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Questions tagged [physics]

For questions about mathematical problems arising from physics, the natural science studying general properties of matter, radiation and energy.

24
votes
2answers
1k views

Runner's High (Speed)

I find the following mind-boggling. Suppose that runner $R_1$ runs distance $[0,d_1]$ with average speed $v_1$. Runner $R_2$ runs $[0,d_2]$ with $d_2>d_1$ and with average speed $v_2 > v_1$. I ...
3
votes
1answer
337 views

Does current follow the path(s) of least (total) resistance?

Consider Poisson equation $\nabla \cdot (\sigma(x)\nabla u)=0$ in a domain $D$, where $\sigma(x)$ is the spatially dependent conductivity. On the boundary we have $2$ electrodes $E_1$ and $E_2$ (...
3
votes
0answers
78 views

Partial Liouville equation

In my master's thesis, I worked on mathematical multi-scale models for muscle tissue. Now after finishing it, I would like to find out if one direction could be a research topic for my PhD. At one ...
2
votes
1answer
160 views

PDE’s whose solutions can be presented using path integrals

It is well known that solutions of the Schroedinger equation and of the heat equation can be presented using path integrals: $$\psi(x,t)=\int K(x,t;y,0)\psi(y,0)dy,$$ where the kernel $K(x,t;y,0)$ is ...
3
votes
1answer
86 views

Quantum tunneling on the line with non-symmetric double well potential

Consider the Schroedinger equation on the line $$i\frac{\partial \Psi(x,t)}{\partial t}=[-\frac{d^2}{dx^2}+V(x)]\Psi(x,t),$$ where one assumes that $V(x)\to +\infty$ as $|x|\to +\infty$, and $V$ has ...
14
votes
4answers
2k views

Which edition of Philosophiae Naturalis Principia Mathematica of Isaac Newton would you recommend to me?

I'm searching for a good edition of Philosophiae Naturalis Principia Mathematica of Isaac Newton in English. Which edition of the Principia can you suggest me? If it's possible, cheap and similar to ...
10
votes
4answers
1k views

Why the unreasonable applicability of complex numbers in physics/engineering? [duplicate]

After years of using complex numbers in every kind of analysis of physical and electrical engineering problems I am starting to wonder: why is this particular algebra so effective in modelling the ...
33
votes
3answers
4k views

On Critical Reviews of Hawking's “Gödel and the End of the Universe” Lecture

The search for a neat Theory of Everything (ToE) which unifies the entire set of fundamental forces of the universe (as well as the rules which govern dark energy, dark matter and anti-matter realms) ...
2
votes
0answers
78 views

Is this correct: Inflection points of Euler number graph in Island-Mainland transition correspond to spanning cluster site percolation threshold?

I'm writing with respect to the paper Khatun, Dutta, and Tarafdar - "Islands in Sea" and "Lakes in Mainland" phases and related transitions simulated on a square lattice. Here's a link to a PDF ...
1
vote
1answer
83 views

wave speed and travelling wave

I have seen a lot of work has been done in the context of travelling wave. For example the work of McKenna and Chen in Journal of Differential Equations Volume 136, Issue 2, 20 May 1997, Pages 325-355....
0
votes
0answers
68 views

Movement of a random walk in the limit (a particle in diffusion)

I asked this question in Math Exchange and obtained no answer. Let $X(t)$ be a stochastic process in time such that $X(0)=0$ and, at each increment of time $\Delta t$, it can move $h$ units in space ...
3
votes
2answers
401 views

Experiments physically performable in a finite amount of time whose results are independent of ZFC [closed]

In On independence and large cardinal strength of physical statements we see that their are physical statements which are independent of ZFC, and even strong cardinal axioms. There were many answers, ...
0
votes
0answers
253 views

What is a self-consistent equation in percolation theory

I was reading papers about percolation theory in which I was confused by the expression "self-consistent equation", for example in Temporal percolation in activity-driven networks. I read some ...
1
vote
0answers
75 views

Diffraction across an absorbing wall

I need help finding the procedure for the solution of the following differential equation. This is equation is: Find $u:\mathbb{R}^2 \to \mathbb{C}$ such that for $C>0$ $ \begin{cases} u_{xx}+ ...
9
votes
0answers
298 views

Which of the physics dualities are closest in essence to the Spanier-Whitehead duality (with a subquestion)?

