C J Isham 1989 Class. Quantum Grav. 6 1509 doi:10.1088/0264-9381/6/11/007
C J Isham
Show affiliationsThe concept of 'quantum topology' is studied via a quantisation of the set tau (X) of all topologies on a given set X. A natural lattice structure exists on this set induced by the idea of one topology having more, or less, open sets than other. This is used to provide a basic set of functions on tau (X) which generate a commutative algebra (the v operation on the lattice) whose spectral theory forms the basis for a general quantisation. It is shown that the analogue of a 'distributional' topology is an ideal in the lattice tau (X) and the spectral theory is used to place a natural topology on the set of all such ideals. The next step is to discuss the existence of variables conjugate to the basic functions on tau (X).
81Rxx Groups and algebras in quantum theory
Issue 11 (November 1989)
C J Isham 1989 Class. Quantum Grav. 6 1509
Marco Bruni et al 1997 Class. Quantum Grav. 14 2585
W Bremser et al 2007 Metrologia 44 495
J T MacGregor-Morris and E Mallett 1923 Proc. Phys. Soc. London 36 139
Bartolo Luque et al 2005 J. Phys. A: Math. Gen. 38 1031
U. R. Fischer and M. Visser 2003 Europhys. Lett. 62 1
A A Risbud 2005 J. Phys. D: Appl. Phys. 38 1081
T Dereli and R W Tucker 2004 Class. Quantum Grav. 21 1459
A J F Metherell and T J Quinn 1986 Metrologia 22 87
Jian Ge et al 2001 ApJ 547 L1