Physics – Quantum Physics
Scientific paper
2009-10-30
Physics
Quantum Physics
128 graphics files
Scientific paper
Using the cubic honeycomb (cubic tessellation) of Euclidean 3-space, we define a quantum system whose states, called quantum knots, represent a closed knotted piece of rope, i.e., represent the particular spatial configuration of a knot tied in a rope in 3-space. This quantum system, called a quantum knot system, is physically implementable in the same sense as Shor's quantum factoring algorithm is implementable. To define a quantum knot system, we replace the standard three Reidemeister knot moves with an equivalent set of three moves, called respectively wiggle, wag, and tug, so named because they mimic how a dog might wag its tail. We argue that these moves are in fact more "physics friendly" because, unlike the Reidemeister moves, they respect the differential geometry of 3-space, and moreover they can be transformed into infinitesimal moves. These three moves wiggle, wag, and tug generate a unitary group, called the lattice ambient group, which acts on the state space of the quantum system. The lattice ambient group represents all possible ways of moving a rope around in 3-space without cutting the rope, and without letting the rope pass through itself. We then investigate those quantum observables of the quantum knot system which are knot invariants. We also study Hamiltonians associated with the generators of the lattice ambient group. We conclude with a list of open questions.
Kauffman Louis H.
Lomonaco Samuel J.
No associations
LandOfFree
Quantum Knots and Lattices, or a Blueprint for Quantum Systems that Do Rope Tricks does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Quantum Knots and Lattices, or a Blueprint for Quantum Systems that Do Rope Tricks, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Quantum Knots and Lattices, or a Blueprint for Quantum Systems that Do Rope Tricks will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-90116