First of all, what I want to ask is slightly more elaborate than what stands in the title (hence the subquestion). I am telling this since as it is, the title contains a meaningful question, but it ...
6
votes
0answers
95 views

Charge distribution of closed surfaces

Consider a closed surface $\Sigma$ which bounds a solid $\Omega$ in ${\mathbb R}^3$. Assume some electric charges, say totally $Q$, is distributed on $\Sigma$ and reaches an "equilibrium" state. In ...
3
votes
1answer
198 views

Wave front set of vector-valued Dirac delta distribution

Context: I am reading a physics paper Local Wick Polynomials and Time Ordered Products of Quantum Fields in Curved Spacetime which applies the notion of the wave front set to operator-valued ...
30
votes
4answers
2k views

Representation theory and elementary particles

I have been looking for a clear expository mathematical text on the relation between the theory of elementary particles and the representation theory of $U(1), SU(2), SU(3)$, I was very disappointed ...
3
votes
0answers
76 views

Multiplicativity of $\zeta$-function regularized determinant

Let $A$ be a selfadjoint elliptic differential operator on a compact manifold. In mathematical physics and differential topology one often defines its determinant using the $\zeta$-function ...
9
votes
2answers
500 views

$\zeta$-function regularized determinants

In (mathematical) physics in order to compute path integrals one often makes an infinite dimensional change of variables and uses infinite Jacobian as a purely formal expression. This step is done in ...
2
votes
1answer
910 views

Why Chern numbers (integral of Chern class) are integers?

I am a physics student trying to self-learn Chern numbers and Chern class. The book I am learning (Nakahara) introduces the total Chern class as an invariant polynomial of local curvature form $F$ $P(...
3
votes
0answers
81 views

Is there any connection between Lagrange points and the icosahedron?

Given the Newtonian two-body problem, one can ask if there are any orbits that allow a test particle to maintain a fixed configuration relative to the two bodies. In other words, in a frame that ...
4
votes
0answers
148 views

$S$-matrix in QED in 2d space-time

I am not completely sure that this question is appropriate for this site, but I have asked a similar question here https://physics.stackexchange.com/questions/271372/s-matrix-in-qed-in-2d-space-time ...
3
votes
1answer
452 views

Boundary conditions for Klein-Gordon equation

Let us consider the Klein-Gordon equation $$(\Box +m^2)u=0,$$ where $u$ is a scalar valued function, $m\geq 0$, $\Box=\frac{\partial^2}{\partial x_0^2}-\sum_{i=1}^d\frac{\partial^2}{\partial x_i^2}$. ...
13
votes
1answer
440 views

Digital physics and “Gandy-like” machines

Various physicists, famously John Wheeler, have asserted that physical information is the central object of study in physics, in the sense that an object or concept is "physically meaningful" if it ...
4
votes
0answers
162 views

Why do we care about simplicity of the spectrum in Oseledets' theorem?

Oseledets' theorem is a fundamental result in Ergodic theory (see for example here, or Chapter 4 of Lectures on Lyapunov Exponents by Marcelo Viana). The simplicity of the spectrum has been studied ...
4
votes
2answers
967 views

Two point function of a free scalar field in Euclidean space-time

This question was previously asked here https://physics.stackexchange.com/questions/251927/two-point-function-of-a-free-massless-scalar-field-in-euclidean-space-time though I did not get there an ...
3
votes
1answer
645 views

origin of analogy “primes as the atoms of number theory/ arithmetic”

a math student recently challenged me on the old comparison/ analogy of prime numbers to "the atoms of number theory or arithmetic" and then was wondering the origin of the phrase. where does this ...
3
votes
1answer
169 views

Conserved quantities for the Cauchy momentum equation

I apologize if this question is too elementary for mathoverflow; I asked it (unsuccessfully) on MATH.SE first. As a bit of background: one way to study the mechanics of deformation of a continuous ...
30
votes
6answers
6k views

Number theory and physics

I was following some lectures by Edward Frenkel about Langlands correspondence. He was describing some analogies between number theory and theoretical physics (Mirror symmetry). At some point ( my ...
8
votes
1answer
684 views

Mathematics of Chiral Rings

Let $A$ be a graded vector space, and suppose that two commuting differentials $d_1$ and $d_2$ of degree +1 act on $A$, such that $A$ equipped with either is a chain complex. We now construct $C(A)$, ...
2
votes
1answer
194 views

Generating Functional for the Dirac Field, equivalence of expressions

As with the Klein-Gordon field, we can alternatively derive the Feynman rules with the free Dirac theory by means of a generating functional. In analogy with the scalar field theory where $Z[J]$ is ...
0
votes
1answer
186 views

Computational Physics or Pure Math Modules for Theoretical Physics [closed]

