Questions tagged [mathematical-physics]
DO NOT USE THIS TAG for elementary 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.
4,256 questions
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Exercise in Acoustic Doppler Effect
I am looking for some guidance on the second part of a geometry type problem which I have given a scan on and partial workings below (likely with a procedure error e.g. wrong Maclaurin series). I ...
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Can one prove that two 2-forms with the same kernel are proportional to one another in this specific setting?
My name is Sarah and I am currently writing my Bachelorthesis about the paper A property of conformally Hamiltonian vector fields; application to the Kepler problem by Charles-Michel Marle (2012).
You ...
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Splitting of the Chiral de Rham differential for affine space
I am currently reading through Malikov, Schechtman and Vaintrob's paper Chiral de Rham Complex. In the proof of Theorem 2.4, i.e. that the chiral de Rham complex extends the usual de Rham complex for ...
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How to understand the twists physicists use in topological string theory?
I have a very hard time to understand something physicists call $A$ or $B$ twists in the context of topological string theory. A canonical reference seems to be this Witten's paper.
Let $\Sigma$ be a ...
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Are the $\sqrt n$ prefactors "natural" in creation/annihilation operator definitions?
On the symmetrized (bosonic) Fock space $\mathcal F_{\mathcal B}$, the standard creation and annhilation operators are defined by
\begin{align*}
A^{\dagger}(e_k) |\, n_1,n_2,...,n_k,... \rangle
& ...
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Origins of the Airy function [closed]
The Airy functions $\text{Ai}(x)$ and $\text{Bi}(x)$, first studied by astronomer George Biddell Airy, are linearly independent solutions to the differential equation $$\frac{d^2 y}{dx^2} - xy = 0$$
I ...
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Optimal way to stack blocks for maximum overhang
The figure shown above shows the optimal way for stacking 30 blocks to get the maximum overhang. How does one verify/prove that this shape is indeed the best way to stack the blocks to achieve the ...
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question about the use of Schwinger Feynman parameters.
Note: This is a crosspost of https://physics.stackexchange.com/questions/860755/use-of-schwinger-feynman-parameters-in-a-complex-integral
I am trying to evaluate the following integral:
$$ -\int \...
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Symmetry-invariant (local) Hodge decomposition
Consider a differential 2-form field $F$ on a 4d oriented smooth spacetime manifold $M$ endowed with a Lorentzian metric $g$. We additionally have an infinitesimal group action $\Gamma$ on $M$ of a ...
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Why must the highest derivative term in an ODE absorb a Dirac delta impulse?
In modeling systems with impulsive inputs, the Dirac delta function often appears on the right-hand side of an ordinary differential equation (ODE), such as:
$$
a_n\frac{d^ny}{d x^n}+a_{n-1}\frac{d^{n-...
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Left-invariant vector fields on super Minkowski space
I'm reading Volume 1 of Quantum Fields and Strings: A Course for Mathematicians.
Let $V$ be a Minkowski vector space of signature $(1,d-1)$, and let $\mathrm{Spin}(V) \curvearrowright S$ be an ...
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Neglecting higher order terms in a PDE: why?
This is quite non-rigorous question since I don't think there is a clear-cut theorem answering it. I am deriving a PDE from a system which I know in the limit should give a heat equation. The ...
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How can universal invariants emerge from a coupled hyperdimensional system with Hadamard-product interactions?
I am investigating the mathematical properties of a nonlinear, coupled system intended to unify structures from several deep areas of mathematics (e.g., Birch and Swinnerton-Dyer, Hodge, Navier–Stokes,...
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Literature on finite-dimensional subrepresentations in $\text{End}(H)$ (including unbounded operators)
I have a question about the representation theory of semisimple Lie groups, motivated by concepts from quantum mechanics.
Let $G$ be a semisimple Lie group and let $(\pi, H)$ be a unitary ...
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Reference request: tensor products of principal series of $SL(2,\mathbb{C})$
I am looking for a reference (a textbook, research paper, or lecture notes) that helps me find the rules for which finite-dimensional representations can appear in operator space of tensor product of ...