DO NOT USE THIS TAG just because your question involves math! If your question is on simplification of a mathematical expression, please ask it at math.stackexchange.com The mathematics tag covers non-applied pure mathematical disciplines that are traditionally not part of the mathematical physics ...
26
votes
10answers
4k views
Best books for mathematical background?
What are the best textbooks to read for the mathematical background you need for modern physics, such as, string theory?
Some subjects off the top of my head that probably need covering:
...
16
votes
9answers
3k views
How should a physics student study mathematics? [closed]
Note: I will expand this question with more specific points when I have my own internet connection and more time (we're moving in, so I'm at a friend's house).
This question is broad, involved, and ...
16
votes
7answers
2k views
Classical mechanics without coordinates book
I am a math grad student who would like to learn some classical mechanics. The caveat is I am not to interested in the standard coordinate approach. I can't help but think of the fields that arise in ...
22
votes
6answers
2k views
Formalizing Quantum Field Theory
I'm wondering about current efforts to provide mathematical foundations and more solid definition for quantum field theories. I am aware of such efforts in the context of the simpler topological or ...
37
votes
14answers
4k views
Number theory in Physics
As a Graduate Mathematics student, my interests lies in Number theory. I am curious to know if Number theory has any connections or applications to physics. I have never even heard of any applications ...
9
votes
3answers
395 views
infinite grid of planets with newtonian gravity
Assuming only Newtonian gravity, suppose that the universe consists of an infinite number of uniform planets, uniformly distributed in a two-dimensional grid infinite in both directions and not moving ...
2
votes
3answers
2k views
What is the math knowledge necessary for starting Quantum Mechanics?
Could someone experienced in the field tell me what the minimal math knowledge one must obtain in order to grasp the introductory Quantum Mechanics book/course?
I do have math knowledge but I must ...
12
votes
8answers
2k views
Crash course on algebraic geometry with view to applications in physics
could you please recommend any good texts on algebraic geometry (just over the complex numbers rather than arbitrary fields) and on complex geometry including Kahler manifolds that could serve as an ...
5
votes
3answers
536 views
What is the physical meaning of a “complete” Hilbert space in QM?
What does the word "complete" means from the physical point of view?
I do not understand what it physically means to say that a Hilbert space is a complete vector space.
19
votes
5answers
2k views
Does Godel preclude a workable TOE?
Godel's incompleteness theorem prevents a universal axiomatic system for math. Is there any reason to believe that it also prevents a Theory of everything for physics?
Edit:
I haven't before seen ...
7
votes
2answers
737 views
A book on quantum mechanics supported by the high-level mathematics
I'm interested in quantum mechanics book that uses high level mathematics (not only the usual functional analysis and the theory of generalised functions but the theory of pseudodifferential operators ...
4
votes
2answers
374 views
Book covering Topology required for physics and applications
I am a physics undergrad, and interested to learn Topology so far as it has use in Physics. Currently I am trying to study Topological solitons but bogged down by some topological concepts. I am not ...
23
votes
9answers
584 views
Examples of number theory showing up in physics
My question is very simple: Are there any interesting examples of number theory showing up unexpectedly in physics?
This probably sounds like rather strange question, or rather like one of the ...
2
votes
3answers
294 views
Mathematics for Quantum Mechanics [duplicate]
What math should I study if I want to get a basic understanding of quantum mechanics and especially to be able to use the Schrodinger's equation.
2
votes
1answer
185 views
Why is physical space equivalent to $\mathbb{R}^3$?
Why is physical space equivalent to $\mathbb{R}^3$, as opposed to e.g. $\mathbb{Q}^3$?
I am trying to understand what would be the logical reasons behind our assumption that our physical space is ...
13
votes
7answers
2k views
Applications of Algebraic Topology to physics
I have always wondered about applications of Algebraic Topology to Physics, seeing as am I studying algebraic topology and physics is cool and pretty. My initial thoughts would be that since most ...
33
votes
18answers
2k views
Quantum Field Theory from a mathematical point of view
I'm a student of mathematics with not much background in physics. I'm interested in learning Quantum field theory from a mathematical point of view.
Are there any good books or other reference ...
9
votes
16answers
2k views
Can pure maths create new theories in physics or does the “idea” ALWAYS come before the math?
I am in a debate with a friend about the value of string theory in physics. He is concerned that we are wasting valuable intellectual and financial resources on a path that is fanciful and can't ever ...
7
votes
4answers
1k views
Number of dimensions in string theory and possible link with number theory
This question has led me to ask somewhat a more specific question. I have read somewhere about a coincidence. Numbers of the form $8k + 2$ appears to be relevant for string theory. For k = 0 one gets ...
13
votes
4answers
4k views
How can area be a vector?
My professor told me recently that Area is a vector. A Google search gave me the following definition for a vector:
Noun: A quantity having direction as well as magnitude, esp. as
determining ...
6
votes
5answers
509 views
Are the solutions in radicals of cubic and quartic of any use in physics?
We all know that there are analytic formulae to solve quadratic, cubic and quartic polynomial equations. But it seems to me that the only solution that widely used is physics is the solution of ...
