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 ...

learn more… | top users | synonyms

3
votes
2answers
393 views

What are some interesting calculus of variation problems? [closed]

That I could create as a classical mechanics class project? Other than the classical examples that we see in textbooks (catenary, brachistochrone, Fermat, etc..)
2
votes
1answer
80 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 ...
0
votes
3answers
804 views

Sine wave, $\pi$ and frequency

Please explain the relation $\sin(2\pi ft)$ such that how the $\pi$ (which is actually circumference/diameter of a circle) relates with the sine wave which is having a longitudinal vibration?
1
vote
0answers
72 views

Reference request: Introductions to current mathematics derived from / related to gauge theories (in physics) [duplicate]

I was searching for introductions to current mathematics derived from / related to gauge theories in physics. Can someone suggest some good references? E.g. Topics in Physical Mathematics by K. ...
3
votes
2answers
189 views

An integral related to QFT

How to show $$\displaystyle\int\int\int f(p,p')e^{ip\cdot x-ip'\cdot x}d^3pd^3p'd^3x=(2\pi)^3\int f(p,p)d^3p$$ ? I have $p\cdot x=Et-\bf p\cdot x$
1
vote
2answers
749 views

What is the physical meaning of a product of vectors?

My teacher told me that Vectors are quantities that behave like Displacements. Seen this way, the triangle law of vector addition simply means that to reach point C from point A, going from A to B ...
6
votes
3answers
8k 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
91 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.
3
votes
7answers
791 views

For a theoretical (not mathematical) physicist, is there a need to learn pure mathematics?

For a theoretical physicist (not a mathematical physicist), is there a need to learn pure mathematics ?
3
votes
2answers
457 views

What is the mathematical formulation for buckling?

Argument: Buckling is an engineering concept that can only be applied to thin columns with compressive loading. (Is it possible to) Prove the above sentence right or wrong with mathematical ...
2
votes
1answer
189 views

What determine whether the dynamical equations are tensor equations or vector equations?

Newton's 2nd law which is central to Newtonian dynamics, is a vector equation $\sum\textbf{F}_{external}=m\textbf{a}$ Same with Maxwell's equations in the covariant form. On the other hand, ...
5
votes
3answers
1k views

What is a antiunitary operator?

In field theory one can define a time reversal operator T such that $T^{-1} \phi (x) T = \phi (\mathcal T x)$. It is then proved that T must be antiunitary: $T^{-1} i T = -i$. How is this equation ...
10
votes
8answers
707 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 ...
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 ...
12
votes
1answer
344 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 ...
3
votes
1answer
284 views

Is there a mathematical way to describe how a flame flickers?

I love the way candles flicker. It's a great effect and I almost want to see it replicated in an actual lightbulb. I was curious if there is any way to express that mathematically? I'm not that ...
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 ...
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 ...
2
votes
2answers
2k views

Calculating uncertainty in the final result (combining uncertainties)

I'm struggling to determine the uncertainty in $F$ so it would match the textbook answer. The problem statement is: A force F is obtained using the equation: $F = \frac{mv^2}{2\pi(x_2 - x_1)}$. The ...
0
votes
1answer
546 views

Reference area of a parachute

I am trying to do an aerodynamic drag equation on a descending parachute (the round variety) and have no idea what the reference area on one would be. I know for a sphere, you can use radius*radius*PI ...
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 ...
9
votes
2answers
508 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: ...
3
votes
4answers
571 views

Generalized functions in physics

Prior to the Dirac delta function, what other distributions functions where physicists using? I find it hard to motivate the theory of generalized functions with just the delta function alone.
-1
votes
1answer
384 views

Functional Derivative of Convolution

How to carry out the following functional derivative? $$\frac{\delta F}{\delta n(r)}$$ where $$F=\int dr n(r) \int C(|r-r'|) n(r') dr'$$ is it simply: $$2 \int dr' C(|r-r'|) ...
14
votes
5answers
9k 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 ...
2
votes
1answer
74 views

What interpretive difference is there between defining a function with or without a differential as a postfactor?

I have thought about this and looked for answers for a long time now, but I do not have any name or label for this problem, which is the reason for the long title of this question. I have come across ...
2
votes
7answers
329 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
280 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 ...
19
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 ...
12
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
257 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
523 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
2k 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
418 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
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 ...
-2
votes
1answer
514 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
414 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
290 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
493 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
621 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
175 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
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 ...
2
votes
2answers
446 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
433 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
631 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
344 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
378 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 ...