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Models of Topology Change · Around

2012

Models of Topology Change

Shapere, Alfred D., Wilczek, Frank, Xiong, Zhaoxi

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We show how changes in unitarity-preserving boundary conditions allow continuous interpolation among the Hilbert spaces of quantum mechanics on topologically distinct manifolds.

We present several examples, including a computation of entanglement entropy production.
We discuss approximate realization of boundary conditions through appropriate interactions, thus suggesting a route to possible experimental realization.
We give a theoretical application to quantization of singular Hamiltonians, and give tangible form to the "many worlds" interpretation of wave functions.

Built on

J. von Neumann, “Allgemeine Eigenwerttheorie Hermitescher Funktionaloperatoren,” Math. Ann., 102
1929
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M. Reed and B. Simon, Methods of Modern Mathematical Physics, Vol. 2: Fourier Analysis, Self Adjointness
1975
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C. Callan, R. Dashen and D. Gross “Structure of the Gauge Theory Vacuum” Phys. Lett. B63
1976
Earlier work this paper cites.

Similar

M. Atiyah, V. Patodi and I. Singer, “Spectral asymmetry and Riemannian geometry”, Math. Proc. Camb. Phil. Soc. 79
1976
Cited alongside, same era.
J. Goldstone and F. Wilczek, “Fractional Quantum Numbers on Solitons”, Phys. Rev. Lett. 47
1981
Cited alongside, same era.
F. Wilczek “Magnetic Flux, Angular Momentum, and Statistics” Phys. Rev. Lett. 48
1982
Cited alongside, same era.
V. Kostrykin and R. Schrader, “Kirchhoff’s rule for quantum wires”, J. Phys. A: Math. Gen. 32
Cited in the paper.
A. Shapere and F. Wilczek, “Branched Quantization,” arXiv:1207.2677 [quant-ph]
Original
Cited in the paper.
A. Shapere and F. Wilczek, “Classical Time Crystals,” arXiv:1202.2537 [cond-mat.other]
Original
Cited in the paper.
L. Zhao, P. Yu and W. Xu, “Hamiltonian description of singular Lagrangian systems with spontaneously broken time translation symmetry,” arXiv:1206.2983 [hep-th]
Original
Cited in the paper.

Then

A. P. Balachandran, G. Bimonte, G. Marmo and A. Simoni, “Topology change and quantum physics,” Nucl. Phys. B 446
1995
Later among the works it cites.
M. Asorey, A. Ibort and G. Marmo, “Global theory of quantum boundary conditions and topology change,” Int. J. Mod. Phys. A 20
2005
Later among the works it cites.
S. Ohya, “Path Integral Junctions,” J. Phys. A A 45
Original
2012
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