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 ...
9
votes
1answer
212 views
How is the Dirac adjoint generalized?
I am wondering how one can generalize the Dirac adjoint to flat "spacetimes" of arbitrary dimension and signature. To be more specific, a standard situation would be to consider 4 dimensional ...
8
votes
1answer
256 views
Integral representation of Thomas-Fermi Equation
The Thomas-Fermi equation with dimensionless variables is identified as;
$$
\frac{d^2\phi}{dx^2} = \frac{\phi^{3/2}}{x^{1/2}}
$$
with the boundary conditions as
$$
\phi(0) = 1 \\
\phi(\infty) = 0.
$$
...
1
vote
1answer
61 views
How to assign coordinates to the elements of a flat metric space
Consider the metric space $(M, d \,)$ where set $M$ contains sufficiently many (at least five) distinct elements,
and consider the assignment $c_f$ of coordinates to (the elements of) set $M$,
$c_f ...
1
vote
1answer
126 views
Validity of the Multi-Species Navier-Stokes Equations for real gases
I'm wondering what are the validity limits of Multi-Species Navier-Stokes equations. I'm aware of the limit for rarefied gases. But is there any new limit that arises in the context of real gases?
I ...
0
votes
1answer
75 views
Higher order covariant Lagrangian
I'm in search of examples of Lagrangian, which are at least second order in the derivatives and are covariant, preferable for field theories. Up to now I could only find first-order (such at ...
0
votes
1answer
170 views
Expansion in solid spherical harmonics on the lattice
I'm interested in calculating scattering processes (e.g. Coulomb scattering of an electron beam by a single ion) in the context of lattice quantum field theory, and wonder if there is something like ...
10
votes
0answers
140 views
Hypersingular Boundary Operator in Physics
This has been a question I've been asking myself for quite some time now. Is there a physical Interpretation of the Hypersingular Boundary Operator?
First, let me give some motivation why I think ...
8
votes
0answers
36 views
Minimal strings and topological strings
In http://arxiv.org/abs/hep-th/0206255 Dijkgraaf and Vafa showed that the closed string partition function of the topological B-model on a Calabi-Yau of the form $uv-H(x,y)=0$ coincides with the free ...
6
votes
0answers
246 views
Classical mechanics: Generating function of lagrangian submanifold
I have a short question regarding the geometrical interpretation of the Hamilton-Jacobi-equation.
One has the geometric version of $H \circ dS = E$ as an lagrangian submanifold $L=im(dS)$, which is ...
5
votes
0answers
158 views
Physical interpretation: weighted eigenvalues of the Laplacian with a potential
I'm a mathematician with only the basic knowledge of Physics, so my question may be trivial: in this case, mercy me. :-)
Let $\Omega \subseteq \mathbb{R}^N$ be a domain and let $V,m:\Omega \to ...
5
votes
0answers
126 views
What is Motivic mathematics and how is it used in physics?
In a few videos I've seen where he discusses the new approach to calculating the super Yang Mills scattering amplitudes, Nima Arkani-Hamed sometimes alludes to the use of Motivic methods as being ...
5
votes
0answers
33 views
What is the importance of studying degeneration on $M_g$
Let $M_g$ be the moduli space of smooth curves of genus $g$. Let $\overline{M_g}$ be its compactification; the moduli space of stable curves of genus $g$.
It seems to be important in physics to study ...
5
votes
0answers
194 views
1-form formulation of quantized electromagnetism
In a perpetual round of reformulations, I've put quantized electromagnetism into a 1-form notation. I'm looking for references that do anything similar, both to avoid reinventing the wheel and perhaps ...
4
votes
0answers
70 views
Noether currents for the BRST tranformation of Yang-Mills fields
The Lagrangian of the Yang-Mills fields is given by
$$
\mathcal{L}=-\frac{1}{4}(F^a_{\mu\nu})^2+\bar{\psi}(i\gamma^{\mu}
D_{\mu}-m)\psi-\frac{1}{2\xi}(\partial\cdot A^a)^2+
...
4
votes
0answers
117 views
Question about the HVZ theorem
In this paper1 the authors cite the HVZ theorem2 saying that it follows from the method used by M. Reed & B. Simon without modifications; I don't really understand this point.
Is there anyone who ...
4
votes
0answers
67 views
Electric potential of a spheroidal gaussian
I'm looking for results that compute the electrostatic potential due to a spheroidal gaussian distribution. Specifically, I'm looking for solutions of equations of the form
$$
...
