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 ...

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54
votes
6answers
2k 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 ...
51
votes
14answers
5k views

Number theory in Physics

As a Graduate Mathematics student, my interest 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 ...
45
votes
13answers
10k 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: ...
43
votes
11answers
5k 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 ...
32
votes
8answers
3k views

Does Gödel preclude a workable ToE?

Gödel'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 ...
30
votes
10answers
1k 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 ...
30
votes
10answers
1k 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. ...
26
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 ...
25
votes
8answers
3k 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
9answers
5k 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 ...
20
votes
11answers
6k 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 ...
20
votes
10answers
4k 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 ...
18
votes
6answers
856 views

Tensor Operators

Motivation. I was recently reviewing the section 3.10 in Sakurai's quantum mechanics in which he discusses tensor operators, and I was left desiring a more mathematically general/precise discussion. ...
17
votes
8answers
2k views

Why are sine/cosine always used to describe oscillations?

What I am really asking is are there other functions that, like $\sin()$ and $\cos()$ are bounded from above and below, and periodic? If there are, why are they never used to describe oscillations in ...
17
votes
2answers
1k views

What interesting physics problems can't be solved because mathematics is not developed enough? [closed]

I'm curious as to what sorts of physical problems to which we don't have an answer, because we haven't developed the right mathematics yet (or advanced-enough mathematics). Related to this question ...
15
votes
4answers
626 views

Hilbert, Gödel, and “God equations” - a 19th century lesson for 21st century physicists?

It seems there are a lot of respected physicists appearing on pop-sci programs (discovery channel, science channel, etc.) these days spreading the gospel of "we can know, we must know." Three ...
14
votes
8answers
3k 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 ...
14
votes
5answers
10k 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 ...
14
votes
3answers
1k 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 ...
14
votes
1answer
1k views

Equation describing magnetic hysteresis

So when you're looking at B-H curves for ferromagnetic substances, you often see these magnetic hysteresis curves, which occur, I gather, largely because of domain formation which has some reversible ...
13
votes
5answers
3k views

Is speed of light and sound rational or irrational in nature?

Just as circumference of circle will remain $\pi$ for unit diameter, no matter what standard unit we take, are the speeds of light and sound irrational or rational in nature ? I'm talking about ...
13
votes
4answers
648 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 ...
13
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 ...
12
votes
17answers
3k 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 ...
12
votes
1answer
358 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 ...
12
votes
2answers
5k 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 ...
11
votes
7answers
1k 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 ...
11
votes
3answers
537 views

What happened with Hilbert's sixth problem (the axiomatization of physics) after Gödel's work?

I'll write the question but I'm not fully confident of the premises I'm making here. I'm sorry if my proposal is too silly. Hilbert's sixth problem consisted roughly about finding axioms for physics ...
11
votes
3answers
700 views

Mathematical Physics Book Recommendation [duplicate]

Possible Duplicate: Best books for mathematical background? I want to learn contemporary mathematical physics, so that, for example, I can read Witten's latest paper without checking other ...
10
votes
4answers
1k 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.
10
votes
3answers
509 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 ...
10
votes
8answers
724 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 ...
10
votes
2answers
1k 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 ...
9
votes
1answer
12k 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 ...
9
votes
3answers
831 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 ...
9
votes
6answers
583 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 ...
9
votes
2answers
157 views

If a theory of everything exists, is it necessarily unique?

There is a lot of interesting debate over whether a "theory of everything" (ToE) is allowed to exist in the mathematical sense, see Does Gödel preclude a workable ToE?, Final Theory in Physics: a ...
9
votes
2answers
514 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
6answers
422 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. ...
8
votes
0answers
229 views

p-Adic String Theory and the String-orientation of Topological Modular Forms (tmf)

I am going to ask a question, at the end below, on whether anyone has tried to make more explicit what should be a close relation between p-adic string theory and the refinement of the superstring ...
8
votes
0answers
521 views

String theory from a mathematical point of view

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 ...
7
votes
2answers
328 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
3answers
2k 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
1answer
247 views

Is there any usage of $x^x$ in physics? [closed]

I am so excited about the function: $x^x$. I would like to know if there is any usage in the physics world of this function. Is there any formula that uses $x^x$?
7
votes
3answers
2k 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 ...
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 ...
7
votes
2answers
305 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 ...
7
votes
2answers
123 views

Mathematical physics text with plenty of applications

I'm looking for texts on mathematical physics. I've seen various other threads, but the texts recommended in those threads were mathematical methods of theoretical physics texts, that is to say those ...
7
votes
1answer
139 views

Are there cases in which we should consider tensors as equivalence classes?

Usually in texts about Physics that uses tensors defines them as multilinear maps. So if $V$ is a vector space over the field $F$, a tensor is a multilinear mapping: $$T:V\times\cdots\times V\times ...
6
votes
3answers
10k 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 ...