Questions tagged [mp.mathematical-physics]
Mathematical methods in classical mechanics, classical and quantum field theory, quantum mechanics, statistical mechanics, condensed matter, nuclear and atomic physics.
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What is an integrable system?
What is an integrable system, and what is the significance of such systems? (Maybe it is easier to explain what a non-integrable system is.) In particular, is there a dichotomy between "...
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A soft introduction to physics for mathematicians who don't know the first thing about physics
There have been similar questions on mathoverflow, but the answers always gave some advanced introduction to the mathematics of quantum field theory, or string theory and so forth. While those may be ...
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Where does a math person go to learn quantum mechanics?
My undergraduate advisor said something very interesting to me the other day; it was something like "not knowing quantum mechanics is like never having heard a symphony." I've been meaning to learn ...
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What makes four dimensions special?
Do you know properties which distinguish four-dimensional spaces among the others?
What makes four-dimensional topological manifolds special?
What makes four-dimensional differentiable manifolds ...
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Does Physics need non-analytic smooth functions?
Observing the behaviour of a few physicists "in nature", I had the impression that among the mathematical tools they use a lot (along with possibly much more sofisticated maths, of course), ...
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Topology and the 2016 Nobel Prize in Physics
I was very happy to learn that the work which led to the award of the 2016 Nobel Prize in Physics (shared between David J. Thouless, F. Duncan M. Haldane and J. Michael Kosterlitz) uses Topology. In ...
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Where does a math person go to learn statistical mechanics?
The more math I read, the more I see concepts from statistical mechanics popping up -- all over the place in combinatorics and dynamical systems, but also in geometric situations. So naturally I've ...
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Has the Lie group E8 really been detected experimentally?
A few months ago there were several math talks about how the Lie group E8 had been detected in some physics experiment. I recently looked up the original paper where this was announced,
"Quantum ...
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Dropping three bodies
Consider the usual three-body problem with Newtonian
$1/r^2$ force between masses. Let the three masses start off at rest,
and not collinear. Then they will become collinear a finite time ...
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Theoretical physics: Why not just $\mathbb{R}^4$?
You and I are having a conversation:
"Okay," I say, "I think I get it. The gauge groups we know and love arise naturally as symmetries of state spaces of particles."
"...
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Examples where physical heuristics led to incorrect answers?
I have always been impressed by the number of results conjectured by physicist, based on mathematically non-rigorous reasoning, then (much) later proved correct by mathematicians. A recent example is ...
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The mathematical theory of Feynman integrals
It is well known that Feynman integrals are one of the tools that physicists have and mathematicians haven't, sadly.
Arguably, they are the most important such tool. Briefly, the question I'd like to ...
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What is Quantization ?
I would like to know what quantization is, I mean I would like to have some elementary examples, some soft nontechnical definition, some explanation about what do mathematicians quantize?, can we ...
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What is the motivation for a vertex algebra?
The mathematical definition of a vertex algebra can be found here:
http://en.wikipedia.org/wiki/Vertex_operator_algebra
Historically, this object arose as an axiomatization of "vertex operators" in "...
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What are good mathematical models for spider webs?
Sometimes I see spider webs in very complex surroundings, like in the middle of twigs in a tree or in a bush. I keep thinking “if you understand the spider web, you understand the space around it”. ...
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Motivating the Laplace transform definition
In undergraduate differential equations it's usual to deal with the Laplace transform to reduce the differential equation problem to an algebraic problem.
The Laplace transform of a function $f(t)$, ...
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What is the symbol of a differential operator?
I find Wikipedia's discussion of symbols of differential operators a bit impenetrable, and Google doesn't seem to turn up useful links, so I'm hoping someone can point me to a more pedantic discussion....
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Geometric / physical / probabilistic interpretations of Riemann zeta($n>1$)?
What are some physical, geometric, or probabilistic interpretations of the values of the Riemann zeta function at the positive integers greater than one?
I've found some examples:
1) In MO-Q111339 ...
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What is the amplituhedron?
The paper ”Scattering Amplitudes and the Positive Grassmannian” by Nima Arkani-Hamed, Jacob L. Bourjaily, Freddy Cachazo, Alexander B. Goncharov, Alexander Postnikov, and Jaroslav Trnka, introduces ...
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The Planck constant for mathematicians
The questions
Q1. What are simple ways to think mathematically about the physical meanings of the Planck constant?
Q2. How does the Planck constant appear in mathematics of quantum mechanics? In ...
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Should water at the scale of a cell feel more like tar?
The Navier-Stokes equations are as follows,
$$\dot{u}+(u\cdot \nabla ) u +\nu \nabla^2 u =\nabla p$$
where $u$ is the velocity field, $\nu$ is the viscosity, and $p$ is the pressure.
Some elementary ...
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A reading list for topological quantum field theory?
Can you suggest a reading list, or at least a few papers that you think would be useful, for a beginner in topological quantum field theory? I know what the curvature of a connection is, know basic ...
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Mathematical applications of quantum field theory
I understand that quantum field theories are interesting as physics; however, there is also a large community of mathematicians who are interested in them. For someone who is not at all interested in ...
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A roadmap to Hairer's theory for taming infinities
Background
Martin Hairer gave recently some beautiful lectures in Israel on "taming infinities," namely on finding a mathematical theory that supports the highly successful computations from quantum ...
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Physical meaning of the Lebesgue measure
Question (informal)
Is there an empirically verifiable scientific experiment that can empirically confirm that the Lebesgue measure has physical meaning beyond what can be obtained using just the ...