I'm beginning my university course in Theoretical Physics next week and we have been asked to choose our modules. We have compulsory modules in Physics, Vector Algebra and Dynamics. But we also have ...
4
votes
0answers
294 views

Unusual generalization of the law of large numbers

I have seen in physical literature an example of application of a very unusual form of the law of large numbers. I would like to understand how legitimate is the use of it, whether there are ...
18
votes
5answers
4k views

Applications of set theory in physics

In the introduction of the paper "Links between physics and set theory", the following quote of Eris Chric is stated: "Set theory perhaps is too important to be left just to ...
12
votes
0answers
173 views

Approximation of the effective resistance on Cayley graph

Let $\Gamma$ be a finitely generated group, and denote by $G$ the Cayley graph of $\Gamma$. Denote by $d_R$ the resistance distance metric on this graph. The resistance distance metric between the ...
4
votes
1answer
176 views

reference for higher spin - not gravitational nor stringy

Other than the papers of Berends, Burgers and van Dam, are there any papers that study the general case of deforming a free field theory with higher spin fields to be interactive?
35
votes
6answers
5k views

Companion to theoretical physics for working mathematicians

In the Princeton Companion to Mathematics one reads that even pure mathematicians should know some theoretical physics and applied mathematics. What are some well-organized comprehensive companions to ...
9
votes
2answers
585 views

What is the BRST-anti-BRST formalism?

What is the BRST-anti-BRST formalism? Is the Sp(2) doublet the ghost, antighost pair? Introductory accounts of this subject seem to be hard to find. I would appreciate a reference for someone who ...
5
votes
1answer
175 views

Interpretation for a condition in fluid dynamics

I have been working with some mathematical models in biology and fluid mechanics. My problem is about the interpretation of a condition that I found for a vector representing the velocity of a fluid. ...
32
votes
2answers
2k views

When exactly and why did matrix multiplication become a part of the undergraduate curriculum?

The story about Heisenberg inventing matrices and matrix multiplication in 1925 is very well known and well documented. A few weeks later, Born and Jordan read this work and recognized matrix ...
0
votes
1answer
131 views

A hyperbolic partial differential equation (wave-like) with variable-dependent coefficient and possibly singular in one variable

First, I beg your pardon since the title of the question is a bit confusing I guess. I'm working on a physical equation of the wave-like form. Explicitly, it reads $$\left[\left(\cos\phi\partial_{z}+\...
-2
votes
1answer
121 views

What are the formula of representation of quasicrystals and the law or mechanism of the formation [closed]

I vaguely recall that formula of representation of quasicrystals is relevant to tiling plane,and tiling plane without period is relevant to recursiveness, and do not know the mechanism or physics ...
4
votes
1answer
213 views

Sites for seeking possible collaborations [closed]

As a material scientist, I have recently constructed algorithms for solving ground state of arbitrary cluster interactions models and prepared publications in the field of physics and material science....
4
votes
2answers
559 views

Gauge-theoretic formulation of Maxwell equations [duplicate]

Does any one know how to write the Maxwell equations as an equation on a principal $U(1)$-bundle? In Freed & Uhlenbeck's Instantons and Four manifolds, the authors claim that the Maxwell ...
3
votes
1answer
555 views

Helmholtz equation Poynting vector integral

The Maxwell's equation for harmonic time dependent field in vacuum is \begin{align} \nabla \times B + i\omega E &= 0\\ \nabla \times E - i\omega B &= 0 \\ \nabla \cdot B &= 0 \\ \nabla \...
8
votes
5answers
2k views

Optical methods for number theory?

I found a paper: 'A New Method of Finding the Distribution of Prime Number', saying We stack discs and annuluses with certain rules then turn on the light to illuminate. The projection of ...
4
votes
2answers
960 views

Analytic solution of a system of linear, hyperbolic, first order, partial differential equations

In a try to solve a physical problem, I've faced a system of first-order partial differential equations of the form $$\cos\left(t\right)\partial_{x}\mathbf{u}+\sin\left(t\right)\partial_{y}\mathbf{u}+...
0
votes
0answers
117 views

Geometric interpretation of table with permutations and inversions

Let $T(n,k)$ is the number of permutations of numbers $1, ..., n$ and each of the permutations has $k$ inversions. We can consider a table for $T(n,k)$ for some $n$ and $k$. For eg. $n=1,...,6$, $k=1,....
2
votes
0answers
149 views
+50

Diffusion equation on mixing of diffusing particles

I am trying to study mixing of diffusing particles like it was done by E. Ben-Naim On the Mixing of Diffusing Particles. The picture below shows the idea how permutations and inversion numbers reflect ...