Questions tagged [mathematical-physics]

DO NOT USE THIS TAG for elemetary physical questions. This tag is intended for questions on modern mathematical methods used in quantum theory, general relativity, string theory, integrable system etc at an advanced undergraduate or graduate level.

146 questions
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Why do zeta regularization and path integrals agree on functional determinants?

When looking up the functional determinant on Wikipedia, a reader is treated to two possible definitions of the functional determinant, and their agreement is trivial in finite dimensions. The first ...
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Do infinity and zero really exist? [closed]

From the first day that I entered college, I was wondering about the relationship between some basic mathematical abstract concepts and nature. I'm going to explain them here and you may find them a ...
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What exactly are pseudovectors and pseudoscalars? And where could I read about them?

I can't find good information on the internet. In my mathematical physics class the definition of a vector was given as: That object with magnitude and direction which doesn't change under ...
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Quantum mechanical books for mathematicians

I'm a mathematician. I have good knowledge of superior analysis, distribution theory, Hilbert spaces, Sobolev spaces, and applications to PDE theory. I also have good knowledge of differential ...
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Is $\nabla$ a vector?

The following passage has been extracted from the book "Mathematical methods for Physicists": A key idea of the present chapter is that a quantity that is properly called a vector must have the ...
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How to evaluate the following items in mathematical methods in physics? [closed]

I had taken a long break from math and physics for months due to stress and an illness so when I returned to it and tried answering problems given, I had difficulty figuring out how to do some of them ...
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Correct spaces for quantum mechanics

The general formulation of quantum mechanics is done by describing quantum mechanical states by vectors $|\psi_t(x)\rangle$ in some Hilbert space $\mathcal{H}$ and describes their time evolution by ...
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Is $1+2+3+4+\cdots=-\frac{1}{12}$ the unique ''value'' of this series?

I'm reading about zeta-function regularization in physics and I have some mathematical doubt. I understand that, since a sum of infinite terms is not well defined in a field, a series that is ...
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Principal value of 1/x- equivalence of two definitions

As far as I know, the principal value of a non-summable function like $1/x$, denoted $\mathcal{P}(1/x)$, is a distribution that that acts on some smooth function $f$ in some test-function space and ...
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Physical interpretation of $L_1$ and $L_2$ norms

In signal analysis, students have no qualms about associating the $L_2$ norm of a square integrable function $f(t)$ as the energy associated with that signal. A good understanding of whether a ...
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Regularity of an infinite series arising with the heat equation

Let $(t,y)\in(0,\infty)\times\mathbf{R}$, and $\displaystyle f(t,y) \equiv \sum_{k=-\infty}^{\infty}\frac{\exp(-(y-2\pi k)^2/2t)}{\sqrt{2\pi t}}$. This infinite series arises if one attempts to solve ...
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What is a good reference for rigorous Electromagnetism and Electrodynamics?

Is there any good book on Electromagnetism from a more mathematical point of view? By this I mean a book which makes use of differential forms and maybe De Rham cohomology. I was also searching for ...
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What are defining & fundamental representations?

