Questions tagged [mathematical-physics]

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 mathematical methods to problems in physics. Examples include partial differential equations (PDEs), variational calculus, functional analysis, and potential theory.

Filter by
Sorted by
Tagged with
0
votes
0answers
14 views

Which non-homogeneous scalar manifolds are possible in supergravity?

The scalar fields in various supergravity theories are restricted (by supersymmetry) to span the target (scalar) manifolds of a certain class (e.g. Hodge-Kahler, quaternion-Kahler etc.), depending on ...
1
vote
0answers
19 views

Hypersurface Orthogonality of Conformal Killing field on Conformal Killing Horizon

Suppose we have a spacetime manifold $(\mathcal{M},g)$ admitting a conformal Killing Horizon $\mathcal{H}_c$ generated by a conformal Killing field $\chi^a$ (which is null only on the conformal ...
1
vote
1answer
62 views

Why to introduce spinor fields we need this map in the definition of a spin structure?

Let me start with what I currently understand. Let ${\rm SO}(1,3)$ be the proper ortochronous Lorentz group. Its universal cover is ${\rm SL}(2,\mathbb{C})$. The representations of its universal cover ...
2
votes
1answer
42 views

Degree of a multilinear product in string field theory

I am going through the paper $L_{\infty}\textit{ Algebras and Field Theory, O. Hohm and B. Zwiebach (2017) }$ (https://arxiv.org/abs/1701.08824) and I cannot for the life of me figure out how and why ...
1
vote
1answer
51 views

Is it enough to give a time-orientation to define a spin structure?

Maybe I got it wrong and my question doesn't make sense, excuse me if that's the case. For a smooth Lorentz 4-manifold $(M, g)$ with signature $(- + + +)$ is it enough to give a time-orientation to ...
5
votes
3answers
295 views

Is the Dirac $\delta$-function necessarily symmetric?

The Dirac $\delta$-function is defined as a distribution that satisfies these constraints: $$ \delta (x-x') = 0 \quad\text{if}\quad x \neq x' \quad\quad\text{and}\quad\quad \delta (x-x') = \infty \...
3
votes
0answers
64 views

Mathematical description of systems of reference - classical mechanics vs special relativity

Notation: In the following, $E^n$ denotes an euclidean space of dimension $n$ (an affine space with inner product $\langle\,\cdot\,,\,\cdot\,\rangle$ on the translation space). The answer to this ...
0
votes
0answers
27 views

Integral of the product of 4 spherical harmonics

Recently, I saw a closed formula for the integral of the product of three spherical harmonics in two dimensions here Integral of the product of three spherical harmonics and I was wondering if someone ...
0
votes
1answer
15 views

Average torque on a Projectile of mass $m$ with initial speed $u$ and angle of projection $θ$ between initial ($P$) and final ($Q$) positions is [closed]

Question is as follows: Average torque on a Projectile of mass $m$ with initial speed $u$ and angle of projection $θ$ between initial $(P)$ and final $(Q)$ positions is I researched a lot but wherever ...
5
votes
1answer
164 views

Proving that the diffusion equation is not time-reversible

The diffusion equation (in appropriate units) is $$ \frac{\partial\rho}{\partial t}(\mathbf r,t)=\nabla^2\rho(\mathbf r,t). $$ By time-reversibility, I mean that there exists a function (bijection?) $...
-6
votes
1answer
58 views

Basic Slope-Intercept Form y=mx+b [closed]

The equation for a line forms a part of my physics work. The equation is: Y = mx+b To refresh myself, I watched the following video on the formula. However, at 3:15 I went off in the wrong direction ...
1
vote
0answers
42 views

Continuous Valued POVMs

I'm thinking about the mathematical details of continuous variable QM, namely the infinite $|x\rangle$ and $|p\rangle$ bases. Is it possible (and should we) think of these bases and their measurements ...
10
votes
1answer
283 views

Is it possible to bound a single $0$-brane to a $4$-brane?

I'm studying the Jafferis solution for twisted $N=4$ Yang-Mills theory in four dimensions from the paper Crystals and intersecting branes. Consider the problem of computing the charges of the allowed ...
0
votes
0answers
27 views

What is the mathematical justification for introducing the surface traction/stress tensor in the derivation of the momentum balance?

In fluid dynamics and continuum mechanics it is common to derive the the momentum balance by the following argument: For some open domain $V$, use the Reynolds Transport Theorem to show: $$\frac{d\...
1
vote
1answer
49 views

What is the domain of momentum operator on $\mathbb{R}$?

Observables in QM are postulated to be self-adjoint operators. Those have to obey $\hat A \vphantom{A}^+ \! = \hat A$, including the equality of their domains. If we work on a finite interval $(a, b)$,...
3
votes
0answers
51 views

Partition function $\mathrm{tr} e^{-\beta H}$ for non-trace-class operator

For Hamiltonian $H$, the partition function is defined as $$Z=\mathrm{tr} e^{-\beta H}.$$ However, consider a free particle $H = -\Delta$ in $\mathbb R^1$. In this case, the operator $e^{-\beta H}$ is ...
5
votes
5answers
376 views

How are vector quantities in three dimensions (velocity, electric field, etc.) modeled in mathematical physics?

