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95 views

A strange audio phenomenon, could there be a physical interpretation to it?

http://mathoverflow.net/q/165038/14414 Motivation : Here is a motivation as to why this problem is so important. Let $f(t)$ be an audio signal. We can safely asume it to be bandlimited to 0-20kHz as ...
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0answers
55 views

product solutions for PDEs, physical motivation

Given a boundary value problem with independent variables $x_1,x_2, \dots , x_n$ and a PDE say $U(x_i, y, \partial_j y,\partial_{ij} y, \dots )=0$ we typically begin constructing a general solution by ...
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1answer
48 views

Do eigenvalues in a cylindrical symmetric problem tell us anything about the Fourier spectrum?

During a lecture we were solving the Helmholtz equation for particular boundary conditions, corresponding to different shapes of an oscillating drum, as in the famous Mark Kac's problem ...
6
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2answers
141 views

Coadjoint orbits in physics

I am looking for some application of coadjoint orbits in physics. If you know some of them please let me know.
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3answers
169 views

TQFT associates a category to a manifold

Any 3d TQFT (topological-quantum-field-theory) associates a number to a closed oriented 3-manifold, a vector space to a Riemann surface, a category to a circle, and a 2-category to a point. This ...
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0answers
62 views

Reference for stochastic processes which helps moving from a basic level to a measure theory one

I'm looking for a reference (books, notes, lectures) which helps a physicist to understand the language of measure theory in the context of stochastic processes (in particular markov chains). I've ...
10
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1answer
97 views

Triality and charge

I have a few questions about triality for the representations of $SU(3)$. (I have seen the wikipedia page, but it does not make the connection with physics.) What is triality, how can you compute ...
6
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2answers
100 views

Yang-Mills existence and mass gap

In the Clay institute problem description of the Yang-Mills existence and mass gap problem it states that the quantum Yang Mills needs to be formulated in $\mathbb{R}^4$ space. I was wondering whether ...
7
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1answer
71 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?
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0answers
56 views

Topology-dependent groud state degeneracy of $B \wedge F + B \wedge B$ and $B \wedge F + B \wedge B \wedge B$

There are some examples of topological BF theory with extra terms allow it still being topological. See this Ref. paper In 4d (3+1D), we have the trace of: $$ \int\frac{k}{2\pi}\text{Tr}[B \wedge F + ...
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1answer
138 views

Reducibility of tensor products of Lorentz group representations

Consider the statement: (34.29 in Srednicki's QFT text) $$\tag{34.29} (2,1)\otimes(1,2)\otimes(2,2)~=~(1,1)\oplus\ldots$$ Where of course, $(a,b)$ label representations of Lorentz group in the usual ...
3
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1answer
98 views

How to construct an isomorphism between the Complexified Special Linear Lie Group and the Special Unitary Group?

This may be an unenlightening question, but I'm just not sure about the result and hoping someone can help me varify it. $\\$ This question is related to these three questions. $\\$ I want to ...
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0answers
18 views

Connecting global conservation laws to local features of a function

I have a heuristic question about using global constraints of a problem to make local estimates of geometric features of a curve, such as its local slope. Consider a suitably well behaved function ...
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0answers
26 views

Section of Phase space

Suppose $\mathfrak{X}$ is the configuration space of some system on a Riemannian manifold $\mathcal{M}$. Then, the phase space is $\mathrm{T}^{*}(\mathfrak{X})$. What is a section of ...
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1answer
29 views

Is $H_0^1$ something reasonable for the electric field for a perfect conductor?

I'm trying to pull over some concepts that were derived for Navier-Stokes like equations to Maxwell's equations for the perfect conductor. At a certain point, I am about to assume that the electric ...
8
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1answer
169 views

Time derivative of the state vector as expressed in abstract Hilbert space vs. as a wavefunction

The Schrodinger equation in Hilbert space is expressed as : $$\frac{\partial}{\partial t} \psi(t) = \frac{-i}{\hbar}H\psi(t). $$ Here $\frac{\partial}{\partial t} \psi(t) \equiv \psi'(t) \equiv\lim ...
5
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1answer
90 views

What is the relationship between Cyclic Coordinates and Killing Vector Fields?

