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 ...
4
votes
0answers
32 views

Solutions of nonlinear systems invariant wrt. perturbations (looking for applications)

I want to ask if the following purely mathematical problem (that I'm working on) might have some applications to physics. The problem in a nutshell: describe properties of solution sets of real ...
1
vote
0answers
606 views

Physicists: Why do mathematicians insist on doing mathematics in a vaccuum and how do you deal with it [closed]

I'm trying to learn the theory of wavelet transform, a concept which is supposedly filled with enormous physical intuition, diagrams, pictures, things with physical analogies...but after 30 pages of ...
3
votes
0answers
79 views

Recent missed opportunities à la Freeman Dyson

There is an excellent paper by Freeman Dyson from 1972 (here) and therein the author cites old talks by Hilbert (here) and Minkowski (chapter 2 here) speaking about similar topics, namely how ...
2
votes
1answer
63 views

What are the proper domains of the position and squared angular momentum operator?

I am looking at the position operator on a compact set $K \subset \mathbb{R}^n$ and the squared angular momentum operator (so essentially the Laplace-Beltrami operator where I just look at the angular ...
0
votes
1answer
71 views

Resources for theory of distributions (Generalized functions) for physicists

I am looking for tutorials, articles or books containing theory of distributions in context of mathematical physics. Please suggest.
1
vote
0answers
77 views

Most useful maths for theoretical and mathematical physics [closed]

I am going to apply for a programme of mathematical and theoretical physics for graduate studies and I'm currently studying maths. What is a good area to do a thesis (that is to say, considerable ...
1
vote
0answers
84 views

mathematician or physicists [closed]

Mathematicians consider physicists as people who simply use mathematics as a tool but are in a way, let's say, inaccurate, as physicists tend to make assumptions a lot in their mathematics and ...
3
votes
0answers
48 views

Scalar product of torsional forms - how are the standard identities modified?

It is known that for any smooth, orientable, compact manifold $X$ without boundary and $\alpha \in \Omega^{r}(X), \beta \in \Omega^{r-1}(X)$ it holds \begin{equation} (d\beta,\alpha)= (\beta, ...
2
votes
4answers
85 views

Infinite series of derivatives of position when starting from rest

Suppose you have an object with zero for the value of all the derivatives of position. In order to get the object moving you would need to increase the value of the velocity from zero to some finite ...
0
votes
1answer
76 views

About Hilbert and Physics [duplicate]

Was one of Hilbert questions regarding physics to make an axiomatic foundation for physics? Regardless of Godels work could some Physics principles that are 'basic' and 'presently verifiable' be ...
4
votes
1answer
118 views

Which is the role of Algebraic Geometry in String Theory? [closed]

Could someone sketch me what algebraic geometry has to do with string theory? Are there other mathematical disciplines that are interwoven with string theory? I'm aware of a similar question on ...
3
votes
1answer
92 views

References on $C^{*}$-algerbas, $W^{*}$-algebras and Quantum Theories

I would like to know some references regarding $C^{*}$ and $W^{*}$-algebras and quantum theories. I'm interested in concrete physical applications, models and problems. Here it is the list of ...
3
votes
1answer
125 views

A question about canonical transformation

I have posted this question in math.stackexchange before with no answer till now. It may be more suitable to post here. There is a problem in Arnold's Mathematical Methods of Classical Mechanics ...
8
votes
0answers
228 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 ...
2
votes
0answers
42 views

Is rigorous functional analysis useful for theoretical physics? [duplicate]

I'm an undergraduate physics without much quantum mechanics at all under my belt. I'm studying functional analysis, and I want to know whether or not this will be useful for me in theoretical physics ...
0
votes
1answer
35 views

A question about Hamiltonian phase flow

Show that if a one-parameter group of difeomorphisms of a symplectic manifold preserves the symplectic structure then it is a locally hamiltonian phase flow. Note that A locally hamiltonian ...
0
votes
0answers
50 views

To all experienced theoretical physicists out there, what is the step by step process in your math education? [duplicate]

I am not doing a physics degree but an engineering degree but i am planning using my free time to self study all the math in preparing myself to self study subjects in theoretical physics. (I've ...
6
votes
1answer
109 views

Determining the Hodge numbers of some orbifold examples

I'm currently reading about complex geometry in order to get a feeling of how to determine the Hodge numbers, e.g. of certain orbifold constructions. Since I'm a physicist with no deeper mathematical ...
3
votes
2answers
147 views

In what way are the Mathematical universe hypothesis and A New Kind of Science connected

The Mathematical universe hypothesis, mainly by Max Tegmark and A new Kind of Science, mainly by Stephen Wolfram both claim (as least as I understand it) that at its innermost core reality is ...
0
votes
0answers
32 views

The sum of positive integers equals minus one twelfth [duplicate]

I was watching a lecture online from the american physicist Lawrence Krauss, when he made an off the cuff remark about the sum of all the positive integers being equal to one twelfth. My question is ...
5
votes
4answers
187 views

Kähler and complex manifolds

I was woundering if anyone knows any good references about Kähler and complex manifolds? I'm studying supergravity theories and for the simplest $\mathcal{N}=1$ supergravity we'll get these. Now in ...
3
votes
2answers
3k views

