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8
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5answers
2k views

Fourier transform of the Coulomb potential

When trying to find the Fourier transform of the Coulomb potential $$V(\mathbf{r})=-\frac{e^2}{r}$$ one is faced with the problem that the resulting integral is divergent. Usually, it is then argued ...
1
vote
1answer
981 views

Amplitude of power spectral density

Why is the amplitude of the Power spectral density higher for shorter period of time as compared to a longer period of time when calculated for any vibration data?
1
vote
1answer
247 views

Power Spectral Density of constant speed data in a car

I recently calculated the PSD of the vibration data in a car at constant speed. I would like to know what this means and what if I calculate PSD of the vibration data in a car for the total journey ...
28
votes
9answers
3k views

Rigor in quantum field theory

Quantum field theory is a broad subject and has the reputation of using methods which are mathematically desiring. For example working with and subtracting infinities or the use of path integrals, ...
4
votes
2answers
919 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 ...
2
votes
0answers
375 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 ...
0
votes
5answers
1k views

Use of the mathematical concept 'function' in theoretical physics

The mathematical concept of function is used in physics to represent different physical quantities. For example the air pressure variation with time and space is called an acoustic wave. We use a ...
9
votes
10answers
2k views

Physics for mathematicians

How and from where does a mathematician learn physics from a mathematical stand point? I am reading the book by Spivak Elementary Mechanics from a mathematicians view point. The first couple of pages ...
2
votes
1answer
356 views

What does the Many-Body Problem say about mathematical physics?

I was interested to read the answers to the other Many-Body Problem questions on this site and was left with one nagging question of my own. What does the Many-Body Problem reveal about reality and ...
6
votes
1answer
549 views

There seems to be no definition of “stability” in axiomatic QFT. Is there? And, if not, is this a problem?

"stability" is invoked as the justification for the axiomatic requirement that the spectrum of the generators of the translation group must be confined to the forward light-cone. The spectrum ...
17
votes
7answers
2k views

Quantum mechanics on a manifold

In quantum mechanics the state of a free particle in three dimensional space is $L^2(\mathbb R^3)$, more accurately the projective space of that Hilbert space. Here I am ignoring internal degrees of ...
5
votes
1answer
236 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, ...
12
votes
7answers
1k views

What are the uses of Hopf algebras in physics?

Hopf algebra is nice object full of structure (a bialgebra with an antipode). To get some idea what it looks like, group itself is a Hopf algebra, considered over a field with one element ;) usual ...
2
votes
2answers
270 views

What mechanism in string theory enforces the consistency of self-couplings of massless vector bosons?

I have been reading the stackexchange questions on enhanced symmetries in string theory, the Leech lattice, monstrous moonshine, etc. , and I have a question to ask. An astute commentator pointed out ...
5
votes
1answer
167 views

Would it be worthwhile to work out a manifestly supersymmetric superspace formalism for 16 and 32 real SUSY generators?

For 4 real SUSY generators, the superspace formalism has been worked out a long time ago. For 8 real SUSY generators, some brilliant theoreticians have worked out the details of harmonic superspace. ...
0
votes
1answer
153 views

Meaning and types of singularity in case of string or any cosmological model (Mathematical description)

What is actual meaning of singularity can we use this term for conclusion in any research paper( related to cosmological models ).what r the types .
2
votes
1answer
225 views

Is the exponential of the distribution $i\Delta^+(x)$, the 2-point function of a free quantized Klein-Gordon field theory, a distribution?

From answers to a previous question, a finite degree polynomial in the distribution $i\Delta^+(x)$, with Fourier transform $2\pi\delta(k^2-m^2)\theta(k_0)$, is a distribution, even though a product of ...
3
votes
1answer
591 views

Time evolution in quantum mechanics

We know that an operator A in quantum mechanics has time evolution given by Heisenberg equation: $$ \frac{i}{\hbar}[H,A]+\frac{\partial A}{\partial t}=\frac{d A}{d t} $$ Can we derive from this ...
2
votes
2answers
307 views

On a principal bundle, why is the horizontal vector space not unique?

On a principal bundle, at each point you have a tangent vector space. At a given point, the vectors tangent to the fiber form the vertical vector space. Then the vector space at that point is a direct ...
1
vote
2answers
443 views

Geodesics and trajectories

I'm a mathematician studying Arnold's Mathematical Methods of Classical Mechanics. On p. 83 the following definition is given. Let $M$ be a differentiable manifold, $TM$ its tangent bundle, and ...
5
votes
1answer
105 views

Is there an upper bound on the gauge group rank in F-theory compactifications on CY 4-folds?

It is known that in F-theory compactifications on CY 4-folds one can get gauge groups with very large ranks. The largest single factor* gauge group for compact CY 4-folds I found in the literature is ...
8
votes
3answers
328 views

Question about associative 3-cycles on G2 manifolds

Let $X$ be a manifold with $G_2$ holonomy and $\Phi$ be the fundamental associative 3-form on $X$. Let $*\Phi$ be the dual co-associative 4-form on $X$. Now consider a particular associative 3-cycle ...
6
votes
1answer
625 views

CFTs and formalizing quantum field theory

Moshe's recent questions on formalizing quantum field theory and lattices as a definition of field theory remind me of something I occasionally idly wonder about, and maybe this site can tell me the ...
2
votes
4answers
4k views

Mathematical background for Quantum Mechanics [duplicate]

What are some good sources to learn the mathematical background of Quantum Mechanics? I am talking functional analysis, operator theory etc etc...
12
votes
5answers
2k views

“Velvet way” to Grassmann numbers

In my opinion, the Grassmann number "apparatus" is one of the least intuitive things in modern physics. I remember that it took a lot of effort when I was studying this. The problem was not in the ...
5
votes
1answer
526 views

Why is the Gupta-Bleuler gauge unfashionable?