My question is related to this question. There are three or four other questions on Killing Vector Fields here, however none of them that I have seen address my question. $\\$ I've been studying ...
0
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1answer
42 views

Magnetic field of a Herzian dipole antenna

If I am given the dipole moment of very short dipole antenna as $P = P_0 sin (\omega t)$, what will be the magnetic field and polarization of far field radiation? Do I need to consider the time ...
5
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0answers
84 views

Meaning of conformal field theory [closed]

Can anyone summarize what conformal field theory is actually about,i.e. 1) what are its goals? (for example, to study such-and-such fields/functions/maps/etc. to see whether they have such-and such ...
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1answer
64 views

Magnitude and Direction of Magnetic Field Homework Question [closed]

A $150~\text{V}$ battery is connected across two parallel metal plates of area $28.5~\text{cm}^2$ and separation $0.00820~\text{m}$. A beam of alpha particles (charge $+2e$, mass $6.64 \times ...
12
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1answer
215 views

Self-dual Maxwell equations, the second homology group, and topological invariants of a four manifold

In Witten's paper Quantum Field Theory and the Jones Polynomial, he mentioned that: Geometers have long known that (via de Rham theory) the self-dual and anti-self-dual Maxwell equations are ...
2
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0answers
46 views

What is the Levi--Civita connection of a Wick rotated metric?

A Wick rotation is a transformation that allows to change from a Lorentzian manifold to a Riemaniann manifold. In the cases when this is possible, is the Levi-Civita connection of the Riemaniann ...
5
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3answers
296 views

Is there any relationship between gauge field and spin connection?

For a spinor on curved spacetime, $D_\mu$ is the covariant derivative for fermionic fields is $$D_\mu = \partial_\mu - \frac{i}{4} \omega_{\mu}^{ab} \sigma_{ab}$$ where $\omega_\mu^{ab}$ are the spin ...
6
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0answers
260 views

When can we take the Brillouin zone to be a sphere?

When reading some literatures on topological insulators, I've seen authors taking Brillouin zone(BZ) to be a sphere sometimes, especially when it comes to strong topological insulators. Also I've seen ...
2
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4answers
81 views

Infinite series of derivatives of position when starting from rest

Suppose you have an object with zero for the value of all the derivatives of position. In order to get the object moving you would need to increase the value of the velocity from zero to some finite ...
0
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1answer
74 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 ...
4
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1answer
94 views

The properity of $\mathbb{R}^4$ that has infinitely many differential structures is related to Yang-Mills field?

I heard a saying that $\mathbb{R}^4$ having infinitely many differential structures which are not diffeomorphic to each other has a relationship with Yang-Mills field. Does anyone can explain it, and ...
6
votes
1answer
154 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 ...
4
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1answer
113 views

Which is the role of Algebraic Geometry in String Theory? [closed]

Could someone sketch me what algebraic geometry has to do with string theory? Are there other mathematical disciplines that are interwoven with string theory? I'm aware of a similar question on ...
7
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1answer
122 views

The curvature of the space of commuting hermitian matrices

This is a question that I asked in the mathematics section, but I believe it may get more attention here. I am working on a project dedicated to the quantisation of commuting matrix models. In the ...
0
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0answers
52 views

PDE from London's Equation with Cylindrical Symmetry

The question is from ISSP by Kittel and as follows: (a)Find a solution of the London equation that has cylindrical symmetry and applies outside a line core. In cylindrical polar coordinates, we want ...
1
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1answer
82 views

Do generalized Pauli Operators generate SU(n)?

A commonly used generalization of Pauli Operators is the "clock" and "shift" operators summarized here: http://en.wikipedia.org/wiki/Generalizations_of_Pauli_matrices Pauli Operators are generators ...
0
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0answers
58 views

Ricci/Tensor Calculus and Matrix Calculus

What are the differences in the types of problems Ricci/Tensor Calculus and Matrix Calculus can solve? One formulation is generally used by the physics community and the other by statisticians and ...
1
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0answers
38 views

Conformal mapping for calculating magnetic reluctance

I work currently on the calculation of magnetic resistance for a air-gap of an electrical machine. For this I am using conformal transformations. I am doing this on a 2D slice. As the machine is ...
3
votes
3answers
329 views

Why Hausdorff and Paracompact manifold in GR?

