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 Mathematical physics is the mathematically rigorous study of the foundations of physics, and the application of advanced ...

learn more… | top users | synonyms

0
votes
0answers
30 views

Can anybody recommend a book on quantum physics for a mathematically minded student? [duplicate]

Basically what the title says. I'm a math/physics double major going into my second year, but I'm much more math oriented. I'll be taking a quantum class in the fall and I'd like a book that ...
0
votes
0answers
46 views

Quantized Banach Spaces

Reading the paper here, it mentions on the very first page that "The requirement of 'closed'-ness is imposed because we want to think of operator spaces as 'quantized (or non-commutative) Banach ...
0
votes
0answers
45 views

Regarding Ampere's Circuital Law

If I am to show that Ampere's Circuital law holds true for any arbitrary closed loop in a plane normal to the straight wire, with its validity already established for the closed loop being a circle of ...
5
votes
1answer
957 views

Representation of operators in quantum mechanics

For which systems we represent the Hamiltonian as a differential operator and for which system we represent it by a matrix? Can the momentum be represented by a matrix operator?
7
votes
2answers
616 views

Vector Potential for Magnetic field when the field is not in simply-connected region

According to Poincare's Lemma, if $U\subset \mathbb{R}^n$ is a star-shaped set and if $\omega$ is a $k$-form defined in $U$ that is closed, then $\omega$ is exact, meaning that there's some ...
5
votes
1answer
103 views

Physical implications of the Gibbs phenomenon for Quantum Mechanics

From Wikipedia: The Gibbs Phenomenon is the peculiar manner in which the Fourier series of a piecewise continuously differentiable periodic function behaves at a jump discontinuity. The nth ...
0
votes
1answer
82 views

Field theory in four dimensions

I was reading Schwartz's book on QFT. In chapter 14.5 at p.267, while speaking about path integral he says: [...] the path integral (and field theories more generally) is only known to exist (i.e. ...
5
votes
0answers
112 views

Gauge potential for locomotion at low Reynolds number

I've been studying some approaches with gauge theory to some problems in Mechanics and I've found the problem of self propulsion at low Reynolds number a quite complicated one. The approach I'm asking ...
5
votes
3answers
334 views

Is there a natural (suitable) definition for functional derivative in Curved space time

If $$\delta S = \int \sqrt g F[\phi] \delta \phi\tag{1}$$ Then is it natural to define the functional derivative as follows, $$\frac{\delta S}{\delta \phi} = F[\phi].\tag{2}$$ In particular does ...
4
votes
1answer
72 views

Constructing differential equation from arbitrary Hamiltonian

Suppose I begin with the time-independent Schrodinger equation $$ \left(-\frac{1}{2m}\partial_x^2 + V(x)\right)\psi_n(x) = E_n\psi_n(x), $$ ordinarily we specify the function $V$ and then solve for a ...
3
votes
2answers
54 views

Necessary and sufficient conditions for a function to be the Wigner function of state

For any quantum state defined with a continuous position, the Wigner function is a quasiprobability distribution on phase space. It has many properties, such as that its marginal are probability ...
1
vote
0answers
15 views

Creating an arbitrary state of the quantum simple harmonic oscillator [duplicate]

Suppose $\mathcal{B}=\{\lvert 0\rangle, \lvert 1\rangle, \lvert 2\rangle, ... \}$ is the energy eigen-basis of a quantum simple harmonic oscillator. I want to create the state \begin{equation} ...
12
votes
4answers
963 views

What happened with Hilbert's sixth problem (the axiomatization of physics) after Gödel's work?

I'll write the question but I'm not fully confident of the premises I'm making here. I'm sorry if my proposal is too silly. Hilbert's sixth problem consisted roughly about finding axioms for physics ...
0
votes
0answers
35 views

How to calculate the eigenenergies of a particle in a triangular billiard?

Suppose we take the Dirichlet boundary condition, namely the wave function must vanish on the boundary. How about a general n-polygon?
0
votes
0answers
50 views

How to solve Laplace equation in a domain with one boundary along a curve?

