Questions tagged [mathematical-physics]

Question 1

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 ...

Question 2

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 ...

Question 3

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 ...

Question 4

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 & ...

Question 5

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 ...

Question 6

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 ...

Question 7

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 \...

Question 8

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 ...

Question 9

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-...

Question 10

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 ...

Question 11

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 ...

Question 12

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,...

Question 13

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 ...

Question 14

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 ...

Question 15

In $3$-dimensional Euclidean space, one can show that the delta function centered at the origin is spherically symmetric in its argument, resulting in the following expression in spherical coordinates:...

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Questions tagged [mathematical-physics]

Can one prove that two 2-forms with the same kernel are proportional to one another in this specific setting?

Splitting of the Chiral de Rham differential for affine space

How to understand the twists physicists use in topological string theory?

Are the $\sqrt n$ prefactors "natural" in creation/annihilation operator definitions?

Origins of the Airy function [closed]

Optimal way to stack blocks for maximum overhang

question about the use of Schwinger Feynman parameters.

Symmetry-invariant (local) Hodge decomposition

Why must the highest derivative term in an ODE absorb a Dirac delta impulse?

Left-invariant vector fields on super Minkowski space

Neglecting higher order terms in a PDE: why?

How can universal invariants emerge from a coupled hyperdimensional system with Hadamard-product interactions?

Literature on finite-dimensional subrepresentations in $\text{End}(H)$ (including unbounded operators)

Reference request: tensor products of principal series of $SL(2,\mathbb{C})$

Delta function in Minkowski space

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