4
votes
0answers
141 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 ...
4
votes
0answers
99 views
K3 gravitational instanton
Could you please recommend a sufficiently elementary introduction to K3 gravitational instanton in general relativity and the problem of finding its explicit form?
Under 'sufficiently elementary' I ...
3
votes
0answers
96 views
Holonomy twisting
There is Witten's topological twist of standard SUSY QFTs with enough SUSY into Witten-type TQFTs. What is a holonomy twist?
3
votes
0answers
61 views
Finding symmetry of a part of an equation, given the group transformation property of another part
I am reading this paper on Dyons and Duality in $\mathcal{N}=4$ super-symmetric gauge theory. The author finds the zero modes or a dirac equation obtained by considering first order perturbations to ...
3
votes
0answers
77 views
Isospin and Hypercharge of the SU(2) bps monopole embedding
I am reading the paper Fundamental monopoles and multimonopole solutions for arbitrary simple gauge groups - Weinberg, Erick J .
In appendix C of this paper the author states, that the solution ...
3
votes
0answers
85 views
Asymptotic limit of the two kink solution of the sine-gordon equation
I am reading a paper on the sine-gordon model. The solution for a two kink solution is given as:
...
3
votes
0answers
63 views
Divergence calculation of a lie algebra valued quantity having spinor indices
I am reading this paper by E. Weinberg - Fundamental monopoles and multimonopole solutions for arbitrary simple gauge groups.
I am having a problem with a calculation. I don't have much experience ...
3
votes
0answers
87 views
What can quantum adiabatic computation provably accomplish?
Let's say I have a quantum adiabatic computer in a black-box that works perfectly, doesn't suffer from decoherence/noise problems, etc. Are there any proven bounds for an adiabatic algorithm that ...
3
votes
0answers
334 views
An alternative, algebraic way to introduce interactions. Are there other ways out there?
An opening paragraph:
The usual approach to introducing interactions in quantum field theory
is to make the constraint on the
amplitude of the field towards smaller
values more forceful than ...
2
votes
0answers
21 views
How to numerically solve a laser driving semi-classical two-level system using Floquet formalism?
Consider the semi-classical laser driving two-level atom, where the laser is treated classically and the atom is treated quantum mechanically. The effect of laser on the atom is a dipole coupling:
$$
...
2
votes
0answers
50 views
About deriving the multi-trace index in terms of the single-trace index
This question is in reference to this paper
Combining their equations 5.2, 5.3, 5.6 and 5.7 one seems to be looking at the integral/partition function,
$Z(x) = \prod_{n=1}^{n =\infty}\left [ \int ...
2
votes
0answers
49 views
Helicity for Zero Rest Mass Field Equations
I'm trying to reconcile the usual definition of the helicity operator, namely
$$ h = \hat{p}.S$$
with the definition of a massless helicity $n$ field as a symmetric spinor field $\phi^{A\dots B}$ ...
2
votes
0answers
87 views
Finite or ∞ set of masses & ∃ gravity center?
Any finite & non empty set of masses has a computable center of gravity:
$\vec{OG} = \frac{\sum_i m_i \vec{OM}_i}{\sum_i m_i}$ .
Does the contrapositive permits to conclude that a mass system ...
2
votes
0answers
101 views
Turboshaft Turbine Mathematical Model
Are there any simplified mathematical models for how two gas coupled turbines (also called a free power turbine) should interact with one another as the speed of the driving turbine changes.
(i.e.) ...
2
votes
0answers
65 views
A doubt about fuchsian functions in physics?
I'm not sure if this is the right place (or math.stackexchange?) to ask the next
What is the difference between fuchsian, theta-fuchsian, and kleinian functions?
Please, suggest me an introductory ...
2
votes
0answers
63 views
Boundaries where AdS/CFT complementarity applies
Usually when I read about AdS/CFT complementarity as a particular case of the Holographic principle, it suggests that physics evolution on a boundary has a map to physics evolution on the bulk.
But ...
2
votes
0answers
129 views
What are the topics of string theory that are comprehensible with only a mathematical background on Manifolds and Algebraic Topology?
What are the topics of string theory that are comprehensible with only a mathematical background on manifolds and algebraic topology? Also, I have read only the first four chapters in Peskin & ...
2
votes
0answers
112 views
Functional determinant approximation
Let the Hamiltonian in one dimension be $H+z$, then I would like to evaluate $\det(H+z)$.
