# Tag Info

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We have also the same notions of derivation, curl, etc... for functions that are less regular. When you write Maxwell's equations, you are writing a system of partial differential equations. To investigate them, you have to specify the type of solution you look for (in the language of PDEs: classic, mild, weak...) and the functional space you set your ...

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I'm the developer of a project called the Physics Derivation Graph. https://sites.google.com/site/physicsderivationgraph https://code.google.com/p/physics-equations-graph/ My intention is to develop a set of derivations into a graph which would capture the current state of knowledge in Physics. Although I consider automated reasoning outside the scope of my ...

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I learned my GR from Landau and Lifshitz Classical Theory of Fields, 2nd edition. Even at 402 (4th Edition) pages it is kind of breathless. The interesting thing about it is the first half is special relativity and electrodynamics which dovetails into the 2nd half which is GR. One has to persivere because it's terse but not too terse. Like Weinberg it has a ...

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My references are very good reviews: Quantum inverse scattering and Algebraic Bethe Ansatz: Faddeev: How Algebraic Bethe Ansatz works for integrable model Kulish and Sklyanin: Quantum Spectral Transform Method. Recent Developments Takhtajan: Introduction to algebraic Bethe ansatz and the Books: Jimbo and Miwa: Algebraic Analysis of Solvable Lattice ...

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Lectures by Ashoke Sen are very deep and insightful. https://www.youtube.com/watch?v=mBytE2daw3k

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One of the major issues that seems to be going on here is the notion of point and surface structures in our 3D world. When we define electrostatic fields by a distribution of point charges, we are being somewhat non-physical. If we keep zooming in on an electron, it's going to start not looking like a point charge anymore. Consider the Darwin Term in the ...

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The Classical Theory of Fields by Landau and Lifshitz fits the bill reasonably well. It doesn't develop electrodynamics from scratch in the context of a curved spacetime, but it does have a three-page section covering the equations of electrodynamics in a curved spacetime, after spending seven chapters developing electrodynamics in the context of flat ...

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This very much depends on what you want to do in the area of quantum theory. If you want to solve specific mathematical problems and to have only a very rough conception of why you are doing what you are doing, then you can in principle omit classical mechanics. But if you want to have a well-rounded knowledge of the subject, you should know some basics of ...

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Both ways are possible. Since you seem to be a mathematician, let me try an analogy from mathematics. Say that you are accomplished in commutative algebra. Now, you want to study algebraic geometry. Sure, you can start with sheaves of local rings and cohomology of schemes, instead of "at the bottom" with classical algebraic varieties defined by polynomial ...

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This is discussed in detail in A Relativists Toolkit by Eric Poisson. The original ADM paper is on the arxiv, and while the notation is old, the arguments are clear.

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I am the author of the astronomy and physics ontology mentioned in the original question. The original purpose of that ontology was to improve search for data and articles in astronomy. The idea was to have data sets tables and individual columns in tables marked up with relevant keywords. The rows of data in astronomy are usually different astronomical ...

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It's hard to understand what exactly is being asked, so here is a first stab. I can update if further clarification is given. First, yes a quantum computer can be used to do classical calculations. In this case there will be no entanglement, and so the result is not probabilistic (except for any issues caused by decoherence, but it is assumed this is ...

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It is indeed possible to make experimental realizations which are very close to the ideal infinite quantum well. The cleanest way to do this is using what are known as nanostructures / heterostructures in semiconductor joints, as well as quantum dots and quantum wires. Semiconductor nanostructures work by confining electrons to the interface between layers ...

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For an introductory book on the topic, consider "Numerical and Analytical Methods for Scientists and Engineers, Using Mathematica" by Daniel Dubin (ISBN-13: 978-0471266105). Whats sets this book apart from the rest is that it combines theoretical physics, teaches the math, and solves practical physics problems both by hand and by using Mathematica. This ...

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I think you should have a look at Reed&Simons classic book on mathematical physics ("Methods of Modern Mathematical Physics", 4 volumes). Excellent and clear writing style, many further references and it covers most of the important analytic methods which are used in physics. For geometry stuff, I recommend Bishops "Tensor analysis on manifolds". Very ...

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What you need is Kirchhoff's Matrix-Tree Theorem which expresses ${\rm det}\ A$ as a sum of trees. You can find an easy "Fermionic" proof of this theorem and a list of original references in my article "The Grassmann-Berezin calculus and theorems of the matrix-tree type" (arXiv version here if you do not have access to the journal).

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There's a discussion of this stuff in Wald, pp. 291ff. It must be a pretty accessible treatment, because I was able to understand some of it. The style is Wald's usual dry, mathematical, concise one, but he also gives some simple interpretations.

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NASA still images; audio files; video; and computer files used in the rendition of 3-dimensional models, such as texture maps and polygon data in any format, generally are not copyrighted. You may use NASA imagery, video, audio, and data files used for the rendition of 3-dimensional models for educational or informational purposes, including photo ...

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You might find Gauge Fields, Knots, and Gravity by Baez & Muniain useful. It doesn't specifically deal with electromagnetism in curved spacetime, however, the first chapter develops differential geometry with the goal of reformulating Maxwell's equations. It assumes no knowledge of GR. The third and final chapter develops some aspects of GR.

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Something like $\textbf{E}(\textbf{r}) \propto (\textbf{r}-\textbf{r}^{\prime})/|\textbf{r}-\textbf{r}^{\prime}|^{3}$ due to a static point charge does not belong to the appropriate class of functions (differentiable, square-integrable, etc.) for $\textbf{E}$ fields. In a mathematically precise sense, it is not a solution to Maxwell's equations. Still, we ...

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If I've understood you correctly, you want rigourous mathematical formalism to treat PDE solutions which are not differentiable or not square-integrable etc. That is, you can have those point charges with fields blown up on them, fields being not differentiable on boundaries and so on. There exists a rigourous formalism to treat such things. It is called ...

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See for example Topics in Koopman-von Neumann Theory by D. Mauro. This should be one of the most extensive overviews of KvN Theory, it also contains some examples of applying this theory to some well known problems such as Aharonov-Bohm Effect.

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