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 ...
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 ...
13
votes
3answers
339 views
Homotopy $\pi_4(SU(2))=\mathbb{Z}_2$
Recently I read a paper using $$\pi_4(SU(2))=\mathbb{Z}_2.$$ Do you have any visualization or explanation of this result?
More generally, how do physicists understand or calculate high dimension ...
4
votes
3answers
547 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 ...
6
votes
2answers
147 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
386 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
118 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.
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, ...
-1
votes
2answers
137 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
263 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 ...
2
votes
1answer
114 views
electrostatic potential, analytic properties
An electrostatic potential associated with some delocalized charge $\int \rho(\mathbf{r}) d{\mathbf{r}}$ is given by:
$$v_H(\mathbf{r}) = \int ...
1
vote
1answer
118 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
1answer
97 views
An issue about the compactness and the existence of CTCs
There is a well known fact that a compact spacetime necessarily contains a closed timelike curve (CTC). Proof can be found in several books on GR (e.g. Hawking, Ellis, Proposition 6.4.2), and in ...
3
votes
2answers
196 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 ...
0
votes
1answer
66 views
What does Friedrichs mean by “Myriotic fields”?
I came across K. O. Friedrichs' very old book (1953) "Mathematical Apsects of the Quantum Theory of Fields", and hardly any of it makes sense to me.
One of the strange things that he refers to are ...
1
vote
4answers
279 views
Generalized quantum mechanics
I wonder if it's possible to discover another version of quantum theory that doesn't depend on complex numbers. We may discover a formulation of quantum mechanics using p-adic numbers, quaternions or ...
3
votes
2answers
182 views
How do I define time-ordering for Wightman functions?
This is a follow-up question to What are Wightman fields/functions
Ok, so based on my reading, the field operators of a theory are understood to be operator-valued distributions, that is, to be ...
0
votes
1answer
131 views
Solution of a partial differential heat equation with derivative and boundary conditions
I want to solve the following partial different equation.
Find $u(x, t)$, satisfying $u_t = u_{xx}$ , $u(x, 0) = x − x^2$ , $u(0, t) = T_0$ , $u_x (1, t) = 0$ and $|u|$ is bounded.
Using separation ...
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.
...
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.
$$
...
7
votes
1answer
203 views
alternatives to supersymmetry and Coleman-Mandule theorem
Humour me for a minute here and let's imagine that all interesting and plausible supersymmetry models have been "cornered" out by the experimental data;
what sort of alternatives are there for having ...
6
votes
5answers
418 views
Is physics rigorous in the mathematical sense?
I am a student studying Mathematics with no prior knowledge of Physics whatsoever except for very simple equations. I would like to ask, due to my experience with Mathematics:
Is there a set of ...
4
votes
1answer
203 views
What are Wightman fields/functions
Simple question: What are Wightman fields? What are Wightman functions?
What are their uses? For example can I use them in operator product expansions? How about in scattering theory?
5
votes
3answers
251 views
Takhatajan's mathematical formulation of quantum mechanics
So I began skimming L. Takhatajan's Quantum Mechanics For Mathematicians, and saw the mathematical formulation of QM that he uses (page 51). (The PDF file is available here.)
I've only taken a basic ...
10
votes
3answers
341 views
Does the axiom of choice appear to be “true” in the context of physics?
I have been wondering about the axiom of choice and how it relates to physics. In particular, I was wondering how many (if any) experimentally-verified physical theories require axiom of choice (or ...
4
votes
1answer
137 views
The use of Hall algebras in physics
I asked the same question in mo. I think maybe here there are more physics guys to help me.
I once read a statement (not memorized precisely) that a certain physics quantity between two states of ...
1
vote
4answers
146 views
Cubic term in gauge theories
In ordinary classical gauge theories the term $-\frac{1}{2}\mathrm{Tr}(F_{\mu\nu}F^{\mu\nu})=-\frac{1}{4}F^a_{\mu\nu}F_a^{\mu\nu}$ in the Lagrangian is completely natural. A somehow rare term would be ...
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
1answer
308 views
A confusion from Weinberg's QFT text (a vanishing term in Lippmann-Schwinger equation)
I was reviewing the first few chapters of Weinberg Vol I and found a hole in my understanding in page 112, where he tried to show in the asymptotic past $t=−∞$, the in states coincide with a free ...
5
votes
1answer
275 views
Reference for mathematics of string theory [closed]
I have a great interest in the area of string theory, but since I am more focused on mathematics, I was wondering if there is any book out there that covers mathematical aspects of string theory. I ...
