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2
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1answer
121 views

Can Minkowski spacetime be redefined as a non-flat riemannian manifold?

Minkowski space time is defined in terms of a flat pseudo-Riemannian manifold. I have wondered if it can be redefined as Riamannian manifold and in the case what type of curvature would there appear. ...
3
votes
3answers
166 views

The Dirac-Delta function as an initial state for the quantum free particle

I want to ask if it is reasonable that I use the Dirac-Delta function as an intial state ($\Psi (x,0) $) for the free particle wavefunction and interpret it such that I say that the particle is ...
1
vote
2answers
648 views

Inverted Harmonic oscillator

what are the energies of the inverted Harmonic oscillator? $$ H=p^{2}-\omega^{2}x^{2} $$ since the eigenfunctions of this operator do not belong to any $ L^{2}(R)$ space I believe that the spectrum ...
6
votes
0answers
95 views

What are the implications for the AdS/Cft program if AdS is unstable?

To my understanding recent progress in the study of the non linear stability of AdS spacetime suggest that $AdS$ might be unstable. If this is true, what are the physical and mathematical ...
2
votes
0answers
77 views

Interesting Hamiltonian System

The definition of a Hamiltonian system I am working with is a triple $(X,\omega, H)$ where $(X,\omega)$ is a symplectic manifold and $H\in C^\infty(X)$ is the Hamiltonian function. I am wondering if ...
4
votes
0answers
32 views

Solutions of nonlinear systems invariant wrt. perturbations (looking for applications)

I want to ask if the following purely mathematical problem (that I'm working on) might have some applications to physics. The problem in a nutshell: describe properties of solution sets of real ...
14
votes
2answers
502 views

How do physicists use solutions to the Yang-Baxter Equation?

As a mathematician working the area of representation of Quantum groups, I am constantly thinking about solutions of the Yang-Baxter equation. In particular, trigonometric solutions. Often research ...
0
votes
0answers
4 views

Verification of Fourier transformationn of Io-sinh function [migrated]

I try to match. What could not match $I_o-\sinh$ pair developed by Ben Logan, transform pair also published in The Practical Application of the Fourier Integral Campbell, George A .Sir J.F. Kaiser ...
2
votes
0answers
34 views

Does the order of variables matter for a quantum Lagrangian in the path integral formula for quantum mechanics? [duplicate]

For a single particle or field, I can't see how the path-integral formulation depends on the order of terms in the Lagrangian. It seems that you integrate the classical Lagrangian to get the action on ...
1
vote
0answers
606 views

Physicists: Why do mathematicians insist on doing mathematics in a vaccuum and how do you deal with it [closed]

I'm trying to learn the theory of wavelet transform, a concept which is supposedly filled with enormous physical intuition, diagrams, pictures, things with physical analogies...but after 30 pages of ...
3
votes
1answer
135 views

Research problems in application of Lie groups to differential equations

Are there any open problems in physics involving Lie groups and differential equations for a phd theses. Some applications are say, Noether's theorem in classical or quantum field theory. But I am ...
2
votes
0answers
33 views

How obtain conserved quantities in integrable models in accordance with Liouville's theorem, via Sklyanin Poisson algebra?

In classical integrable models, in the discrete case we have the Sklyanin algebra, $$\lbrace T_{a}(u),T_{b}(v)\rbrace =[r_{ab}(u,v),T_{a}(u)T_{b}(v)].$$ How to prove that the conserved quantities are ...
7
votes
2answers
99 views

What are the linear maps which preserve the time-like cone?

I'm looking at the set of time-like vectors: $\mathcal{T}_+ = \{ x \in \mathbb{R}^4 \mbox{ s.t. } x^T \eta x \geq 0 \:, x^0\geq 0\} $, where $\eta = \mbox{diag}(1, -1, -1, -1)$. I want to be able to ...
0
votes
0answers
15 views

3-dimensional quasicrystals

As is well known, quasicrystals (i.e. their diffraction patterns) show patterns which can be deciphered and understood via the use Penrose tilings (and aperiodic tilings of the plane in general). ...
6
votes
1answer
45 views

Is the subadditivity of quantum entropy valid in the infinite-dimensional case?

