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 ...
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 ...
36
votes
6answers
777 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 ...
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 ...
26
votes
10answers
653 views
Readable books on advanced topics [closed]
I realise that there are already a few questions looking for general book recommendations, but the motivation and type of book I'm looking for here is a little different, so I hope you can indulge me.
...
25
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:
...
23
votes
9answers
553 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 ...
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 ...
18
votes
6answers
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 ...
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 ...
15
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 ...
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 ...
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 ...
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 ...
11
votes
1answer
215 views
Covariant derivatives
I need correctly define covariant derivatives on the coset space $G/H$, where a group $G \equiv \{X_i, Y_a\}$ ($X$ and $Y$ are generators) have a subrgroup $H \equiv \{X_i\}$
Lie algebra of $G$ has ...
10
votes
2answers
2k views
How is the Saddle point approximation used in physics?
I am trying to understand the saddle point approximation and apply it to a problem I have but the treatments I have seen online are all very mathematical and are not giving me a good qualitative ...
10
votes
7answers
1k views
The philosophy behind the mathematics of quantum mechanics
My field of study is computer science, and I recently had some readings on quantum physics and computation.
This is surely a basic question for the physics researcher, but the answer helps me a lot ...
10
votes
3answers
341 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 ...
10
votes
2answers
889 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 ...
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 ...
9
votes
4answers
3k 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 ...
9
votes
3answers
392 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 ...
9
votes
2answers
474 views
Transforming a sum into an integral
I posted this in the mathematical forums. Maybe you will help me. I found an hard article http://prola.aps.org/abstract/PR/v105/i3/p776_1 of yang huang and luttinger. The authors begins with the sum: ...
8
votes
1answer
6k views
Where does this equation originate from? (found in the Big Bang Theory)
Recently, I've been watching "The Big Bang Theory" again and as some of you might know, it's a series with a lot of scientific jokes in it - mostly about Physics or Mathematics. I understand most of ...
7
votes
6answers
384 views
Objects in Physics as a mathematician would see them
I'm a mathematician with hardly any knowledge of physics. Before I start reading volumes of physics books, I have a few questions that have been bugging me and that will help me start reading physics.
...
7
votes
2answers
202 views
Advice on doing physics under the umbrella of mathematics and the converse
In the current scenario of research in QFT and string theory (and related mathematical topics), which of the following would an undergraduate student, like me, be advised to do and why if s/he is ...
7
votes
8answers
586 views
Mathematical Universe Hypothesis
What is the current "consensus" on Max Tegmark's Mathematical Universe Hypothesis (MUH) which claims every concievable mathematical structure exists, including infinite different Universes etc.
I ...
7
votes
2answers
702 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 ...
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 ...
6
votes
5answers
418 views
Is physics rigorous in the mathematical sense?
I am a student studying Mathematics with no prior knowledge of Physics whatsoever except for very simple equations. I would like to ask, due to my experience with Mathematics:
Is there a set of ...
6
votes
5answers
502 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 ...
6
votes
2answers
1k views
What is the covariant derivative in mathematician's language?
In mathematics, we talk about tangent vectors and cotangent vectors on a manifold at each point, and vector fields and cotangent vector fields (also known as differential one-forms). When we talk ...
6
votes
5answers
172 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 ...
6
votes
2answers
386 views
How should a theoretical physicist study maths? [duplicate]
Possible Duplicate:
How should a physics student study mathematics?
If some-one wants to do research in string theory for example, Would the Nakahara Topology, geometry and physics book and ...
6
votes
2answers
185 views
Quantum mechanics on Cantor set?
Has quantum mechanics been studied on highly singular and/or discrete spaces? The particular space that I have in mind is (usual) Cantor set. What is the right way to formulate QM of a particle on a ...
6
votes
1answer
402 views
Is C60 really the “most spherical” fullerene?
In the late 80's and early 90's, Smalley and others made claims that the C60 fullerene bearing icosahedral symmetry was the most spherical molecule known, and perhaps the most spherical that could ...
5
votes
6answers
2k views
How is gradient the maximum rate of change of a function?
Recently I read a book which described about gradient. It says
$${\rm d}T~=~ \nabla T \cdot {\rm d}{\bf r},$$
and suddenly they concluded that $\nabla T$ is the maximum rate of change of $f(T)$ ...
5
votes
7answers
694 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 ...
5
votes
3answers
220 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 ...
5
votes
3answers
985 views
What math do I need for mathematical physics? In what manner should I learn math? [closed]
I'm a freshman undergraduate. I've got my sight on mathematical physics. I love math but I don't have the talent nor the inclination for purely abstract mathematics. I also love physics.
The only ...
5
votes
1answer
275 views
Reference for mathematics of string theory [closed]
I have a great interest in the area of string theory, but since I am more focused on mathematics, I was wondering if there is any book out there that covers mathematical aspects of string theory. I ...
5
votes
0answers
472 views
Good theoretical physics introduction for 6 year old very advanced in math? [duplicate]
I think now is a good time to introduce my son to theoretical physics. He asks so many questions about the universe, black holes, gravity, atoms, molecules, light, etc. He's borderline obsessed with ...
4
votes
4answers
560 views
How do you do an integral involving the derivative of a delta function?
I got an integral in solving Schrodinger equation with delta function potential. It looks like
$$\int \frac{y(x)}{x} \frac{\mathrm{d}\delta(x-x_0)}{\mathrm{d}x}$$
I'm trying to solve this by ...
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
$$\pmb{H}=\pmb{\nabla} \phi +\pmb{\nabla} \times \pmb{G},$$
...
4
votes
3answers
504 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.
4
votes
2answers
254 views
Combinatorial sum in a problem with a Fermi gas
I'm solving a problem involving a Fermi gas. There is a specific sum I cannot figure my way around.
A set of equidistant levels, indexed by $m=0,1,2 \ldots$, is populated by spinless fermions with ...
4
votes
2answers
244 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 ...
4
votes
1answer
226 views
Differentiating inside an integral sign
I'm reading John Taylor's Classical Mechanics book and I'm at the part where he's deriving the Euler-Lagrange equation.
Here is the part of the derivation that I didn't follow:
I don't get how ...
4
votes
1answer
186 views
How deep can my knowledge of particle physics go without the maths?
Successfully just got my first question answered on here, and now time for the second.
So I recently gained interest in particle physics and was wondering.
By no means do I have the mathematical ...
4
votes
2answers
130 views
Quantum Mechanics in terms of *-algebras
I'm currently trying to find my way into the geometric description of Quantum Mechanics. I therefor started reading:
Geometry of state spaces. In: Entanglement and Decoherence (A. Buchleitner et ...
4
votes
2answers
345 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 ...