In introductory courses, vectors are defined as objects with direction and magnitude. I guess everyone has arrows in mind when talking about vectors and that's probably the most intuitive description, ...
37
votes
3answers
3k views

Do all Noether theorems have a common mathematical structure?

I know that there are Noether theorems in classical mechanics, electrodynamics, quantum mechanics and even quantum field theory and since this are theories with different underlying formalisms, if was ...
2
votes
0answers
29 views

Does microcausality plus the time-slice property imply local primitive causality?

In quantum field theory, observables are associated with regions of spacetime. One of the basic principles of relativistic quantum field theory is microcausality, which says that observables ...
3
votes
1answer
94 views

Axiomatic Quantum Theory

Is there any practical advantage/disadvantage between using the axioms for the Hilbert Space formulation as opposed to the C* Algebra formulation of Quantum Theory? If not, then is it possible to ...
7
votes
1answer
420 views

Spectral decomposition vs Taylor Expansion

This question and the comments and answers it received encouraged me to ask this question, although I know that there will be some people who think that this belongs in the math forum. But I think ...
1
vote
0answers
89 views

How to know if a spinor $\Psi\left(x\right)$ is the ground state of the system?

Suppose we have time independent one-dimensional single particle Schrödinger-like equation$$-\frac{d}{dx}\left(A\left(x\right)\frac{d}{dx}\psi\left(x\right)\right)+V\left(x\right)\psi\left(x\right)=E\...
2
votes
1answer
63 views

Spacetimes with “celestial Riemann surface” other than the sphere

In the standard study of asymptotically flat spacetimes one defines null infinity demanding that topologically ${\cal I}^\pm \simeq \mathbb{R}\times S^2$ (c.f. Definition 1 of this review by Ashtekar)....
0
votes
1answer
38 views

How to handle a delta-function divergence from an infinite-dimensional trace of a quantum operator with a general continuous parameter?

Say I am working in the standard Schrödinger-style Hilbert space that corresponds to square-integrable functions on 3-space. Some normal operator $\hat{A}$ therefore has an eigenbasis indexed by 3 ...
2
votes
0answers
54 views

What is the Weyl algebra?

I have a question about Weyl algebras. It arose reading this (page 30) and this (page 11), but I think the physical context is not very important, so I can summarize here what they say. They consider ...
1
vote
1answer
60 views

Shadow method of solving differential equations

While reading this answer by Rishab Navneet here, it is shown how we can visualize the harmonic oscillator as the shadow of a body moving in a circle onto a line. How was it found that the plane curve ...
1
vote
0answers
68 views

Another Solution To Brachistochrone Problem

Recalling the statement of the problem : Given two points A and B in a vertical plane, what is the curve traced out by a point acted on only by gravity, which starts at A and reaches B in the ...
0
votes
0answers
30 views

How possible is using complex variables to model the electric field system of a dipole? [duplicate]

If one considera a dipole system, is it possible to model the system using complex variables and if ao, how can we use complex analysis to model it? I have the idea that we can model dipole moment as ...
2
votes
1answer
84 views

On the number of spacetime atoms in a Calabi-Yau crystal

This question is about an application of crystallography to topological string theory. Plane partitions are discrete models of the Planck scale geometry of Calabi-Yau manifolds in the A-model ...
2
votes
1answer
55 views

Chemical potentials for $D$-brane bound states

This question is about a mathematical subtlety arising in the computation of the partition function of a supersymmetric ensemble of some lower dimensional $D$-branes attached to a stack of higher ...
7
votes
4answers
1k views

Is continuity of the wavefunction “put in by hand” for the Dirac delta potentials?

In 1d, for $V(x) = g\delta(x)$, integrating the TISE yields (assuming that $\psi$ is bounded$^\dagger$, so as to suppress the term containing $E$) $$ -\frac{\hbar^2}{2m} \left( \psi'(\varepsilon) - \...
2
votes
0answers
90 views

Is there a more theoretical approach to studying physics? [closed]

I have read some physics papers in theoretical particle physics and all of them were based on computation, they had some mile long equations and the result was always the proof of some formula. I am ...
1
vote
1answer
57 views

There can be degeneracy in 1D energy eigenfunctions even if one of them and its derivative does to zero as $x\to\infty$?

In 1D, the energy eigenvalue equation for an energy value $E$ $$ -\frac{\hbar^2}{2m}\psi''(x) + V(x)\psi(x) = E\psi(x) $$ can have at most two linearly independent solutions, $\psi_1$ and $\psi_2$, ...
0
votes
0answers
21 views

Do the free particle energy eigenfunctions satisfy the closure relation?

