Related papers: Quantum Mechanics of Geometry
In this scientific preface to the first issue of International Journal of Geometric Methods in Modern Physics, we briefly survey some peculiarities of geometric techniques in quantum models.
Recent advancements in the discipline of quantum algorithms have displayed the importance of the geometry of quantum operators. Given this thrust, this paper develops a rigorous geometric framework to analyze how the Riemannian structure of…
In this paper we review a proposed geometrical formulation of quantum mechanics. We argue that this geometrization makes available mathematical methods from classical mechanics to the quantum frame work. We apply this formulation to the…
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 last two decades has seen quantum thermodynamics become a well established field of research in its own right. In that time, it has demonstrated a remarkably broad applicability, ranging from providing foundational advances in the…
Over the last three years, a number of fundamental physical issues were addressed in loop quantum gravity. These include: A statistical mechanical derivation of the horizon entropy, encompassing astrophysically interesting black holes as…
We consider some simple examples of supersymmetric quantum mechanical systems and explore their possible geometric interpretation with the help of geometric aspects of real Clifford algebras. This leads to natural extensions of the…
The geometrodynamics of the spherical gravity with a selfgravitating thin dust shell as a source is constructed. The shell Hamiltonian constraint is derived and the corresponding Schroedinger equation is obtained. This equation appeared to…
Quantum mechanics is among the most important and successful mathematical model for describing our physical reality. The traditional formulation of quantum mechanics is linear and algebraic. In contrast classical mechanics is a geometrical…
This work explores the intersection of quantum mechanics and curved spacetime by employing the Wigner formalism to investigate quantum systems in the vicinity of black holes. Specifically, we study the quantum dynamics of a probe particle…
In physics, two systems that radically differ at short scales can exhibit strikingly similar macroscopic behaviour: they are part of the same long-distance universality class. Here we apply this viewpoint to geometry and initiate a program…
Spacetime geometry is supposed to be measured by identifying the trajectories of free test particles with geodesics. In practice, this cannot be done because, being described by Quantum Mechanics, particles do not follow trajectories. As a…
Over the last three years, a number of fundamental issues in quantum gravity were addressed in the framework of quantum geometry, discussed extensively by John Baez in this conference. In particular, these include: A statistical mechanical…
Quantum geometry, characterized by the quantum geometric tensor, is pivotal in diverse physical phenomena in quantum materials. In condensed matter systems, quantum geometry refers to the geoemtric properties of Bloch states in the…
Phase space is the state space of classical mechanics, and this manifold is normally endowed only with a symplectic form. The geometry of quantum mechanics is necessarily more complicated. Arguments will be given to show that augmenting the…
We discuss the quantum mechanics and thermodynamics of the (2+1)-dimensional black hole, using both minisuperspace methods and exact results from Chern-Simons theory. In particular, we evaluate the first quantum correction to the black hole…
Several years ago the so-called quantum geometrodynamics in extended phase space was proposed. The main role in this version of quantum geometrodynamics is given to a wave function that carries information about geometry of the Universe as…
We explore the quantum nature of black holes by introducing an effective framework that takes into account deviations from the classical results. The approach is based on introducing quantum corrections to the classical Schwarzschild…
Computational complexity is a new quantum information concept that may play an important role in holography and in understanding the physics of the black hole interior. We consider quantum computational complexity for $n$ qubits using…
Geometric quantum mechanics aims to express the physical properties of quantum systems in terms of geometrical features preferentially selected in the space of pure states. Geometric characterisations are given here for systems of one, two,…