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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3
votes
3answers
654 views

Can a functional derivative be calculated if we have a function of more than one variable?

Can a functional derivative be calculated if we have a function of more than one variable? The functional derivative of, for example, $F[b(x)]=e^{\int_0^{x'} dx a(x,y) b(x)}$ is ...
7
votes
4answers
2k 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 ...
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 ...
1
vote
1answer
159 views

Time evolution of wave spectrum

A useful way of thinking (not only) oceanic waves is to consider them as a superimposition of linear modes: the elevation η of the sea surface is given by: 1: $\eta({\bf x}, t) = ...
1
vote
2answers
2k views

Solving a Young Laplace equation for a meniscus against a flat plate

This is more of a math question and one, furthermore, that I know the final answer to. What I am asking is more of a "how do I get there" question as this question was generated during a self study ...
27
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 ...
4
votes
2answers
570 views

Existence and uniqueness of solutions for Einstein equations

Now that an equivalence of Navier Stokes and Einstein equations has been established, and it is known solutions to Einstein-Maxwell-Boltzmann exist and are unique, and it is known that Einstein ...
1
vote
3answers
2k views

Can vectors in physics be represented by complex numbers and can they be divided? [closed]

Below is attached for reference, but the question is simply about whether vectors used in physics in a vector space can be represented by complex numbers and whether they can be divided. In ...
4
votes
1answer
688 views

Boundary conditions for Couette flow

I'm trying to reproduce a result from a paper (T. Thatcher, Boundary Conditions for Grad's 13 moment equations, equation (32), page 6), however, I haven't been able to do so. Hopefully someone can ...
16
votes
8answers
4k 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 ...
24
votes
10answers
5k 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 ...
27
votes
8answers
4k views

Classical mechanics without coordinates book

I am a graduate student in mathematics who would like to learn some classical mechanics. However, there is one caveat: I am not interested in the standard coordinate approach. I can't help but think ...
3
votes
1answer
2k views

Spherical wave as sum of plane waves

How can we do this computation? $\iiint_{R^3} \frac{e^{ik'r}}{r} e^{ik_1x+k_2y+k_3z}dx dy dz$ where $r=\sqrt{x^2+y^2+z^2}$ ? I think we must use distributions... Physically, it's equivalent to ...
4
votes
2answers
363 views

Are gauge choices in electrodynamics really always possible?

If $B$ is magnetic field and $E$ electric Field, then $$B=\nabla\times A,$$ $$E= -\nabla V+\frac{\partial A}{\partial t}.$$ There is Gauge invariance for the trnasformation $$A'\rightarrow ...
-1
votes
4answers
3k views

Meaning and application of convolution or deconvolution in physical sciences

In which real case scenarios a convolution or deconvolution operation is useful ?
54
votes
14answers
6k views

Number theory in Physics [closed]

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 ...
22
votes
8answers
6k 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 ...
53
votes
14answers
14k 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: ...