Does the subadditivity (and strong subadditivity) of quantum entropy hold for infinite dimensional quantum systems as well? Unfortunately the books in my hand give proof for finite dimensional cases ...
3
votes
1answer
117 views

Instantons in Witten's supersymmetry and Morse theory

I'm reading Witten's paper on supersymmetry and Morse theory and am confused about the details of the instanton calculation which he uses to define a Morse complex (beginning at page 11 of the pdf) . ...
7
votes
1answer
112 views

Recommendation on mathematical physics book of Symplectic geometry

I want to learn the applications of symplectic geometry in physics. Which mathematical physics textbook will have a detailed and heuristic explanation of this aspect?
1
vote
2answers
151 views

Can we describe mathematics using filters and matrices? [closed]

Can mathematical filters or ultrafilters be used to predict quantum physics 'events' as accurately as using matrices like Schrodinger did? Is there a way to explain some of the predictive power of ...
0
votes
1answer
77 views

About Hilbert and Physics [duplicate]

Was one of Hilbert questions regarding physics to make an axiomatic foundation for physics? Regardless of Godels work could some Physics principles that are 'basic' and 'presently verifiable' be ...
-3
votes
1answer
100 views

How to get funding for research on something that can revolutionize the quantum world! [closed]

I think this can revolutionize the quantum world! Any ideas on how to impress physicists to get a full fledged funding for research?
2
votes
1answer
70 views

Finding the stabilizer group given a state

Consider general pure state $|\psi\rangle$ in some hilbert space $\mathcal{H}$ (which could be a tensor product of other Hilbert spaces) I would like to know whether there is a way to ...
4
votes
2answers
68 views

2 entangled electrons in QFT

In field theory, by quantizing a dirac field, we can obtain a creation operator for a single electron of definite momentum, of definite spin up or down, these respectively are: ...
17
votes
1answer
1k views

Why is there a deep mysterious relation between string theory and number theory, elliptic curves, $E_8$ and the Monster group?

Why is there a deep mysterious relation between string theory and number theory (Langlands program), elliptic curves, modular functions, the exceptional group $E_8$, and the Monster group as in ...
3
votes
0answers
79 views

Recent missed opportunities à la Freeman Dyson

There is an excellent paper by Freeman Dyson from 1972 (here) and therein the author cites old talks by Hilbert (here) and Minkowski (chapter 2 here) speaking about similar topics, namely how ...
0
votes
1answer
38 views

(Level: Undergrad) Continuity Conditions on the Wavefunction and Initial Values

I know that a physically meaningful $\Psi$ needs to be continuous. However, recently I came across a problem in which they were considering a wavefunction for the infinite square well potential and ...
1
vote
1answer
90 views

A Spin up particle in QFT

This appears like a question that is rarely addressed in field theory pedagogy (perhaps because the answer is obvious): how does one describe a particle of definite spin in quantum field theory? For ...
2
votes
1answer
63 views

What are the proper domains of the position and squared angular momentum operator?

I am looking at the position operator on a compact set $K \subset \mathbb{R}^n$ and the squared angular momentum operator (so essentially the Laplace-Beltrami operator where I just look at the angular ...
2
votes
2answers
127 views

A rigorous treatment of distributions in quantum mechanics

In many introductory courses to quantum mechanics, we see $\delta$-functions all over the place. For example when expressing an arbitrary wave function $\psi(x)$ in the basis of eigenfunctions of the ...
3
votes
1answer
67 views

Justification of discrete spectrum for V(x) unbounded at $\pm \infty$ in Pauling and Wilson

In Pauling and Wilson, Introduction to Quantum Mechanics, they offer the following intuitive reason for the discrete spectrum of a potential which is unbounded at $\pm \infty$: This is ...
1
vote
1answer
113 views

Subtlety in derivation of Noether's theorem by Di Francesco

In the book 'Conformal Field Theory' by Di Francesco et al, a derivation of Noether's theorem is demonstrated by imposing that, what I believe is said to be a more elegant approach, the parameter ...
1
vote
0answers
53 views

Are there any known (closed form even if approximate) solutions to problems in relativistic elasticity?

There are several useful known solutions to the EFE with relatively simple / trivial stress-energy-momentum tensor, such as the Schwarzschild solution. Despite the idealizations made therein they are ...
6
votes
3answers
311 views

Basis in quantum mechanics

My quantum mechanics textbook (Primer of Quantum Mechanics, by Marvin Chester) says that both the momentum space and the position space are basis spaces. It also says that the momentum space is ...
3
votes
1answer
301 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?
0
votes
2answers
63 views

Eigenstates of an observable

Can we use eigenstates of ANY observable as base of the Hilbert space? If we can, is this equal to the statement that those eigenstates are orthogonal to each other and normalizable?
3
votes
1answer
195 views

Explanation of Dirac's proof of arbitrary ket being expressible with eigenkets of observable

In P.A.M. Dirac's The Principles of Quantum Mechanics, Chapter 10 (Observables), pp. 40, at the end of the chapter there is a proof that I don't understand at all. Here is a pdf link to the book ...
5
votes
1answer
78 views

Is there a physical interpretation to invariant random matrix ensembles?