In physics terminology, one hears of the fundamental & defining representations of lie algebras or groups - are these the same as irreducible representations?
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I got an assignment to prove that in a straight homogeneous rod, you can always choose a coordinate system in such a way that $$\int_S x_1 \, dx_1 \, dx_2=0$$ $$\int_S x_2 \, dx_1 \, dx_2=0$$ $$\... 2answers 13k views Open problems in General Relativity I would like to know if there are some open mathematical problems in General Relativity, that are important from the point of view of Physics. Is there something that still needs to be justified ... 4answers 14k views String Theory: What to do? This is going to be a relatively broad/open-ended question, so I apologize before hand if it is the wrong place to ask this. Anyways, I'm currently a 3rd year undergraduate starting to more seriously ... 4answers 7k views What's the Clifford algebra? I'm reading a book on Clifford algebra for physicists. I don't quite understand it conceptually even if I can do most algebraic manipulations. Can some-one teach me what the Clifford algebra really is?... 2answers 2k views Prerequisite for Takhtajan's “Quantum Mechanics for Mathematicians” I want to know the math that is required to read Quantum Mechanics for Mathematicians by Takhtajan. From the book preview on Google, I gather that algebra, topology, (differential) geometry and ... 11answers 7k views Find the height of a bar, given the lengths of shadows cast by it and another bar [duplicate] What is the height of the red bar? My try: with respect to the picture, it seems for the green bar \frac{h}{H}=\frac{2}{3}. So, I think that ratio is the same for the red bar, and the height of the ... 1answer 1k views Guide to mathematical physics? I am currently a math phd student specializing in algebraic geometry aspiring to work at the boundaries of the the fields of mathematics and physics and so, was looking into the field of mathematical ... 5answers 1k views In what ways has physics spurred the invention of new mathematical tools? I came across this comment: Mathematical rigor is not a criterion that physicists have for evaluating their theories. From a mathematical perspective, the non-rigorous theories are far more ... 2answers 1k views Intuition behind definition of spinor Some time ago I searched for the definition of spinors and found the wikipedia page on the subject. Although highly detailed the page tries to talk about many different constructions and IMHO doesn't ... 4answers 2k views Is there any abstract theory of electrical networks? Designing electrical networks is among the highly mathematical engineering disciplines, which uses a vast scope of techniques from Fourier analysis and complex function theory, to logic, combinatorics ... 4answers 4k views Gentle introduction to fibre bundles and gauge connections To better understand papers like this for example, which makes heavy use of fibre bundles and gauge connections to represent gauge fields, I am looking for a nice introduction to this topic. The only ... 4answers 952 views Gathering books on Lorentzian Geometry I find it very hard to find books on Lorentzian Geometry, more focused on the geometry behind it, instead of books that go for the physics and General Relativity approach. More specifically, I'm ... 2answers 830 views Applications of Algebra in Physics Often I have heard about the link between Algebra (in particular Representations of Groups and Algebras) and some "indefinite" field of Physics. I have a good preparation in Algebra and ... 4answers 2k views What is Octave Equivalence? This is an updated copy of a question I asked on Physics Stack Exchange not too long ago. Since I work primarily in mathematics, I thought it would be a good idea to ask it here as well (especially ... 1answer 636 views Mathematical background for TQFT I am physicist. I`ve started studying Topological QFT. What would you recommend to read in mathematical field for understanding Witten’s old articles of 80s-90s? What books/articles could help form ... 2answers 943 views Existence and uniqueness of Stokes flow What are the solution existence and uniqueness conditions for Stokes' flow?$$\begin{gathered} \nabla p = \mu \Delta \vec{u} + \vec{f} \\ \nabla \cdot \vec{u} = 0 \end{gathered}$$Maybe you could ... 2answers 3k views What are elements in SU(1, 1)? I am reading some papers in physics. I don't know some notations in those papers. For example, SU(1, 1), U(1). I think these are Lie groups which consist of matrices. But I don't know what kind of ... 2answers 793 views Reference request: toric geometry What is a good book on algebraic geometry, with focus on toric varieties, similar both in the philosophy and in the prestige of the authors to Modern Geometric Structures and Fields by Novikov and ... 2answers 886 views Evaluate the Integral using Contour Integration (Theorem of Residues)$$ J(a,b)=\int_{0}^{\infty }\frac{\sin(b x)}{\sinh(a x)} dx  This integral is difficult because contour integrals normally cannot be solved with a sin(x) term in the numerator because of ...
In Quantum mechanics we said that $\langle x'|\psi \rangle = \psi(x)$, where $\langle \phi|\psi \rangle$ is the dot product in $L^2(\mathbb{C})$. I found out, that this is true, if you set x' to ...