The energy eigenfunction of the free particle ($V(x)=0$) are given by $\psi_{E, \pm}=A(E)e^{\pm ik_Ex}$ where $A(E)=\left( m/\left(8\pi^2\hbar^2 E\right) \right)$ and $k_E=\sqrt{2mE}/\hbar$ for each $...
-5
votes
1answer
63 views

Trying to understand how to connect the most general concept of a function to real world? [closed]

I'm a beginner wrapping my head around how general a definition a "function" really is when connected to the real world, please help. I am trying to connect the mathematical definition of a ...
1
vote
0answers
36 views

Is there a systematic way to construct a SUSY theory?

For the sake of simplicity, I am considering a 0+0d scalar field theory with multiple bosonic and fermionic fields/variables. The fields are coupled together up to a certain order (say 4) with ...
0
votes
0answers
29 views

Why is $f\in C_{\infty}=\{f\in C(\mathbb{R})\mid \lim_{R\to\infty} \sup_{∣∣x∣∣>R} ∣f(x)∣=0\}$ [duplicate]

Today in my mathematical quantum theory lecture our professor told us without any explanation, that if $f\in L^1(\mathbb{R}) \cap C^1(\mathbb{R})$ and $f'\in L^1(\mathbb{R})$ it follows that $f\in C_{\...
3
votes
1answer
139 views

References on mathematical stacks for a string theory student

This question was posted on mathoverflow (here) without too much success. I'm hoping to read the famous Kapustin-Witten Paper "Electric-magnetic duality and the geometric Langlands program" ...
4
votes
1answer
102 views

Number of bras and kets

My quantum mechanics teacher told us during the class that there were many more "bra" than "kets", but I confess that I don't quite understand this. Indeed, in quantum mechanics, ...
1
vote
0answers
43 views

$f\in L^1(\mathbb{R}) \cap C^1(\mathbb{R})$ and $f'\in L^1(\mathbb{R})$ [closed]

Today in my mathematical quantum theory lecture our professor told us without any explanation, that if $f\in L^1(\mathbb{R}) \cap C^1(\mathbb{R})$ and $f'\in L^1(\mathbb{R})$ it follows that $f\in C_{\...
0
votes
0answers
39 views

What does the Hausdorff-Young inequality tell us?

The Hausdorff-Young Inequality relates the size of a function and its Fourier coefficients. What is meant the by "the size of a function"?
0
votes
0answers
35 views

On Goldstone fermions / goldstino: SUSY breaking

There are statements about Goldstone fermions, or goldstino, seem confusing to me. (1) Goldstone boson requires a continuous symmetry spontaneously broken. Does Goldstone fermion imply continuous SUSY ...
1
vote
0answers
47 views

Polarization procedure in geometric quantization

The geometric quantization can be considered as an approach the formalize the way of associating a quantum theory corresponding to a given classical theory. Suppose we start with a sympetic manifold $(...
0
votes
2answers
37 views

Orthogonality of two randomly chosen velocity vectors in the kinetic theory of gas and the relative velocity

I was looking for the average value of the relative velocity of ideal gas molecules in the kinetic theory. The following is from this article. The vector notation is not mathematically rigorous, just ...
1
vote
1answer
56 views

Dirac delta equalities in physics

Earlier I asked this question on the Math Exchange but I'm looking for a physics point of view. How do you interpret an equation like $$x^n \delta(x) = 0, \qquad n\in \mathbb{N},$$ around $x=0$? Why ...
2
votes
2answers
91 views

Confusion about the dimension of a Hilbert Space in Quantum Mechanics [duplicate]

In Quantum Mechanics, the quantum state of the physical system lives in an infinite-dimensional Hilbert space and can be written in terms of two different bases, the position basis (uncountably ...
3
votes
0answers
51 views

Convergence of $c^* Ac$ in second quantization

Let $A$ denote a bounded operator on a complex separable Hilbert space $\mathscr{H}$. Let $\mathscr{F} = \bigoplus \mathscr{F}_N$ be the Fock space generated by $\mathscr{H}$ where $\mathscr{F}_N$ is ...
0
votes
1answer
47 views

What equation should I use if I am estimating the distance of a rocket's landing point to the point it was launched from?

I am trying to figure out how to estimate how far (in meters) that a solid fuel model rocket will land from its launching point. To do this, I have figured out I will need to estimate the maximum ...
1
vote
1answer
40 views

Superalgebra and BRST supersymmetry 2: why Lie algebra and groups?

This follows a comment to split to a 2nd question Superalgebra and BRST supersymmetry 1: odd vs even It is said that most of theories, the even elements of the superalgebra correspond to bosons and ...
1
vote
1answer
49 views

Superalgebra and BRST supersymmetry 1: odd vs even

It is said that most of theories, the even elements of the superalgebra correspond to bosons and odd elements to fermions (but this is not always true; for example, the BRST supersymmetry is the other ...

1
2 3 4 5
40