4
votes
2answers
252 views
Sum total distance of electrons on a spherical surface
What is the sum total distance between every possible pair of point charges when there are n point charges on a spherical surface?
All point charges can only and are located on the infinitesimal ...
0
votes
0answers
89 views
Literature request for books / review papers on gravitation, gauge theories and related mathematics [duplicate]
Similar to this reference, are there more such references / works [including textbooks] available in the literature?
(A list would be greatly welcomed and appreciated.)
With great appreciation.
10
votes
2answers
903 views
Applications of the Spectral Theorem to Quantum Mechanics
I'm currently learning some basic functional analysis. Yesterday I arrived at the spectral theorem of self-adjoint operators. I've heard that this theorem has lots of applications in Quantum ...
38
votes
6answers
831 views
The Role of Rigor
The purpose of this question is to ask about the role of mathematical rigor in physics. In order to formulate a question that can be answered, and not just discussed, I divided this large issue into ...
13
votes
9answers
3k views
What is the logarithm of a kilometer? Is it a dimensionless number?
In log-plots a quantity is plotted on a logarithmic scale. This got me thinking about what the logarithm of a unit actually is.
Suppose I have something with length $L = 1 km$.
$\lg L = \lg km$
It ...
5
votes
3answers
244 views
What is a dual / cotangent space?
Dual spaces are home to bras in quantum mechanics; cotangent spaces are home to linear maps in the tensor formalism of general relativity. After taking courses in these two subjects, I've still never ...
3
votes
11answers
764 views
Is it possible for a physical object to have a irrational length?
Suppose I have a caliper that is infinitely precise. Also suppose that this caliper returns not a number, but rather whether the precise length is rational or irrational.
If I were to use this ...
2
votes
1answer
419 views
which areas in physics overlap with those of social network theory for the analysis of the graphs?
I am studying social networks in terms of graph theory and linear algebra. I know that physicists have published and worked alot in this field. This causes me to assume that there are sub-fields in ...
10
votes
3answers
354 views
Does the axiom of choice appear to be “true” in the context of physics?
I have been wondering about the axiom of choice and how it relates to physics. In particular, I was wondering how many (if any) experimentally-verified physical theories require axiom of choice (or ...
7
votes
6answers
259 views
In coordinate-free relativity, how do we define a vector?
Relativity can be developed without coordinates: Laurent 1994 (SR), Winitzski 2007 (GR).
I would normally define a vector by its transformation properties: it's something whose components change ...
4
votes
1answer
1k views
Uniqueness of Helmholtz decomposition?
Helmholtz theorem states that given a smooth vector field $\pmb{H}$, there are a scalar field $\phi$ and a vector field $\pmb{G}$ such that
$$\pmb{H}=\pmb{\nabla} \phi +\pmb{\nabla} \times \pmb{G},$$
...
3
votes
5answers
327 views
What is the meaning of following expresion $C=\frac{\delta Q}{dT}$ mathematicly
Our professor raised the following question during our lecture in Statistical Physics (even so it's related to Thermodynamics):
Many text books (even wikipedia) writes wrong expressions (from ...
3
votes
2answers
277 views
What are some interesting calculus of variation problems? [closed]
That I could create as a classical mechanics class project? Other than the classical examples that we see in textbooks (catenary, brachistochrone, Fermat, etc..)
5
votes
7answers
735 views
Why are radians more natural than any other angle unit?
I'm convinced that radians are, at the very least, the most convenient unit for angles in mathematics and physics. In addition to this I suspect that they are the most fundamentally natural unit for ...
3
votes
4answers
297 views
How do I go from exponents to a formula?
This is a continuation of this question.
http://ocw.mit.edu/courses/physics/8-01-physics-i-classical-mechanics-fall-1999/video-lectures/lecture-1/ skip this lecture to around 25:50.
After doing ...
2
votes
1answer
346 views
What is the mathematical nature of space time quantization in string theory/super string theory?
I don't know much about string theory, apart from it being a theory of everything which brings QM, QED and nuclear forces and gravity under one single roof. I am curious to know from a mathematical ...
1
vote
1answer
144 views
Potential for charge distribution, finiteness
Consider a potential for charge distribution:
$$v_H(\mathbf{r}) ~=~ \int \frac{\rho(\mathbf{r'})}{|\mathbf{r}-\mathbf{r'}|}d\mathbf{r'}$$
where $\rho(\mathbf{r'})$ is the charge density.
This ...
0
votes
1answer
147 views
Universal Sequence and relationship of mathematics and reality [closed]
In "The Special and General Theory of Relativity" Einstein says:
How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably ...
0
votes
0answers
131 views
Journals on mathematics similar to the American Journal of Physics and the Physics Teacher [closed]
For the moderators: Please feel free to transfer this question to math.stackexchange if you find that it does not fit physics.stackexchange.
It is known that American Journal of Physics and the ...
-1
votes
1answer
261 views
Functional Derivative of Convolution
How to carry out the following functional derivative?
$$\frac{\delta F}{\delta n(r)}$$ where $$F=\int dr n(r) \int C(|r-r'|) n(r') dr'$$
is it simply:
$$2 \int dr' C(|r-r'|) ...