Is there a way to solve the 2D Laplace equation $\frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} =0$ on $0 <x<\infty$ and $0 < y < \infty$, such that the domain is ...
10
votes
5answers
491 views

Motivation for tensor product in Physics

This question is about a mathematical object (the tensor product) but thinking about the motivation that comes from Physics. Algebraists motivate the tensor product like that: "given $k$ vector spaces ...
3
votes
2answers
140 views

Consequences of compactness in physics

If we understand spacetime as a $4$-dimensional manifold $M$, from the point of view of physics what are the consquences of a subset of it being compact? My point here is simple: in math we usually ...
5
votes
1answer
231 views

Symplectic leaves, tori and Poisson manifolds

For classical systems we can define a configuration manifold, whose cotangent bundle is a momentum phase space equipped with a closed, non-degenerate 2-form. Upon the commutative algebra of smooth ...
0
votes
0answers
29 views

Integral of absolute value of spin angular momentum of $N$-body system

There are $N$ particles moving freely in a plane. Let $J(t)$ be the spin angular momentum of the system of particles about its center of mass. (even center of mass keeps changing with time as ...
2
votes
1answer
100 views

Learning physics from a strong math background? [closed]

I have a master's degree in operations research and took several PhD level math courses. In particular I'm most familiar with analysis/measure theory, probability theory, and stochastic processes, and ...
2
votes
1answer
61 views

Distributional Extension of a Hilbert Space

This question comes from the Complexification section of Thomas Thiemann's Modern Canonical Quantum General Relativity, but I believe it just deals with the foundations of quantum mechanics. The ...
0
votes
0answers
38 views

Energy Oscillations in a One Dimensional Crystal?

Can anyone help me find articles on similar topics "Energy Oscillations in a One Dimensional Crystal" (I have links to one article on this subject)? article, that I have Especially interested in ...
5
votes
2answers
533 views

Teach me Wick's theorem the honest way

Generally speaking the average guy marginally acquainted with quantum field theory or advanced combinatorics describes Wick's theorem as some sort of correspondence between higher order differential ...
13
votes
3answers
746 views

$\mathrm{SU(3)}$ decomposition of $\mathbf{3} \otimes \mathbf{\bar{3}} = \mathbf{8} \oplus \mathbf{1}$?

I have a question about the tensor decomposition of $\mathrm{SU(3)}$. According to Georgi (page 142 and 143), a tensor $T^i{}_j$ decomposes as: \begin{equation} \mathbf{3} \otimes \mathbf{\bar{3}} = ...
3
votes
2answers
75 views

Commuting observables and CSCO's

I've been looking at some basic quantum mechanics all day in an attempt to better my understanding of the subject. While going over the proof that commuting operators are compatible, I started getting ...
4
votes
2answers
74 views

Amplitude-phase decomposition as a canonical transformation

I am studying a classical dynamical system defined on $\mathbb{CP}^2$: the phase space is parametrized in terms of three complex coordinates $\psi_i$ ($i=1,2,3$) and Hamilton's equations of motion ...
19
votes
0answers
508 views

Can Lee-Yang zeros theorem account for triple point phase transition?

Now the prominent Lee-Yang theorem (or Physical Review 87, 410, 1952) has almost become a standard ingredient of any comprehensive statistical mechanics textbook. If the volume tends to infinity, ...
1
vote
1answer
75 views

Relationship between those two “exponentials”

Let $G$ be a Lie group and $L(G)$ it's Lie algebra. We know that every left-invariant vector field $X$ in $G$ is complete, and so one can consider the integral curve defined for all $t\in \mathbb{R}$ ...
7
votes
2answers
270 views

Motivation to introduce von Neumann algebras in addition to $C^*$algebras?

Observables are self-adjoint elements of a $C^*$algebra. As such, this structure seems sufficient to describe physics. A theorem by Gelfand and Naimark says that a $C^*$algebra can always be ...
2
votes
1answer
57 views

Origin of integral of field strength tensor in path-ordered exponential in gauge field theory

When studying some gauge theories approach to problems in Mechanics, I've found the following integral $$P\exp\left[\oint A \ dt\right]=1+\dfrac{1}{2}\oint_{\partial ...
6
votes
0answers
122 views

Monstrous Moonshine outside of String Theory

My question concerns applications of monstrous moonshine, which is the connection between the $j$-function and the monster group. Recently, physicists have applied it to string theory and, ultimately, ...
0
votes
1answer
50 views

Can binary sequences generated from ergodic maps be chaotic?

Chaotic Sequences of IID Binary Random variables with their applications to Communications and related papers by the same author, Tohru Kohda, talk about the statistical properties of binary symbolic ...
1
vote
0answers
37 views

Theory of chaotic systems : Bijective mapping

Considering a one-dimensional chaotic map $T$. The domain of the map (the closed interval $[0,\,1]=I_1 \cup I_1$) is partitioned into two regions (i.e. $I_0\cap I_1=\emptyset$): $[0,\,A] = I_0$ and ...
1
vote
0answers
38 views

mathematical Physics + fluid mechanics, thermodynamics + mass transfer? beginner [closed]

I am completely new to the world of physics and am interested in learning the aforementioned topics. I have previously studied biochemistry, but am fascinated by physics and am interested in ...
2
votes
1answer
59 views

A boundary term for a Bessel Function?

