Related papers: New anatomy of quantum holonomy
The gravity is classically formulated as the geometric curvature of the space-time in general relativity which is completely different from the other well-known physical forces. Since seeking a quantum framework for the gravity is a great…
We review recent developments in the treatment of spherically symmetric black holes in loop quantum gravity. In particular, we discuss an exact solution to the quantum constraints that represents a black hole and is free of singularities.…
We introduce a particular nonlinear generalization of quantum mechanics which has the property that it is exactly solvable in terms of the eigenvalues and eigenfunctions of the Hamiltonian of the usual linear quantum mechanics problem. We…
A recently introduced class of quantum spherical spin models is considered in detail. Since the spherical constraint already contains a kinetic part, the Hamiltonian need not have kinetic term. As a consequence, situations with or without…
We implement a non-adiabatic universal set of holonomic quantum gates based on abelian holonomies using dynamical invariants, by Lie-algebraic methods. Unlike previous implementations, presented scheme does not rely on secondary methods…
Various examples of exactly solvable `discrete' quantum mechanics are explored explicitly with emphasis on shape invariance, Heisenberg operator solutions, annihilation-creation operators, the dynamical symmetry algebras and coherent…
In this paper we establish the existence of the non-perturbative theory of quantum gravity known as quantum holonomy theory by showing that a Hilbert space representation of the QHD(M) algebra, which is an algebra generated by…
Euclidean gravity provides an interesting test system for an analysis of cosmological perturbations in an effective Hamiltonian constraint with holonomy modifications from loop quantum gravity. This paper presents a discussion of scalar…
We study a type of geometric theory with a non-dynamical one-form field. Its dynamical variables are an $su(2)$ gauge field and a triad of $su(2)$ valued one-forms. Hamiltonian decomposition reveals that the theory has a true Hamiltonian,…
The geometric aspects of quantum mechanics are underlined most prominently by the concept of geometric phases, which are acquired whenever a quantum system evolves along a closed path in Hilbert space. The geometric phase is determined only…
A new family of analytically solvable quantum geometric models is proposed. The structure of the energy spectra as well as the form of the corresponding eigenfunctions are presented pointing out their main specific properties.
Further properties of a recently proposed higher order infinite spin particle model are derived. Infinitely many classically equivalent but different Hamiltonian formulations are shown to exist. This leads to a condition of uniqueness in…
A key aspect of a recent proposal for a {\em generalized loop representation} of quantum Yang-Mills theory and gravity is considered. Such a representation of the quantum theory has been expected to arise via consideration of a particular…
We propose a new holonomy formulation for spin foams, which naturally extends the theory space of lattice gauge theories. This allows current spin foam models to be defined on arbitrary two-complexes as well as to generalize current spin…
We investigate lattice and continuous quantum gauge theories on the Euclidean plane with a structure group that is replaced by a $H$-algebra; non-commutative analogues of groups and contain the class of Voiculescu's dual groups. We are…
The new integrable quantum spin model is proposed. The model has a biaxial magnetic anisotropy of alternating coupling between spins together with multiple spin interactions. Our model gives the possibility to exactly find thermodynamic…
A new diffeomorphism invariant of integral homology 3-spheres is defined using a non-abelian 'quaternionic' version of the Seiberg-Witten equations.
We have recently constructed a large class of open quantum spin chains which have quantum-algebra symmetry and which are integrable. We show here that these models can be exactly solved using a generalization of the analytical Bethe Ansatz…
We develop a non-adiabatic generalization of holonomic quantum computation in which high-speed universal quantum gates can be realized by using non-Abelian geometric phases. We show how a set of non-adiabatic holonomic one- and two-qubit…
Berry phase, which had been discovered for more than two decades, provides us a very deep insight on the geometric structure of quantum mechanics. Its classical counterpart--Hannay's angle is defined if closed curves of action variables…