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 ...
10
votes
2answers
44 views
Examples of heterotic CFTs
I'm trying to get a global idea of the world of conformal field theories.
Many authors restrict attention to CFTs where the algebras of left and right movers agree. I'd like to increase my intuition ...
1
vote
1answer
165 views
Lorentz Invariant Equation of Motion for Scalar Field
I'm trying to understand why you can't write down a first order equation of motion for a scalar field in special relativity.
Suppose $\phi(x)$ a scalar field, $v^{\mu}$ a 4-vector. According to my ...
3
votes
2answers
447 views
What is the symmetry that corresponds to conservation of position?
We know that conserved quantities are associated with certain symmetries. For example conservation of momentum is associated with translational invariance, and conservation of angular momentum is ...
7
votes
1answer
249 views
Diffeomorphisms, Isometries And General Relativity
Apologies if this question is too naive, but it strikes at the heart of something that's been bothering me for a while.
Under a diffeomorphism $\phi$ we can push forward an arbitrary tensor field $F$ ...
8
votes
1answer
279 views
Representations of Lorentz Group
I'd be grateful if someone could check that my exposition here is correct, and then venture an answer to the question at the end!
$SO(3)$ has a fundamental representation (spin-1), and tensor product ...
3
votes
1answer
112 views
What is the physical meaning of a flux of gravitational field in classics?
I've stumbled upon an answer to a question about square power in Newton's law of gravity. After reading it I got a question whether the flux of gravitational field has actually any physical meaning.
...
2
votes
2answers
148 views
Gaussian type integral with negative power of variable in integrand
How can we compute the integral $\int_{-\infty}^\infty t^n e^{-t^2/2} dt$ when $n=-1$ or $-2$? It is a problem (1.11) in Prof James Nearing's course Mathematical Tools for Physics. Can a situation ...
2
votes
0answers
192 views
Interesting Math Topics Useful for Physics [closed]
What are some interesting, but less popular, math topics that are useful for physics that can be self-studied? Specifically, topics that might ultimately be useful in high energy theory (even if it is ...
37
votes
14answers
4k views
Number theory in Physics
As a Graduate Mathematics student, my interests lies in Number theory. I am curious to know if Number theory has any connections or applications to physics. I have never even heard of any applications ...
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:
...
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 ...
8
votes
1answer
256 views
AGT conjecture and WZW model
In 2009 Alday, Gaiotto and Tachikawa conjectured an expression for the Liouville theory conformal blocks and correlation functions on a Riemann surface of genus g and n punctures as the Nekrasov ...
14
votes
1answer
54 views
Miura transform for W-algebras of exceptional type
Miura transform for W-algebras of classical types can be found in e.g. Sec. 6.3.3 of Bouwknegt-Schoutens. Is there a similar explicit Miura transform for W-algebras of exceptional types, say, E6? It's ...
15
votes
6answers
201 views
Which QFTs were rigorously constructed?
Which QFTs have mathematically rigorous constructions a la AQFT? I understand there are many such constructions in 2D, in particular 2D CFT has been extensively studied mathematically. But even in 2D ...
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 ...
5
votes
1answer
169 views
Expectation value calculation for a weird operator
In the paper Fundamental monopoles and multimonopole solutions for arbitrary simple gauge groups.- E weinberg
I am not being able to see one of the calculation. The author states (eqn 3.26)
$$\langle ...
4
votes
2answers
243 views
WKB method of approximation
Would it be legitimate to use the WKB approximation for a particle in a spherically symmetric Gaussian potential?
$$V(r)~=~V_0(1-e^{-r^2/a^2}).$$
I'm not sure when to use which approximation ...
12
votes
2answers
142 views
Topological twists of SUSY gauge theory
Consider $N=4$ super-symmetric gauge theory in 4 dimensions with gauge group $G$. As is explained in the beginning of the paper of Kapustin and Witten on geometric Langlands, this
theory has 3 ...
23
votes
11answers
827 views
Negative probabilities in quantum physics
Negative probabilities are naturally found in the Wigner function (both the original one and its discrete variants), the Klein paradox (where it is an artifact of using a one-particle theory) and the ...
1
vote
2answers
201 views
Angular Momentum Operators Non-Degenerate
Typically one writes simultaneous eigenstates of the angular momentum operators $J_3$ and $J^2$ as $|j,m\rangle$, where
$$J^2|j,m\rangle = \hbar^2 j(j+1)|j,m\rangle$$
$$J_3 |j,m\rangle = \hbar ...
5
votes
1answer
102 views
How Exactly Does Linear Regge Trajectories Imply Stability?
(for a more muddled version, see physics.stackexchange: http://physics.stackexchange.com/questions/14020/whats-with-mandelstams-argument-that-only-linear-regge-trajectories-are-stable)
There is a ...
-1
votes
1answer
146 views
What will happen when measuring unmeasurable object?
There is a set called Vitali Set which is not Lebesgue measurable.
Analogously, there also exists a Vitali set $Y$ in $\mathbb R^3$ which is a subset of $[0,1]^3$ and $|Y\cap q|=1$ for all $q\in ...
13
votes
5answers
129 views
Other processes than formal power series expansions in quantum field theory calculations
I am not sure if this question is too naive for this site, but here it goes. In QFT calculations, it seems that everything is rooted in formal power series expansions, i.e. , what dynamical systems ...
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 ...
9
votes
5answers
196 views
Where do theta functions and canonical Green functions appear in physics
In the beginning of Section 5 in his article, Wentworth mentions a result of Bost and proves it using the spin-1 bosonization formula. This result provides a link between theta functions, canonical ...
4
votes
3answers
1k views
Use of advanced mathematics in astronomy, like topology, abstract algebra, or others
I know that topology, abstract algebra, K-theory, Riemannian geometry and others, can be used in physics. Are some of these areas used in astronomy, and are some astronomical theories based on them?
