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2 votes

Why radial quantization gives different spectrum?

I guess I’ve figure out what’s going on, the notion of translation is different (translation on cylinder is rotation and dilation on plane), so we are working with different momentum operators in this ...
Peter Wu's user avatar
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6 votes

Why radial quantization gives different spectrum?

TL;DR: The spectrum is discrete (continuous) since space is a compact circle $\mathbb{S}^1$ (non-compact line $\mathbb{R}^1$), respectively, cf e.g. this Phys.SE post. In more details: The radially ...
Qmechanic's user avatar
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1 vote
Accepted

Understanding Exceptional Points

Regarding the definition of exceptional points, the easiest way to think about them is that the matrix of the eigenvalue problem is not diagonalizable there. They called “points” since almost all ...
Wolpertinger's user avatar
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-1 votes

Understanding Exceptional Points

Most QT books have a chapter of higher order perturbation theory in case of degeneration. Exact quantum theory and the working numerical examples sometimes produce parametrized eigenvalue curves in ...
Roland F's user avatar
0 votes

When one discusses the "boundary" of Anti-de Sitter space, what do they mean precisely?

TL;DR: The conformal boundary of (Euclidean) $AdS_{d+1}$ is easiest to analyse in stereographic coordinates (3), cf. Ref. 1. The bulk of $AdS_{d+1}$ is isomorphic to an open ball $B_{d+1}=\{y\in\...
Qmechanic's user avatar
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4 votes

Are there reasonable models of Earth's surface as the space $\mathbb{R}P^2$?

Often, we treat the Earth's surface as being embedded in 3-dimensional space. Since the real projective plane cannot be embedded in 3-space, the Earth's surface is clearly not equivalent to it in any ...
Sandejo's user avatar
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