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Schematic of a Möbius strip. es and er are two tangent unit basis vectors, and en is the normal unit basis vector of Möbius strip. The local frames F 1 , F 2 and F 3 are localized at θ = 0, 4π 3 , 8π 3 , respectively.
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The geometric effects of two-dimensional curved systems have been an interesting topic for a long time. A Möbius surface is specifically considered. For a relativistic particle confined to the nontrivial surface, we give the effective Dirac equation in the thin-layer quantization formalism, and we find a geometric gauge potential that results from...
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Context 1
... θ and r are two variables with θ ∈ [0, 4π] and r ∈ [−w, w], R can be taken as a constant. The Möbius strip is denoted as M 2 and sketched in Fig. 1. For convenience, we can adapt an orthogonal frame spanned by two tangent vectors e s and e r and a normal vector e n . According to Eq. (1), we can obtain the three basis vec-tors ...
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