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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2
votes
7answers
332 views

Book request for an abstract treatment of QM without using any particle formalism

I am an electronics and communication engineer, specializing in signal processing. I have some touch with the mathematics concerning communication systems and also with signal processing. I want to ...
4
votes
2answers
281 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 ...
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 ...
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 ...
2
votes
4answers
267 views

Can we make a change of variables (for example to polar coordinates) into a divergent integral?

I know that if the integral is convergent we can always make a change of variable to make it better, however what happens with DIVERGENT integrals? can we make a change of variable into a divergent ...
6
votes
1answer
544 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 ...
2
votes
6answers
3k views

real world applications of Mathematics which use functions with singularities, not just as a matter of mathematical taste but for conceptual reasons

EDIT [for aptness of this question to this site, read 'real world applications' as 'applications in Physics'] The concept of function (of the form $f : \mathbb{R} \to \mathbb{R}$ ) has been used in ...
8
votes
6answers
423 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. ...
9
votes
1answer
13k 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 ...
-2
votes
1answer
562 views

How to simplify e to power of j.t [closed]

I have exam tommorow and cant get this figured out :( dont blame me but please answer this question. I Want to simplify this term: 3 times ((e topowerof 5jt) + (e topowerof -5jt)) Thanks.
2
votes
2answers
437 views

How do you find conserved quantities for linear second order ODEs?

I have a differential equation of the form $ \frac{d^2 y}{dt^2} + f(t) \frac{dy}{dt} + g(t) y = 0 $ where $f$ and $g$ are known functions of time. Is there a systematic (or otherwise) way of ...
2
votes
2answers
291 views

a question on Lagrange's equation when the time derivative of the generalized co-ordinates is constant

Consider a system whose generalized co-ordinates are $q_i$ and is under the constraints $\dot{q_i} = K_i \forall i = 1,2,3,...$ where $K_i$ are constants. I have a problem in writing the Lagrange's ...
10
votes
3answers
514 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
2answers
651 views

Helmholtz decomposition in the plane

Prove or disprove the following proposition: For any smooth plane vector field $\mathbf{H}=\left(H_x,H_y\right)$, there exist scalar potentials $\phi$, $\psi$ such that $H_x=\frac{\partial \phi ...
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 $$\pmb{H}=\pmb{\nabla} \phi +\pmb{\nabla} \times \pmb{G},$$ ...
0
votes
1answer
176 views

A question on smooth 1-manifolds

Consider two people living on two different smooth 1-manifolds $S$ and $T$ as shown in figure 1. The manifold $S$ is a bump function joining the points $A$ and $B$ and the manifold $T$ is formed by ...
3
votes
4answers
3k views

How many digits of Pi are required in physics?

In other words: which physics experiment requires to know Pi with the highest precision?
14
votes
4answers
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 ...
2
votes
2answers
460 views

Diffusion across an interface and conservation of mass

I am reading a physiology book chapter (Mathematical Physiology, by Keener --Respiration chapter) about the gas exchange between capillaries and alveoli. It seems that this gas exchange can be modeled ...
2
votes
1answer
477 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 ...
3
votes
0answers
652 views

How do I derive the critical temperature for bose condensation in two dimensions?

In class we derived the 3D case, but there's a step I don't understand: $$ N = g \cdot {V \over (2 \pi \hbar)^3} \cdot \int\limits_{0}^{\infty}{1 \over{e^{\left( E_p \over{K_B T}\right)}-1}} d^3 p = ...
1
vote
6answers
347 views

Are the laws of physics applied mathematics? [closed]

This questions started with a question I had about gravity. If two objects of different weights fall to the earth at the same rate of acceleration, then it seems to me that gravity is in some ways ...
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 ...
2
votes
1answer
389 views

Problem deriving kinetic energy from work

I'm currently reading a nice introductory book (german, could be translated as "Physics with a pencil"). The author works a lot with differential calculus and antiderivatives (integrals will be used ...
2
votes
0answers
351 views

A question about Dirac operator

The Dirac operator at 2 dimension can be written as $$ D=\sum_{k=1,2}\sigma^{k}D_{k}=\left( \begin{array}{cc} 0 & \partial_{x}-i\partial_{y}-i(A_x-iA_y)\\ ...
6
votes
5answers
637 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 ...
2
votes
2answers
149 views

Mathematical Elegance in a Cosmological Theory Considered Necessary?

In general, it seems cosmological theories that encompass more and more of the phenomena of the universe are expected to be more and more mathematically elegant, in conception if not in detail. Our ...
2
votes
1answer
275 views

Can the geodesic propagators in the Euclidean BTZ black hole can be written in terms of meromorphic functions on its conformal boundary?

I'm interested in knowing if ,in the context of $AdS_{3}/CFT_{2}$, we can (and how to) express the geodesic propagators on the bulk space of the Euclidean $AdS_{3}$ black holes, in terms of ...
3
votes
3answers
630 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
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 ...
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
155 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 ...
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 ...
4
votes
2answers
511 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
1k 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
633 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 ...
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 ...
21
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 ...
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 ...
2
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
321 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 ...
-2
votes
4answers
2k views

Meaning and application of convolution or deconvolution in physical sciences

In which real case scenarios a convolution or deconvolution operation is useful ?
52
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 ...
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 ...
46
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: ...