromagnetic equations for math students

I am a graduate student in applied mathematics and I am looking for a concise introduction to Maxwell's equations / basic principles of electromagnetism. (I have enjoyed the book by Purcell, ...
4
votes
2answers
412 views

$SU(2)$ Representation of $SO(3)$

I've often seen it written that $SU(2)$ is a "two-valued representation" of $SO(3)$ (in theoretical physics books mainly). I have a major conceptual issue with this however. I know there is a Lie ...
19
votes
1answer
439 views

How does one parameterize the surface formed by a *real paper* Möbius strip?

Here is a picture of a Möbius strip, made out of some thick green paper: I want to know either an explicit parametrization, or a description of a process to find the shape formed by this strip, as ...
1
vote
3answers
136 views

What do I need to read to understand dimensions and spacetime?

The concept of dimension seems to be: In physics and mathematics, the dimension of a space or object is informally defined as the minimum number of coordinates needed to specify any point ...
6
votes
3answers
387 views

Learning about the universe or special/general relativity

I have done a standard course in differential geometry/Riemannian geometry. Am I now able to understand the concepts people talk about when they say things like "spacetime is curved" and when I see ...
5
votes
2answers
265 views

Is there a mathematical theory of physical knots?

From the point of view of people tying real knots (canonically, sailors) mathematical knot theory ignores much of what makes the problem of knot-tying interesting. Some matters that come up in the ...
0
votes
3answers
167 views

Resource request: history of and interconnections between math and physics

Reading this article I became curious to learn more of (- study more thoroughly and *seriously*$^{\star}$-) the topic. Is / are there some good references - either papers, books and/or other ...
4
votes
2answers
87 views

What do I need to know to simulate many particles, waves, or fluids?

I've never had a numerical analysis course so I don't know what I need to know. I'm just wondering what kind of books I should get to make me able to simulate these things. I'm wanting to simulate ...
1
vote
1answer
55 views

Question about Lie superalgebra.

What are the generators and relations for the Lie superalgebra $\mathfrak{psu}(2, 2 | 4)$? Thank you very much.
2
votes
1answer
182 views

Are there introductions to mathematics through physics?

I'm studying mathematics through three books: Calculus: Early Transcendentals, Stewart; Discrete Mathematics, Kevin Ferland; Polynomials, Barbeau. I have also some invitations to mathematics which ...
12
votes
3answers
351 views

Why can't you simulate isotropic fluid flow on a square lattice?

There are easy methods for discrete simulations of gas dispersion in two dimensions. If you take a large square lattice, each cell of which is assumed to contain at most one gas molecule, and you ...
5
votes
1answer
424 views

reference for multidimensional gaussian integral

I was reading on Wikipedia in this article about the n-dimensional and functional generalization of the Gaussian integral. In particular, I would like to understand how the following equations are ...
4
votes
2answers
436 views

Learning general relativity

Warning : this question may be borderline with physics.stackexchange, but I would like a mathematician's point of view. Lately, I've been working quite a lot with (among others) hyperbolic spaces, ...
12
votes
1answer
313 views

Understanding sub-atomic particles, for mathematicians

I have a masters degree in pure mathematics and I'm working towards my dream of a PhD, but I know very very little about sub-atomic particles. I would like to find some good popular science books or ...
1
vote
0answers
140 views

Extra Dimensions in String Theory

This is a whole other question that you maybe expect from me, but it is bugging me since I heard of a long time ago. Bosonic string theory (to take the simplest one of string theories) is consistent ...
2
votes
1answer
358 views

Illustration of vector calculus vs. differential forms

I am looking for a nice illustration of how vector calculus relates to differential forms. A demonstration that employs physics is appreciable (e.g. electromagnetism). In particular, while dualizing ...
13
votes
3answers
965 views

Quantum mechanics for mathematicians

I'm looking for books about quantum mechanics (or related fields) that are written for mathematicians or are more mathematically inclined. Of course, the field is very big so I'm in particular ...
6
votes
2answers
2k views

What are “Super Numbers”?

I'm reading Hyperspace by Michio Kaku and in the chapter on SuperGravity "Super Numbers" are mentioned and are described as a number system where for any super number $a$, $a*a=-a*a$. I was wondering ...
14
votes
6answers
2k views

Books to learn physics, being a math major

What books would you recommend to learn physics, being a a Math major, from classical mechanics, electricity, etc. to modern physics?
6
votes
2answers
405 views

sl(2,C) and the harmonic oscillator

I've been studying the finite-dimensional representations of the lie algebra sl(2,C). I've read that these representations are related to the harmonic oscillator and the associated raising and ...
8
votes
0answers
222 views

What are D-branes (in a topological field theory)?

In the past couple years, I've read many words pertaining to D-branes without feeling I have really comprehended them. In broad terms, I think I get what they're about: They're supposed to serve as ...