Disclaimer. I am a graduate student in pure mathematics, so my knowledge of physics more advanced than basic 1st/2nd year undergraduate physics is very limited. I welcome corrections on any ...
8
votes
1answer
248 views

7 sphere, is there any physical interpretation of exotic spheres?

Basically an exotic sphere is topologically a sphere, but doesn't look like a one. Or more accurately: homeomorphic but not diffeomorphic to the standard Euclidean n-sphere The first exotic ...
1
vote
1answer
69 views

Darboux theorem and the canonical decomposition of a two-fermion wave function

It is a classical theorem in quantum mechanics or quantum chemistry or quantum information that a two-fermion wave function has a beautiful canonical expansion: $$f(x_1, x_2) = \sum_{j=1}^N ...
4
votes
3answers
94 views

Analytical problems with Green's function

I have a question about the right definition of the Green's function in physics. Why do we introduce (or not) an infinitesimal, positive number $\eta$ to the following definition: $$\left[ ...
1
vote
0answers
78 views

Most useful maths for theoretical and mathematical physics [closed]

I am going to apply for a programme of mathematical and theoretical physics for graduate studies and I'm currently studying maths. What is a good area to do a thesis (that is to say, considerable ...
1
vote
0answers
51 views

Serious advice/ plan for getting into Physics/Math Grad schools of choice [closed]

I am currently studying a Bachelor of Technology in the subject "Food Technology". I have completed 2 years just now.Yes, I have been exposed to Mathematics in my first year of college studying ...
4
votes
1answer
262 views

Tangent bundles and $\mathbb{C}P^n$ and $\mathbb{C}^n$

As discussed here the complex projective space $\mathbb{C}P^n$ is the set of all lines on $\mathbb{C}^n$ passing through the origin. It would seem natural to assume that any $\mathbb{C}P^n$ can be ...
1
vote
0answers
84 views

mathematician or physicists [closed]

Mathematicians consider physicists as people who simply use mathematics as a tool but are in a way, let's say, inaccurate, as physicists tend to make assumptions a lot in their mathematics and ...
6
votes
1answer
158 views

Does Feynman path integral include discontinuous trajectories?

While reading this derivation of relation of Schrödinger equation to Feynman path integral, I noticed that $q_i$ can differ form $q_{i+1}$ very much, and when the limit of $N\to\infty$ is taken, there ...
7
votes
2answers
181 views

How should I throttle my rocket to reach highest altitude? [closed]

"Real world" problem. Suppose we want to launch a rocket equipped with an engine which can be throttled as we prefer. Suppose also that the amount of fuel burnt per time is directly proportional ...
5
votes
3answers
149 views

Global vs. local gauge group in mathematical sense - physics examples?

Upon reading about the principal bundle picture of (quantum) field theory I encountered two different definitions of the gauge group: Local gauge group $G$. Corresponds to the fibers of the ...
3
votes
0answers
38 views

How coordinate system shifting is related to similarity transformations?

I know that coordinate system shifting can be represented using matrices. But how exactly are similarity transformations related to coordinate shifts ?
2
votes
0answers
33 views

How to prove that the ground state of the Hubbard model is not a Slater determinant?

Of course it is expected. But how to prove it analytically? Slater determinant is mentioned in almost every quantum mechanics textbook. But it is necessary to warn the undergraduate students that not ...
7
votes
0answers
266 views

Noether currents for the BRST tranformation of Yang-Mills fields

The Lagrangian of the Yang-Mills fields is given by $$ \mathcal{L}=-\frac{1}{4}(F^a_{\mu\nu})^2+\bar{\psi}(i\gamma^{\mu} D_{\mu}-m)\psi-\frac{1}{2\xi}(\partial\cdot A^a)^2+ ...
7
votes
0answers
106 views

Role of physics in the zeta function $\zeta$ and the Riemann hypothesis

Hilbert and Polya suggested a physical way to verify the Riemann hypotesis about $\zeta(x)$. If the Riemann hypotesis is true, we can state all eigenvalues of physical problems are real. What is the ...