0
votes
0answers
112 views
Research in Quantum Physics [closed]
I am Suvankar, a student of engienering. My branch is Electrical & Electronics Engineering. Although this is a Physics oriented website, I want to know whether it is possible to do M.Sc. after ...
3
votes
1answer
219 views
Mathematical definitions in string theory
Does anyone know of a book that has mathematical definitions of a string, a $p$-brane, a $D$-brane and other related topics. All the books I have looked at don't have a precise definition and this is ...
5
votes
2answers
199 views
Can auxiliary fields be thought of as Lagrange multipliers?
In the BRST formalism of gauge theories, the Lautrup-Nakanishi field $B^a(x)$ appears as an auxiliary variable
$$\mathcal{L}_\text{BRST}=-\frac{1}{4}F_{\mu\nu}^a F^{a\,\mu\nu}+\frac{1}{2}\xi B^a B^a + ...
3
votes
3answers
306 views
Why we use $L_2$ Space In QM?
I asked this question for many people/professors without getting a sufficient answer, why in QM Lebesgue spaces of second degree are assumed to be the one that corresponds to the Hilbert vector space ...
2
votes
2answers
114 views
Compactness of spacetime: experiment and math
It is common to find models built on a compact spacetime. In mathematics, compactness is a very nice property $-$ and lot of powerful results depend on it.
But
how safe is assuming compactness of ...
11
votes
5answers
505 views
Reading list in topological QFT
I'm interested in learning about topological QFT including Chern Simons theory, Jones polynomial, Donaldson theory and Floer homology - basically the kind of things Witten worked on in the 80s. I'm ...
3
votes
1answer
123 views
Inverting an anisotropic distribution
I have come across a research problem where I need to solve an integral equation of the form
$\int A^{-1}(x,y) \nabla_z\cdot\left[\nabla_y\cdot\left(v(y) G(y-z) \right) v(z)\right]dy = \delta(x-z)$,
...
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
...
5
votes
1answer
229 views
How to prove Gegenbauer's addition theorem?
I asked this at: http://math.stackexchange.com/questions/210153/, but didn't get any reply, so I am trying here, since I actually need this in physics anyway.
How can one prove the following ...
0
votes
0answers
145 views
Riemann Hypothesis and String [closed]
I believe that this is a math's question, but
what is the connection between RIEMANN HYPOTHESIS or RIEMANN ZEROS and String Theory ??
3
votes
2answers
227 views
Mathematically challenging areas in Quantum information theory and quantum cryptography
I am a physics undergrad and thinking of exploring quantum information theory. I had a look at some books in my college library. What area in QIT, is the most mathematically challenging and rigorous? ...
0
votes
1answer
164 views
State normalization in Dirac's formulation of quantum mechanics
Let us divide the time $T$ into $N$ segments each lasting $δt = T/N$. Then
we write $\langle q_F | e^{−iHT} |q_I \rangle = \langle q_F | e^{−iHδt} e^{−iHδt} . . . e^{−iHδt} |q_I \rangle $
Our ...
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 ...
1
vote
1answer
141 views
Problem in Hamiltonian
I need to elaborate the equation ,and need to know what is the physical significance and how matrices will manipulate in the equation $$
\hat{H} = (\hat{\tau_3}+i\hat{\tau_2})\frac{\hat{p}^2}{2m_0}+ ...
3
votes
1answer
187 views
Question on Sakurai's treatment of the Harmonic Oscillator:
In Section 2.3 of the second edition of Modern Quantum Mechanics (which discusses the harmonic oscillator), Sakurai derives the relation $$Na\left|n\right> = (n-1)a\left|n\right>,$$ and states ...
12
votes
4answers
570 views
Reason for the discreteness arising in quantum mechanics?
What is the most essential reason that actually leads to the quantization. I am reading the book on quantum mechanics by Griffiths. The quanta in the infinite potential well for e.g. arise due to the ...
2
votes
1answer
133 views
Open boundary condition and Glauber Dynamics
Warning: by background is in math, not physics. I've just recently started working with things that are close to theoretical physics. So please note that
I'm still very confused by the jargon.
Maybe ...
4
votes
2answers
130 views
Quantum Mechanics in terms of *-algebras
I'm currently trying to find my way into the geometric description of Quantum Mechanics. I therefor started reading:
Geometry of state spaces. In: Entanglement and Decoherence (A. Buchleitner et ...
12
votes
3answers
445 views
When is Lebesque integration useful over Riemann integration in physics?
Riemann integration is fine for physics in general because the functions dealt with tend to be differentiable and well behaved. Despite this, it's possible that Lebesque integration can be more ...