...
11
votes
1answer
82 views
Metric interpretation of self-adjoint extensions?
I am wondering if beyond physical interpretation, the one dimensional contact interactions (self-adjoint extensions of the the free Hamiltonian when defined everywhere except at the origin) have a ...
36
votes
6answers
771 views
The Role of Rigor
The purpose of this question is to ask about the role of mathematical rigor in physics. In order to formulate a question that can be answered, and not just discussed, I divided this large issue into ...
10
votes
2answers
29 views
Extensions of DHR superselection theory to long range forces
For Haag-Kastler nets $M(O)$ of von-Neumann algebras $M$ indexed by open bounded subsets $O$ of the Minkowski space in AQFT (algebraic quantum field theory) the DHR (Doplicher-Haag-Roberts) ...
13
votes
1answer
350 views
Onsager's Regression Hypothesis, Explained and Demonstrated
Onsager's 1931 regression hypothesis asserts that “…the average regression of fluctuations will obey the same laws as the corresponding macroscopic irreversible process". (Here is the links to ...
10
votes
0answers
139 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 ...
13
votes
3answers
63 views
Status of local gauge invariance in axiomatic quantum field theory
In his recent review...
Sergio Doplicher, The principle of locality: Effectiveness, fate, and challenges, J. Math. Phys. 51, 015218 (2010), doi
...Sergio Doplicher mentions an important open ...
22
votes
1answer
175 views
Mermin-Wagner theorem in the presence of hard-core interactions
It seems quite common in the theoretical physics literature to see applications of the "Mermin-Wagner theorem" (see wikipedia or scholarpedia for some limited background) to systems with hard-core ...
16
votes
6answers
301 views
Applications of delay differential equations
Being interested in the mathematical theory, I was wondering if there are up-to-date, nontrivial models/theories where delay differential equations play a role (PDE-s, or more general functional ...
11
votes
1answer
66 views
Are possible gauge fields in a Lagrangian theory always determined by the structure of the charged degrees of freedom?
An elementary example to explain what I mean. Consider introducing a classical point particle with a Lagrangian $L(\mathbf{q} ,\dot{\mathbf{q}}, t)$. The most general gauge transformation is $L ...
0
votes
0answers
101 views
Spherical tensor [closed]
These equations are out of Sakurai and Napolitano Modern Quantum Mechanics.
I'm trying to show that $T_q^{(2)}$--which is defined as the bilinear of two vector operators $V_i$ and $W_j$--transforms ...
1
vote
0answers
72 views
Does the attached “poster” work as a hook into the arXiv paper cited, “Nonlinear Wightman fields”? [closed]
"Nonlinear Wightman fields" are my current response to a wish to do interacting quantum field theory differently, no matter how successful what we currently do may be. The following image of a single ...
4
votes
3answers
544 views
Canonical Commutation Relations
Is it logically sound to accept the canonical commutation relation (CCR)
$$[x,p]~=~i\hbar$$
as a postulate of quantum mechanics? Or is it more correct to derive it given some form for $p$ in the ...
2
votes
4answers
302 views
Why the Hamiltonian and the Lagrangian are used interchangeably in QFT perturbation calculations
Whenever one needs to calculate correlation functions in QFT using perturbations one encounters the following expression:
$\langle 0| some\ operators \times \exp(iS_{(t)}) |0\rangle$
where, ...
6
votes
2answers
145 views
Is the step of analytic continuation unavoidable or can you model around it?
One sometimes considers the analytic continuation of certain quantities in physics and take them seriously. More so than the direct or actual values actually. For example if you use the procedure for ...
6
votes
2answers
385 views
How should a theoretical physicist study maths? [duplicate]
Possible Duplicate:
How should a physics student study mathematics?
If some-one wants to do research in string theory for example, Would the Nakahara Topology, geometry and physics book and ...
-4
votes
4answers
117 views
Is the mathematical truth 1+1=2 analogous to the conservation of energy? [closed]
They seem to express the same concept in different fields.
-1
votes
2answers
136 views
can we investigate physics through investigation of pure number? [closed]
If the consistency between the two is so absolute, why can we not investigate the physical nature of the universe through analysis of pure number? Particularly at the quantum scale?
2
votes
2answers
262 views
(Co)homology of the universe
In this post let $U$ be the universe considered as a manifold.
From what I gather we don't really have any firm evidence whether the universe is closed or open. The evidence seems to point towards it ...
5
votes
1answer
230 views
Natural systems that test the primality of a number?
There might be none. But I was thinking of links between number theory and physics, and this would seem like an example that would definitely solidify that link.
Are there any known natural systems, ...
4
votes
2answers
654 views
Calculate stainless steel pole necking limit
Background
Trying to determine how much weight a post can support without necking when a monitor is attached to an articulated arm: a cantilever problem.
Problem
There are three objects involved in ...
1
vote
1answer
117 views
What is the definition of density as a function?
(Before I start, I don't know which tag is suitable for this post. Please retag my post if it bothers you.)
Let's say there is a string on $[0,1]$ with a mass given by $m(x)$. ($m(x)$ means the mass ...
3
votes
2answers
194 views
Electromagnetism for Mathematician
I am trying to find a book on electromagnetism for mathematician (so it has to be rigorous).
Preferably a book that extensively uses Stoke's theorem for Maxwell's equations
(unlike other books that on ...
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
1answer
184 views
Killing vectors for SO(3) (rotational) symmetry
I am reading a paper$^1$ by Manton and Gibbons on the dynamics of BPS monopoles. In this, they write the Atiyah-Hitchin metric for a two-monopole system. The first part is for the one monopole moduli ...
