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 ...
6
votes
5answers
150 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 ...
0
votes
0answers
27 views
Problem with Discrete Parseval's Theorem [migrated]
I think I must be missing something obvious, but I can't for the life of me see what it is. The discrete version of Parseval's theorem can be written like this:
$\sum_{n=0}^{N-1} |x[n]|^2 = ...
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 ...
3
votes
2answers
59 views
Expanding two-variable function $f(x,y)$ over the complete sets $\{ g_{i}(x) \}$ and $\{ h_{j}(y) \}$
Quite often (see, for example, this PDF, 50 KB) when discussing the Born-Oppenheimer approximation the following assertion is made: any well-behaved function of two independent variables $f(x,y)$ can ...
1
vote
2answers
61 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 ...
-3
votes
2answers
105 views
Why is $r'/r^2 = -1/r$? [closed]
If $r=r(t)$, why is $\frac{r'(t)}{(r(t))^2}$ = $\frac{1}{r(t)}$ where $'$ denotes the derivative? I saw it in a lecture.
Can you please explain?
-2
votes
2answers
80 views
Is there any phenomenon in physics which is sensitive to irrational numbers?
We can measure only rational numbers by our scale. Here is an example where irrational numbers does makes sense. If so then this question may have some theoretical importance. Is irrational numbers ...
4
votes
1answer
113 views
Does nature tetrate?
We see addition, multiplication and exponentiation in the natural formulae that make up physics.
However, do we ever see tetration (repeated exponentiation) or higher hyper-operators in nature?
...
0
votes
0answers
89 views
Literature request for books / review papers on gravitation, gauge theories and related mathematics [duplicate]
Similar to this reference, are there more such references / works [including textbooks] available in the literature?
(A list would be greatly welcomed and appreciated.)
With great appreciation.
4
votes
2answers
144 views
Integer physics
Are there interesting (aspects of) problems in modern physics that can be expressed solely in terms of integer numbers? Bonus points for quantum mechanics.
1
vote
2answers
126 views
Studying the logical structure of physics as a mathematical object per se? [closed]
I was wondering is there a branch of mathematical physics which studies the underlying logical structure of physics as a mathematical object per se?
Let me explain what I mean by that.
I'm ...
1
vote
1answer
77 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 ...
2
votes
2answers
69 views
continuity of the electric potential due to a surface charge
The Electric potential due to a charge distribution on a surface is :
$\Phi \left ( x \right )=\int \frac{\sigma \left ( {x^{}}' \right )dx{}'}{\left \| x-x{}' \right \|}da$ I want to show that it's ...
1
vote
2answers
114 views
Suggestions on a particular arXiv publication on math needed for theoretical physicists [closed]
I'm going to start my PhD in a year and I'll be taking a gap year doing other stuff. But I also wanted to fill in the gaps in my math knowledge and I came across an arXiv publication called ...
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 ...
0
votes
1answer
139 views
Universal Sequence and relationship of mathematics and reality [closed]
In "The Special and General Theory of Relativity" Einstein says:
How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably ...
0
votes
1answer
84 views
Math for Thermodynamics Basics
I am studying Statistical Mechanics and Thermodynamics from a book that i am not sure who has written it, because of its cover is not present.
There is a section that i can not understand:
...
4
votes
1answer
183 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 ...
1
vote
2answers
160 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 ...
2
votes
1answer
71 views
Taylor expansion of an integral in spherical co-ordinates
I've some difficulty deriving this equation from jackson electrodynamics (The equation after 1.30)
$\nabla^2 \Phi_a\left({\textbf{x}}\right)=-\frac{1}{\epsilon_0}\int_{0}^{R} ...
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
3answers
217 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 ...
4
votes
1answer
137 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 ...
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 ...
3
votes
0answers
108 views
Is there a physical motivation to study finite fields?
Clearly finite groups are of immense value in physics and these are also substructures of fields. However I never came across any computations involving finite fields at university and so I never ...
4
votes
2answers
344 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 ...
3
votes
4answers
477 views
Topology needed for Differential Geometry [duplicate]
I am a physics undergrad, and need to study differential geometry ASAP to supplement my studies on solitons and instantons. How much topology do I need to know. I know some basic concepts reading from ...
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:
...
1
vote
1answer
106 views
Topology for physicists [duplicate]
Which are the best introductory books for topology, algebraic geometry, manifolds etc, needed for string theory?
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 ...
10
votes
2answers
887 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
3answers
2k 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 ...
0
votes
0answers
38 views
How much math do I need to know to learn about quantum mechanics? [duplicate]
I am not good at math, so I needed to know if quantum mechanics involves a lot of math like, astrophysics for example, if it does, is there any book that can teach me this level of math?
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 ...
2
votes
1answer
157 views
Impact of LHC on other science and technologies, in particular on mathematics?
The Large Hadron Collider (LHC) "remains one of the largest and most complex experimental facilities ever built" (Wikipedia); it may even be the most complex project in humankind's history (?).
Such ...
3
votes
11answers
749 views
Is it possible for a physical object to have a irrational length?
Suppose I have a caliper that is infinitely precise. Also suppose that this caliper returns not a number, but rather whether the precise length is rational or irrational.
If I were to use this ...
5
votes
1answer
274 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 ...
1
vote
1answer
140 views
Potential for charge distribution, finiteness
Consider a potential for charge distribution:
$$v_H(\mathbf{r}) ~=~ \int \frac{\rho(\mathbf{r'})}{|\mathbf{r}-\mathbf{r'}|}d\mathbf{r'}$$
where $\rho(\mathbf{r'})$ is the charge density.
This ...
1
vote
1answer
94 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 ...
4
votes
4answers
551 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 ...
2
votes
3answers
278 views
Mathematics for Quantum Mechanics [duplicate]
What math should I study if I want to get a basic understanding of quantum mechanics and especially to be able to use the Schrodinger's equation.
11
votes
1answer
214 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 ...
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 ...
2
votes
0answers
159 views
A solvable model for the finite rectangular potential well with a bump in the middle
A well known example in quantum mechanics is that of a finite rectangular potential well with a rectangular bump in the middle. I guess this closely approximates the "umbrella" effect of the $NH_3$ ...
-2
votes
1answer
300 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.
0
votes
2answers
292 views
Level of calculus required for physics [closed]
First time for me here so kindly let me know if I violate the rules - especially if this is a duplicate.
After reading the page how to become a good theoretical phycist, I started a serious revision ...
2
votes
1answer
58 views
Causality and operationalism: from sets and functions to monads
When working in a laboratory, the most basic behaviour is to turn a knob or dial and then see a transformation of some data output. An example is increasing a magnetic field and seeing Zeeman ...
2
votes
0answers
192 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 ...
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
775 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 ...