How does the sum of the series “1 + 2 + 3 + 4 + 5 + 6…” to infinity = “-1/12”? [duplicate]

How does the sum of the series “1 + 2 + 3 + 4 + 5 + 6…” to infinity = “-1/12”, in the context of physics? I heard Lawrence Krauss say this once during a debate with Hamza Tzortzis ...
2
votes
1answer
202 views

A question about Fermi-Dirac Distribution function

It seems more like a mathematical question, about the property of Fermi-Dirac Distribution function $$f=\frac{1}{e^{(E-\mu)/k_BT}+1}$$ where $\mu$ is the chemical potential and $k_B$ is the Boltzmann ...
0
votes
0answers
46 views

Are there some websites for self learning of advanced mathematics? [duplicate]

Are there some websites for self learining of advanced mathematics? For example there is perimeterscholars for self study of theoretical physics, but I haven't found some good websites providing ...
1
vote
3answers
216 views

Can we construct Axiomatic system of physical laws?

If we construct axiomatic system of physical laws that are independent one another as in axioms in mathematics, what should they be? Can there be such a finite system of physical laws that can explain ...
11
votes
3answers
520 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 ...
7
votes
1answer
138 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
2answers
752 views

How important is mathematical proof in physics?

How important are proofs in physics? If something is mathematically proven to follow from something we know is true, does it still require experimental verification? Are there examples of things that ...
4
votes
2answers
438 views

Normalization of the path integral

When one defines the path integral propagator, there is the need to normalize the propagator (since it would give you a probability density). There are two formulas which are used. 1) Original ...
0
votes
0answers
52 views

Books for learning Mathematics in Physics? [duplicate]

Currently I'm doing Advanced Classical 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 ...
18
votes
6answers
832 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. ...
3
votes
2answers
318 views

Tensor Product of Hilbert spaces

This question is regarding a definition of Tensor product of Hilbert spaces that I found in Wald's book on QFT in curved space time. Let's first get some notation straight. Let $(V,+,*)$ denote a set ...
4
votes
3answers
756 views

Direct Sum of Hilbert spaces

I am a physicist who is not that well-versed in mathematical rigour (a shame, I know! But I'm working on it.) In Wald's book on QFT in Curved spacetimes, I found the following definitions of the ...
1
vote
0answers
83 views

Periodic sequence with exponentially increasing period?

I have to develop a physical model for a certain type of biological oscillation that can be built upon periodic sequences. From earlier questions I know that any periodic sequence (containing $0$s ...
2
votes
3answers
1k views

Differences between symmetric, Hermitian, self-adjoint, and essentially self-adjoint operators

I am a physicist. I always heard physicists used the terminology "symmetric", "Hermitian", "self-adjoint", and "essentially self-adjoint" operators interchangeably. Actually what is the difference ...
1
vote
0answers
46 views

Ascertaining a mathematical equality to derive a partition function

we have an equation like this: $$\mathcal N(x)=\sum_{q=1}^\infty (\psi(x,q) \log(q)) \qquad (1)$$ while $\psi(x)$ is the function for some oscillations (may contain complex part), $x\in \Bbb R$ and ...
1
vote
0answers
69 views

Applications of a certain wave equation in Physics? [closed]

I am doing research in the field of number theory and as part of this looking for correspondencies to other discilines and particularly physics. I am searching for examples in physics where the ...
9
votes
6answers
576 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 ...
1
vote
1answer
186 views

Spin(n) group SO(n) relation

Is it correct to state that the elements of Spin(n) fulfill a Clifford algebra and that the Lie group generators of Spin(n) is given by the commutator of the elements? If not, then what is the ...
9
votes
3answers
805 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 ...
1
vote
2answers
653 views

How much pure math should a physics/microelectronics person know [duplicate]

I do condensed matter physics modeling in my phd and I was struck up learning quite an amount of physics. But while having done lot of physics courses, I see that if I learn pure math I would ...
1
vote
1answer
201 views

Topology for physicists [duplicate]

Which are the best introductory books for topology, algebraic geometry, manifolds etc, needed for string theory?
2
votes
1answer
165 views

Calculation of spherical Bessel functions - meaning of $\left(\frac{1}{x}\frac{d}{dx}\right)^{l}$

I'm trying to understand the calculation of spherical Bessel functions in chapter four of Griffiths' Introduction to Quantum Mechanics (2nd ed, p142). He gives ...
3
votes
0answers
300 views

Interesting Math Topics Useful for Physics [closed]

What are some interesting, but less popular, math topics that are useful for physics that can be self-studied? Specifically, topics that might ultimately be useful in high energy theory (even if it is ...
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 ...
3
votes
2answers
351 views

(Co)homology of the universe

In this post let $U$ be the universe considered as a manifold. From what I gather we don't really have any firm evidence whether the universe is closed or open. The evidence seems to point towards it ...
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 ...
13
votes
4answers
632 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 ...
4
votes
1answer
150 views

The use of Hall algebras in physics

I asked the same question in mo. I think maybe here there are more physics guys to help me. I once read a statement (not memorized precisely) that a certain physics quantity between two states of ...