What can we say about the transition map if the manifold is a Hausdorff space? Why do we need the manifolds to be Hausdorff and paracompact in General Relativity?
6
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2answers
170 views

When can we assume that the wavefunction is separable

While working out the stationary states of a single particle in a 3d infinite potential box ($V=0$ inside a cuboid of known dimensions, $V=\infty$ everywhere else), I realized I had to assume the ...
3
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1answer
165 views

Rigorous mathematical formalism of particle physics

Can anyone provide me with a rigorous mathematical definition of the fundamental particles (all fundamental bosons and fermions), reflecting the analogy of action of groups with interaction of ...
4
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1answer
94 views

Some question about symplectic transformation

I read Arnold's book Mathematical Methods of Classical Mechanics and come across with three problems in page 229. 1.Let $\lambda$ and $\bar{\lambda}$ be simple (multiplicity 1) eigenvalues of a ...
0
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0answers
58 views

Is assuming spacetime to have |2^N| points overkill?

The physical continuum is commonly assumed to have a mathematical continuum of points, that is, with a cardinality equinumerous with the Power Set of the set of natural numbers. However, since [ZFC + ...
1
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2answers
147 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 ...
4
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0answers
66 views

Intuitively what's the relationship between forces and connections?

In Einstein's General Relativity we relate the effects of gravity with the curvature of the Levi-Civita connection on the spacetime manifold. Also, when we get the electromagnetic tensor $F = dA$ ...
4
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1answer
185 views

Mandelstam variables 1 positive 2 negative

The three Mandelstam-variables are defined as: $$s=(p_A+p_B)^2=(p_C+p_D)^2,$$$$t=(p_A-p_C)^2=(p_B-p_D)^2$$$$u=(p_A-p_D)^2=(p_B-p_C)^2.$$ Where A and B are the incoming particles and C and D are the ...
3
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1answer
145 views

Diagonalization of Hamiltonian

Typically, one way of understanding the physics of an interacting quantum system is by diagonalizing the Hamiltonian. In principle, can we always diagonalize a Hamiltonian, such that it is expressed ...
7
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2answers
247 views

Lie algebra and Lie group about quantum harmonic oscillator

We know that in the quantum harmonic oscillator $H=a^\dagger a$, $a^\dagger$, $a$, $1$ will span a Lie algebra, where $a, a^\dagger$ are the annihilation and creation operators, and $H$ is the ...
3
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2answers
77 views

Defining quantum effective action (Legendre transformation), existence of inverse (field - source)?

Given a Quantum field theory, for a scalar field $\phi$ with generic Action $S[\phi]$, we have the generating functional $$Z[J] = e^{iW[J]} = \frac{\int \mathcal{D}\phi e^{i(S[\phi]+\int d^4x ...
3
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1answer
87 views

References on $C^{*}$-algerbas, $W^{*}$-algebras and Quantum Theories

I would like to know some references regarding $C^{*}$ and $W^{*}$-algebras and quantum theories. I'm interested in concrete physical applications, models and problems. Here it is the list of ...
2
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1answer
88 views

Mathematical Physics SUSY QM Resource Recommendation

I want to study SUSY QM. I found some excellent physically motivated articles on Arxiv. Despite, I am especially interested in the mathematical structure behind SUSY QM. Does anybody know whether ...
3
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1answer
123 views

A question about canonical transformation

I have posted this question in math.stackexchange before with no answer till now. It may be more suitable to post here. There is a problem in Arnold's Mathematical Methods of Classical Mechanics ...
1
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2answers
147 views

Trace in non-orthogonal basis?

Physicists define the trace of an operator $\rho$ as the follows, $Tr(\rho)=\sum\limits_{|s\rangle \in B} \langle s| \rho |s\rangle$ where B is some orthonormal basis, and this quantity is ...
2
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0answers
91 views

Solving the Schrodinger equation with appropriate symmetry

In the paper Markov Fields by Edward Nelson the introduction section claims that analytically continuing a Markov process with appropriate symmetry properties yields the solution of the Schrodinger ...