I have thought that if I know the function $Z(t) = \sum_{n>0}\exp(-tE_{n})$ I can use
$$\sum_{n} ...
2
votes
0answers
88 views
Convergence and well-definedness of Lorentzian path integrals
Wick rotation of quantum field theories to Euclidean path integrals with a nonnegative measure everywhere is a wonderful tool. Not so with Lorentzian path integrals. Events far separated in ...
2
votes
0answers
355 views
Heat equation and Bessel's function
Could someone please explain why if the time-independent heat equation can, via changing of variables, take the form of Bessel's equation that the $\sqrt\lambda$ should take the values of the zeros of ...
2
votes
0answers
210 views
Singularities in Bianchi models in general relativity ( physical science)
what are the conditions to check point type singularity in a bianchi type model ?
bianchi type model are of Type I,II,III,IX,IV or u can say we use different Bianchi type models having some specific ...
1
vote
0answers
102 views
A question from Hilbert and Courant's Vol II of Methods of Mathematical Physics (I might have spotted an error)
In page 751 (I hope some folks have a copy of it, legal or otherwise, I have a legal one :-D), I am attaching scans of pages 750-751.
http://www.mediafire.com/view/?7hu91s2t5866lqj
...
1
vote
0answers
115 views
How is the poincare conjecture(and perelman proof) helpful in studying the properties of the universe?
Can someone tell me how the poincare's famous conjecture or its proof by perelmen can be helpful in deciding some properties like the shape of the universe?
1
vote
0answers
139 views
What does it mean for a phase space trajectory to be “long” and “stable”?
What does it mean for a phase space trajectory to be "long" and "stable"?
I understand the concept of a trajectory in phase space but not how these adjectives can be applied to one.
Thanks.
1
vote
0answers
124 views
Question on energies obtained via WKB approximation
Suppose we are given an ODE problem $$ y''(x)+V(x)f(x)=E_{n} y(x) $$
with boundary conditions $ y(0)=y(\infty)=0$. Here $V(x)$ is a potential function.
Then is it always true that (for $n ...
0
votes
0answers
36 views
An application of Toeplitz operators
I want to find an application of the Toeplitz operators. All I need is a known problem (not an open problem) which solution use the theory of Toeplitz operators. I don't need all the details but I ...
0
votes
0answers
33 views
What is the result of applying a fourier transform n times to a distribution?
For a function applying the fourier transform twice is equivalent to the parity transformation, applying it three times is the same as applying the inverse of the fourier transform, and applying four ...
0
votes
0answers
21 views
What is the magnetic quadrupole moment of a nucleus in cylindrical coordinates?
What is the magnetic quadruple moment of a nuclei in cylindrical coordinates?
The quadrupole moment of a nucleus is zero in spherical coordinates but in the cylindrical coordinates it can't be ...
0
votes
0answers
81 views
Quantum uncertainty can explain the Riemann Hypothesis?
In the recent paper "Riemann Hypothesis as an Uncertainty Relation" (http://arxiv.org/abs/1304.2435) the author claims that the presence of zeros out of the critical line may lead to the violation of ...
0
votes
0answers
106 views
P-adic Numbers and Eternal Inflation
In October(??) 2011, Leonard Susskind gave a talk and with few other people wrote papers about p-adic numbers and measure problems in cosmology, see e.g. arXiv:1110.0496. Has there been any recent ...
0
votes
0answers
47 views
Cauchy Problem in Convex Neighborhood
While reading the reference
Eric Poisson and Adam Pound and Ian Vega,The Motion of Point Particles in Curved Spacetime, available here,
there is something that I don't quite understand.
...
0
votes
0answers
197 views
Proof of equality of the integral and differential form of Maxwell's equation
Just curious, can anyone show how the integral and differential form of Maxwell's equation is equivalent? (While it is conceptually obvious, I am thinking rigorous mathematical proof may be useful in ...
0
votes
0answers
76 views
Searching for clues on “spacelike”-ness by “impossible figures”
Remark on version (3):
In the first version of my question main text the already lengthy "logic statement" -- let's call it "paradigm statement" in the following -- involved conditions on only 24 ...
0
votes
0answers
248 views
Approximation of a summation by an integral
Is it valid to approximate the function $$ Z(t)=\sum_{n}e^{-tE_{n}} ,\ t\ge 0$$
by the integral over phase space: $$ \frac{ 1}{2\sqrt \pi}\int_{0}^{\infty}dxe^{-tV(x)}?$$
For example, in order to ...