In the early days of quantum electrodynamics, the most popular gauge chosen was the Gupta-Bleuler gauge stating that for physical states, $$\langle \chi | \partial^\mu A_\mu | \psi \rangle = 0.$$ ...
2
votes
0answers
221 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 ...
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
1answer
278 views

A question about a vibrating membrane

The usual way to model a vibrating membrane is by using the wave equation. Is it possible to do that from "within"? Probably the answer is yes, but where can I see it done explicitly. What I mean is ...
2
votes
1answer
148 views

Does the positive mass conjecture indicate a necessity of interactions in our universe?

The positive mass conjecture was proved by Schoen and Yau and later reproved by Witten. Total mass in a gravitating system must be positive except in the case of flat Minkowski space, where energy is ...
4
votes
2answers
1k views

What's the point of having an einbein in your action?

One often comes across actions written with an extra auxiliary field, with respect to which if you vary the action, you get the equation of motion of the auxiliary field, which when plugged into the ...
11
votes
2answers
1k views

What does John Conway and Simon Kochen's “Free Will” Theorem mean?

The way it is sometimes stated is that if we have a certain amount of "free will", then, subject to certain assumptions, so must some elementary particles."(Wikipedia) That is confusing to me, ...
4
votes
4answers
1k views

Non-linear Schrödinger equation

I have read about the existence of a non-linear scrhödinger equation. What is its utility and application? And how can it be derived? Is it in a relativistic or non-relativistic context?
26
votes
6answers
2k views

Formalizing Quantum Field Theory

I'm wondering about current efforts to provide mathematical foundations and more solid definition for quantum field theories. I am aware of such efforts in the context of the simpler topological or ...
-2
votes
2answers
205 views

Question on particles

Is there any theory in which every particle can be further subdivided into any number of particles and the total number of particles any where in the space time are infinity in theory and only due to ...
3
votes
2answers
344 views

Variational method applied to brownian motion

It's possible apply the variational method to the brownian motion ? I mean, one of requisites on $y(t)$ is that it must be continuous and $\partial_t{y(t)}$ too, and in this case, $\partial_t{y(t)}$ ...
2
votes
2answers
290 views

Renormalization and Infinites

Measuring a qubit and ending up with a bit feels a little like tossing out infinities in renormalization. Does neglecting the part of the wave function with a vanishing Hilbert space norm amount to ...
6
votes
2answers
752 views

The derivation of fractional equations

Recently I saw some physical problems that can be modeled by equations with fractional derivatives, and I had some doubts: is it possible to write an action that results in an equation with fractional ...
3
votes
1answer
534 views

What is a maximal analytic extension?

Can someone explain (as rigorously as possible) what is involved in analytically continuing, say, the Schwarzschild solution to the Kruskal manifold? I understand the two metrics separately but I'm ...
18
votes
5answers
2k views

Haag's theorem and practical QFT computations

There exists this famous Haag's theorem which basically states that the interaction picture in QFT cannot exist. Yet, everyone uses it to calculate almost everything in QFT and it works beautifully. ...
9
votes
9answers
1k views

Is causality a formalised concept in physics?

I have never seen a “causality operator” in physics. When people invoke the informal concept of causality aren’t they really talking about consistency (perhaps in a temporal context)? For example, if ...
6
votes
2answers
449 views

How do we resolve operator ordering ambiguities when quantizing generic nonlinear second-class constraints?

Dirac came up with a general theory of constraints, including second-class constraints. To quantize such systems, he first computed the Dirac bracket classically, and only then "promoted" the ...
2
votes
2answers
374 views

What is the quantum / Berry-Pancharatnam phase for a spin-j state with z-component m?

Quantum phase arises when a spin-j state is sent through a sequence of transitions that return it to its original position. For example with spin-1/2, a state picks up a complex phase of $\pi/4$ when ...
13
votes
3answers
2k views

What is the relation between renormalization in physics and divergent series in mathematics?

The theory of Divergent Series was developed by Hardy and other mathematicians in the first half of the past century, giving rigorous methods of summation to get unique and consistent results from ...
2
votes
5answers
477 views

Black Hole Singularities

If two black holes collide and then evaporate, do they leave behind two naked sigularities ore? If there are two, can we know how they interact?
10
votes
2answers
312 views

What is known about some massive Gaussian models on a lattice?

Recently I started to play with some massive Gaussian models on a lattice. Motivation being that I work on massless models and want to understand the massive case because it seems easier to handle ...
4
votes
1answer
587 views

Properties of graph of subatomic particle interactions

Say there was some situation where you have a lot of subatomic particles interacting with each other and decided to draw (say, by joining Feynmann diagrams) those interactions- so that you got some ...
14
votes
8answers
3k views

Crash course on algebraic geometry with view to applications in physics

Could you please recommend any good texts on algebraic geometry (just over the complex numbers rather than arbitrary fields) and on complex geometry including Kahler manifolds that could serve as an ...
20
votes
4answers
413 views

Paradox?: What is the form of radiation experienced by a harmonically accelerated observer?

Theory predicts that uniform acceleration leads to experiencing thermal radiation (so called Fulling Davies Unruh radiation), associated with the appearance of an event horizon. For non uniform but ...
1
vote
1answer
338 views

Cheetah prosthesis efficiency

I want to compare the much-talked about Cheeta running prosthesis to a the normal running process in terms of force and energy, but I don't know where to start. How would you start the comparison? A ...