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Although you might find most applications of the concept of Berry's phases in condensed matter physics, it is really present in most areas of physics as it captures the deep connection between geometry and physics. Plainly stated, this connection stems from the fact that for the really interesting problems in physics, wave functions are not functions on the ...


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Physically, the question of what happens precisely at the corner points isn't especially meaningful. Instead, you could think about phenomena in a neighborhood of the points (e.g. flux through a circle or tube enclosing the singularity), and use that to characterize the point itself. By definition, a manifold should be locally Euclidean. Any open ...


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I would like to add two concrete examples where topology plays a major role in classical and perhaps every day physics. The topologic relevance here is that in both examples the space non simply connected and that makes all the difference. The references are in the titles below. Aharonov-Bohm analogue in water waves: This was proposed and also verified by ...


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I think this is approach is the correct one. Here is from a paper I have written: The primary insight of this is that if we modify our concept of ‘local’, much of the strangeness may disappear. Specifically, consider that 4-dimensional space-time is a construct that is projected onto an underlying topology that I will call ‘true space’. The fundamental idea ...


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The general story Here's an attempt to formalize how physicists build spacetime manifolds. Let $N$ be one of $\mathbb R^n$ Some dimension $n$ product manifold of $S^1$ and $\mathbb R$ (corresponding to periodic solutions). Pick one such $N$. Now Take stress tensor $T$ defined on some open subset $U \subset N$ and some boundary conditions (e.g. ...



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