Models of Topology Change

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

Models of Topology Change

Oct, 2012

7 pages

e-Print:

1210.3545 [hep-th]

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Abstract: (arXiv)

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.

Note:

7 pages, 3 figures

entropy: entanglement
entropy: production
topology: transition
boundary condition
quantum mechanics
wave function
Hilbert space
quantization
Hamiltonian

References(14)

Figures(3)

[1]

Topology change and quantum physics

A.P. Balachandran
(
- Syracuse U.
)
,
G. Bimonte
(
- ICTP, Trieste and
- INFN, Naples
)
,
G. Marmo
(
- INFN, Naples and
- Naples U.
)
,
A. Simoni
(
- INFN, Naples and
- Naples U.
)

- Nucl.Phys.B 446 (1995) 299-314
•
e-Print:
- gr-qc/9503046
•
DOI:
- 10.1016/0550-3213(95)00260-Y

[2]

Global theory of quantum boundary conditions and topology change

M. Asorey
(
- Zaragoza U.
)
,
A. Ibort
(
- Carlos III U., Madrid
)
,
G. Marmo
(
- Naples U. and
- INFN, Naples
)

- Int.J.Mod.Phys.A 20 (2005) 1001-1026
•
e-Print:
- hep-th/0403048
•
DOI:
- 10.1142/S0217751X05019798

[3]

Allgemeine Eigenwerttheorie Hermitescher Funktionaloperatoren

J. v. Neumann

- Math.Ann. 102 (1930) 1, 49-131
•
DOI:
- 10.1007/bf01782338

[4]

Methods of Modern Mathematical Physics, Vol. 2: Fourier Analysis, Self Adjointness Press, 1975]

M. Reed
,
B. Simon

[5]

Kirchoff's rule for quantum wires

V. Kostrykin
(
- Aachen, Tech. Hochsch.
)
,
R. Schrader
(
- Freie U., Berlin
)

- J.Phys.A 32 (1999) 595-630
•
e-Print:
- math-ph/9806013
•
DOI:
- 10.1088/0305-4470/32/4/006

[6]

Branched Quantization

Alfred Shapere
(
- Kentucky U.
)
,
Frank Wilczek
(
- MIT, LNS
)

- Phys.Rev.Lett. 109 (2012) 200402
•
e-Print:
- 1207.2677
•
DOI:
- 10.1103/PhysRevLett.109.200402

[7]

Classical Time Crystals

Alfred Shapere
(
- Kentucky U.
)
,
Frank Wilczek
(
- MIT, LNS
)

- Phys.Rev.Lett. 109 (2012) 160402
•
e-Print:
- 1202.2537
•
DOI:
- 10.1103/PhysRevLett.109.160402

[8]

Hamiltonian description of singular Lagrangian systems with spontaneously broken time translation symmetry

- Mod.Phys.Lett.A 28 (2013) 1350002
•
e-Print:
- 1206.2983
•
DOI:
- 10.1142/S0217732313500028

[9]

Path Integral Junctions

Satoshi Ohya
(
- Harish-Chandra Res. Inst.
)

- J.Phys.A 45 (2012) 255305
•
e-Print:
- 1201.5115
•
DOI:
- 10.1088/1751-8113/45/25/255305

[10]

The Structure of the Gauge Theory Vacuum

Curtis G. Callan, Jr.
(
- Princeton U.
)
,
R.F. Dashen
(
- Princeton, Inst. Advanced Study
)
,
David J. Gross
(
- Princeton U.
)

- Phys.Lett.B 63 (1976) 334-340,
- Also in *Mohapatra, R. N. (ed.), Lai, C. H. (ed.): Gauge Theories Of Fundamental Interactions*, 378-384,
- Also in *Rebbi, C. (ed.), Soliani, G. (ed.): Solitons and Particles*, 770-776. ( Phys. Lett. B63 ( 1976) 334-340) and Preprint - CALLAN, C.G. (REC.AUG.76) 18p,
•
DOI:
- 10.1016/0370-2693(76)90277-X

[10]

Vacuum Periodicity in a Yang-Mills Quantum Theory

R. Jackiw
(
- MIT, LNS
)
,
C. Rebbi
(
- MIT, LNS
)

- Phys.Rev.Lett. 37 (1976) 172-175,
•
DOI:
- 10.1103/PhysRevLett.37.172

[11]

Magnetic Flux, Angular Momentum, and Statistics

Frank Wilczek
(
- Santa Barbara, KITP
)

- Phys.Rev.Lett. 48 (1982) 1144-1146
•
DOI:
- 10.1103/PhysRevLett.48.1144

[12]

Spectral asymmetry and Riemannian geometry

M. Atiyah
,
V. Patodi
,
I. Singer

- Math.Proc.Cambridge Phil.Soc. 79 (1976) 99

[13]

Fractional Quantum Numbers on Solitons

Jeffrey Goldstone
(
- SLAC
)
,
Frank Wilczek
(
- Santa Barbara, KITP
)

- Phys.Rev.Lett. 47 (1981) 986-989,
•
DOI:
- 10.1103/PhysRevLett.47.986