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Is there a mathematical and information theoretic explanation for this cube packing phenomenon?
I saw this unintuitive result on dice packing:
A jumble of thousands of cubic dice, agitated by an oscillating
rotation, can rapidly become completely ordered, a result that is hard
to produce with ...
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Mathematician trying to learn string theory
I'm a mathematician. I want to be able to read recent ArXiv postings on high energy physics theory (String theory) (and perhaps be able to do research). I want to understand compactifications, ...
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Recent observation of gravitational waves
It was exciting to hear that LIGO detected the merging of two black
holes one billion light-years away. One of the black holes had 36
times the mass of the sun, and the other 29. After the merging the
...
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Poincaré Conjecture and the Shape of the Universe
Has the solution of the Poincaré Conjecture helped science to figure out the shape of the universe?
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(How) is category theory actually useful in actual physics?
An answer to a recent question motivated the following question:
(how) is category theory actually
useful in actual physics?
By "actual physics" I mean to refer to areas where the underlying ...
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Why is Quantum Field Theory so topological?
I understand that my question suffers from my lack of knowledge about the field, but as a mathematician without much knowledge of physics I have been wondering much about the following and I always ...
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Mathematical explanation of the failure to quantize gravity naively
One often hears in popular explanations of the failure to find a "Grand Unified Theory" that "Gravity goes off to infinity, but cutting off the edges gives us wrong answers", and other similar ...
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The Unreasonable Effectiveness of Physics in Mathematics. Why ? What/how to catch?
Starting from 80-ies the ideas either coming from physics, or by physicists themselves (e.g. Witten) are shaping many directions in mathematics. It is tempting to paraphrase E. Wigner, saying about "...
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What is a symplectic form intuitively?
Hi,
to completely describe a classical mechanical system, you need to do three things:
-Specify a manifold $X$, the phase space. Intuitively this is the space of all possible states of your system.
-...
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What are the main contributions to the mathematics of general relativity by Sir Roger Penrose, winner of the 2020 Nobel prize?
I received an email today about the award of the 2020 Nobel Prize in Physics to Roger Penrose, Reinhard Genzel and Andrea Ghez. Roger Penrose receives one-half of the prize "for the discovery ...
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are there natural examples of classical mechanics that happens on a symplectic manifold that isn't a cotangent bundle?
I'm curious about just how far the abstraction to a symplectic formalism can be justified by appeal to actual physical examples. There's good motivation, for example, for working over an arbitrary ...
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Classical geometric interpretation of spinors
A lot of notions in differential geometry have direct meaning in Physics. For example:
A Riemannian metric is a way to encode distances on a manifold and in Physics it is the gravitational field. The ...
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Standard model of particle physics for mathematicians
If a mathematician who doesn't know much about the physicist's jargon and conventions had the curiosity to learn how the so called Standard Model (of particle physics, including SUSY) works, where ...
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The two ways Feynman diagrams appear in mathematics
I've heard about two ways mathematicians describe Feynman diagrams:
They can be seen as "string diagrams" describing various type of arrows (and/or compositions operations on them) in a monoidal ...
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Quantum mechanics formalism and C*-algebras
Many authors (e.g Landsman, Gleason) have stated that in quantum mechanics, the observables of a system can be taken to be the self-adjoint elements of an appropriate C*-algebra. However, many ...
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Good references for Rigged Hilbert spaces?
Every now and then I attempt to understand better quantum mechanics and quantum field theory, but for a variety of possible reasons, I find it very difficult to read any kind of physicist account, ...
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What is Chern-Simons theory?
What is Chern-Simons theory? I have read the wikipedia entry, but it's pretty physics-y and I wasn't really able to get any sense for what Chern-Simons theory really is in terms of mathematics.
Chern-...
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Book on mathematical "rigorous" String Theory?
I've been looking high and low for a mathematical book on String Theory. The only book I could find was "A Mathematical Introduction to String Theory" by Albeverio, Jost, Paycha and ...
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The 'real' use of Quantum Algebra, Non-commutative Geometry, Representation Theory, and Algebraic Geometry to Physics
In this question, Orbicular made the following comment to Feb7 and my own answers;
Please keep in mind that - even though it is stated very often - noncommutative geometry does not give "real" ...
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Number theory and physics
I was following some lectures by Edward Frenkel about Langlands correspondence. He was describing some analogies between number theory and theoretical physics (Mirror symmetry). At some point ( my ...
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Is there a mathematical axiomatization of time (other than, perhaps, entropy)?
Since Euclid's axiomatization of space, we have developed a sophisticated mathematical model of space. Given a category of structures (measures), local space is modeled the spectrum of measurements ...
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Examples of non-rigorous but efficient mathematical methods in physics
There are situations of applications of mathematics in physics which
seem to work well enough for physicists (for example they agree with the experimental data)
but are considered unacceptable or at ...
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How much of mathematical General Relativity depends on the Axiom of Choice?
One of the cornerstones of the mathematical formulation of General Relativity (GR) is the result (due to Choquet-Bruhat and others) that the initial value problem for the Einstein field equations is ...
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Recent fundamental new directions in PDEs
My main interests are in modern geometry/topology, algebra and mathematical physics. I observe that there is a raising communication, language and social barrier between this community and the ...
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Dimensional Analysis in Mathematics
Is there a sensible and useful definition of units in mathematics? In other words, is there a theory of dimensional analysis for mathematics?
In physics, an extremely useful tool is the Buckingham Pi ...