Related papers: Geometric Phase in Quaternionic Quantum Mechanics
We develop the theory of the nonadiabatic geometric phase, in both the Abelian and non-Abelian cases, in quaternionic Hilbert space.
The basic framework for a systematic construction of a quantum theory of Riemannian geometry was introduced recently. The quantum versions of Riemannian structures --such as triad and area operators-- exhibit a non-commutativity. At first…
The phase structure of four-dimensional simplicial quantum gravity coupled to U(1) gauge fields has been studied using Monte-Carlo simulations. The smooth phase is found in the intermediate region between the crumpled phase and the branched…
Geometrical and topological phases play a fundamental role in quantum theory. Geometric phases have been proposed as a tool for implementing unitary gates for quantum computation. A fractional topological phase has been recently discovered…
The concept of supersymmetry in a quantum mechanical system is extended, permitting the recognition of many more supersymmetric systems, including very familiar ones such as the free particle. Its spectrum is shown to be supersymmetric,…
Quantum mechanical methods for getting geometric phases for mixed states are analyzed. Parallel transport equations for pure states are generalized to mixed states by which dynamical phases are eliminated. The geometric phases of mixed…
It is proposed the scheme of quantum mechanics, in which a Hilbert space and the linear operators are not primary elements of the theory. Instead of it certain variant of the algebraic approach is considered. The elements of noncommutative…
We use tools from the theory of dynamical systems with symmetries to stratify Uhlmann's standard purification bundle and derive a new connection for mixed quantum states. For unitarily evolving systems, this connection gives rise to the…
In this paper $4$ dimensional Riemannian (or Euclidean) vacuum general relativity is recovered from a phase transition by spontaneous symmetry breaking within a quantum field theory (all in the sense of the operator algebraic approach to…
The method of geometric quantization is applied to a particle moving on an arbitrary Riemannian manifold $Q$ in an external gauge field, that is a connection on a principal $H$-bundle $N$ over $Q$. The phase space of the particle is a…
The pure state space of Quantum Mechanics is investigated as Hermitian Symmetric Kaehler manifold. The classical principles of Quantum Mechanics (Quantum Superposition Principle, Heisenberg Uncertainty Principle, Quantum Probability…
We construct the quaternion algebra [10] "geometrically" by a three dimensional analogue of the classic two dimensional geometric description of the complex field. The algebraic description of the multiplication operation in three…
Practical implementations of quantum computing are always done in the presence of decoherence. Geometric phase is useful in the context of quantum computing as a tool to achieve fault tolerance. Recent experimental progresses on coherent…
The study of geometric phase in quantum mechanics has so far be confined to discrete (or continuous) spectra and trace preserving evolutions. Consider only the transmission channel, a scattering process with internal degrees of freedom is…
I present a selective survey of the phases of quantum matter with varieties of many-particle quantum entanglement. I classify the phases as gapped, conformal, or compressible quantum matter. Gapped quantum matter is illustrated by a simple…
We show that the principles of a ''complete physical theory'' and the conclusions of the standard quantum mechanics do not irreconcilably contradict each other as is commonly believed. In the algebraic approach, we formulate axioms that…
A unified framework for different formulations of quantum theoery is introduced specifying what is meant by a quantum mechanical theory in general.
An Abelian gerbe is constructed over classical phase space. The 2-cocycles defining the gerbe are given by Feynman path integrals whose integrands contain the exponential of the Poincare-Cartan form. The U(1) gauge group on the gerbe has a…
Geometric phase is a key player in many areas of quantum science and technology. In this review article, several foundational aspects of quantum geometric phases and their relations to classical geometric phases are outlined. How the…
A renormalizable theory of gravity is obtained if the dimension-less 4-derivative kinetic term of the graviton, which classically suffers from negative unbounded energy, admits a sensible quantisation. We find that a 4-derivative degree of…