I am reading 't Hooft lectures on black holes and on p. 35, it is stated, that it is not difficult to show that $$ K^*(\omega,a)=\int_0^{\infty} \frac{ds}{s} e^{-i\omega \ln{s} + ia(s-\frac{1}{s})} = ...
3
votes
3answers
68 views

Uniqueness of expression of a Lie group element

Just take the SU(2) group as an example. The three generators are $J_z$, $J_+$, and $J_-$. For an element $ g $, sometimes we want to express it as $$ g = e^{i a J_+} e^{i b J_z} e^{i c J_-} . $$ ...
5
votes
1answer
140 views

Does regularity of distributions have anything to do with definiteness of their product?

Recently I've gone through some literature concerning causal perturbation theory (CPT). As is well known, it deals with UV divergences in QFT by defining products of (operator-valued) distributions ...
0
votes
1answer
75 views

I want to solve Mathieu Equation $y''(x)+(a−2q \cos(2x))y(x)=0$. How to solve it using Floquet solution?

I want to solve Mathieu Equation $$y''(x)+(a−2q \cos(2x)) \, y(x)=0.$$ How to solve it using Floquet solution? In Floquet solution for integer order of $v$ and $π$ periodicity We have Solution ...
3
votes
1answer
46 views

Complex scaling method for solving resonance states

I am now reading about the complex scaling method for solving resonance states. As far as I understand, the procedure goes like this: Let us take the 1d potential $V(x) = A e^{-x^2} x^2 $ as an ...
0
votes
0answers
58 views

Transition Amplitude vs. Transition Probability

In quantum mechanics, a physical system corresponds to a Hilbert space $\mathscr{H}$. States correspond (not in a one-to-one way) to points in $\mathscr{H}$ and the physical postulate is that the ...
6
votes
2answers
174 views

What type of non-differentiable continuous paths contribute for the path integral in quantum mechanics

Consider the path integral for a 1D particle subjected to a potential $V(x)$ in imaginary time $$ \int_{x(0)=x_0}^{x(T)=x_T} [dx] \, e^{- \int_0^T d\tau \left[\frac{1}{2}\dot{x}^2 + ...
3
votes
1answer
73 views

Rigorous definition of superselection sector/quasiparticle type in anyon systems

The systems I have in mind are for example Kitaev's toric code model (arXiv:quant-ph/9707021) and Kitaev's honeycomb model (arXiv:cond-mat/0506438). What I'm looking for is a mathematically rigorous ...
1
vote
2answers
35 views

A binary operator required for observing whether the particle is present in a given spatial region

Consider the wave function $\psi(x)$, I want to define an experiment using quantum mechanical rules. The experiment is to find whether the particle is in the region of space (a,b). The observable is ...
0
votes
0answers
145 views

Flow rate Calculation with Pipe Diameter and pressure?

I am using a constant Diameter pipe from a motor to a machine for oil flow.A pressure trasmitter is kept near the machine to know the pressure.So can we calculate the Flow rate using the parameters ...
1
vote
0answers
52 views

Is it possible to express continuous growth without using transcendental numbers? [closed]

Continuous growth is typically expressed using some variant on $A = Pe^{rt}$, I understand where $e$ comes from in general, it is the amount something grows in a given time interval, when continuously ...
1
vote
0answers
31 views
4
votes
1answer
109 views

How does one express a Lagrangian and Action in the language of forms?

In Lipschitzs Classical Mechanics a Lagrangian is defined as: $L(q,q',t)$ for some trajectory $q(t)$ of a particle And the action is defined as: $S:=\int^a_b L(q,q',t) dt$ How does one ...
31
votes
0answers
1k views

Linear sigma models and integrable systems

I'm a mathematician who recently became very interested in questions related to mathematical physics but somehow, I already have difficulties in penetrating the literature... I'd highly appreciate any ...
3
votes
1answer
82 views

What really are perturbation expansions?

I'm unsure if this question belongs here or at Math.SE, but since I've got to it by reading some articles about Physics I'm going to post it here anyway. In this particular article (Theoretical ...
0
votes
0answers
56 views

Does model theory in mathematics have any usefulness in the modeling of physical systems?

The term Model Theory in mathematics seems to have a somewhat precise definition here. Reading through that reference you'll largely see discussions strictly relating to mathematical concepts, but one ...