Quantum holonomy theory
نویسندگان
چکیده
منابع مشابه
Topological Field Theory and Quantum Holonomy Representations of Motion Groups
Canonical quantization of abelian BF -type topological field theory coupled to extended sources on generic d-dimensional manifolds and with curved line bundles is studied. Sheaf cohomology is used to construct the appropriate topological extension of the action and the topological flux quantization conditions, in terms of the Čech cohomology of the underlying spatial manifold, as required for t...
متن کاملNew Anatomy of Quantum Holonomy
The interest in Berry’s geometric phase is now two-fold. Theoretical interest to this quintessentially quantum phenomenon is well documented [1]. The central importance is in the appearance of the gauge structure in parametric space [2–4]. Immediate utility of geometric phase is recently highlighted by the suggestion of holonomic and adiabatic quantum computings [5–9]. Consider the change of a ...
متن کاملOff-diagonal quantum holonomy along density operators
Uhlmann’s concept of quantum holonomy for paths of density operators is generalised to the off-diagonal case providing insight into the geometry of state space when the Uhlmann holonomy is undefined. Comparison with previous off-diagonal geometric phase definitions is carried out and an example comprising the transport of a Bell-state mixture is given.
متن کاملHolonomy Loops, Spectral Triples & Quantum Gravity
We review the motivation, construction and physical interpretation of a semi-finite spectral triple obtained through a rearrangement of central elements of loop quantum gravity. The triple is based on a countable set of oriented graphs and the algebra consists of generalized holonomy loops in this set. The Dirac type operator resembles a global functional derivation operator and the interaction...
متن کاملManifestations of quantum holonomy in interferometry
Abelian and non-Abelian geometric phases, known as quantum holonomies, have attracted considerable attention in the past. Here, we show that it is possible to associate nonequivalent holonomies to discrete sequences of subspaces in a Hilbert space. We consider two such holonomies that arise naturally in interferometer settings. For sequences approximating smooth paths in the base (Grassmann) ma...
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ژورنال
عنوان ژورنال: Fortschritte der Physik
سال: 2016
ISSN: 0015-8208
DOI: 10.1002/prop.201600073