相关论文: The Pure State Space of Quantum Mechanics as Hermi…

We first recall a fact which is well-known among mathematical physicists although lesser-known among theoretical physicists that the standard quantum mechanics over a complex Hilbert space, is a Hamiltonian mechanics, regarding the Hilbert…

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 have previously presented a version of the Weak Equivalence Principle for a quantum particle as an exact analog of the classical case, based on the Heisenberg picture analysis of free particle motion. Here, we take that to a full…

In physics, experiments ultimately inform us as to what constitutes a good theoretical model of any physical concept: physical space should be no exception. The best picture of physical space in Newtonian physics is given by the…

We consider symmetry as a foundational concept in quantum mechanics and rewrite quantum mechanics and measurement axioms in this description. We argue that issues related to measurements and physical reality of states can be better…

The classical Hilbert space formulation of the axioms of Quantum Mechanics appears to leave open the question whether the Hermitian operators which are associated with the observables of a finite non-relativistic quantum system are uniquely…

The manifold of pure quantum states is a complex projective space endowed with the unitary-invariant geometry of Fubini and Study. According to the principles of geometric quantum mechanics, the detailed physical characteristics of a given…

States of a quantum mechanical system are represented by rays in a complex Hilbert space. The space of rays has, naturally, the structure of a K\"ahler manifold. This leads to a geometrical formulation of the postulates of quantum mechanics…

We show how quantum mechanics can be understood as a space-time theory provided that its spatial continuum is modelled by a variable real number (qrumber) continuum. Such a continuum can be constructed using only standard Hilbert space…

Symmetric states are defined in the kinematical sector of loop quantum gravity and applied to spherical symmetry and homogeneity. Consequences for the physics of black holes and cosmology are discussed.

The physical world is quantum. However, our description of the quantum physics still relies much on concepts in classical physics and in some cases with `quantized' interpretations. The most important case example is that of spacetime. We…

The complex Hilbert space of standard quantum mechanics may be treated as a real Hilbert space. The pure states of the complex theory become mixed states in the real formulation. It is then possible to generalize standard quantum mechanics,…

This paper presents a comprehensive perspective of the metric of quantum states with a focus on the background independent metric structures. We also explore the possibilities of geometrical formulations of quantum mechanics beyond the…

In a quantum universe with a strong arrow of time, we postulate a low-entropy boundary condition (the Past Hypothesis) to account for the temporal asymmetry. In this paper, I show that the Past Hypothesis also contains enough information to…

The tomographic picture of quantum mechanics has brought the description of quantum states closer to that of classical probability and statistics. On the other hand, the geometrical formulation of quantum mechanics introduces a metric…

In this paper, we investigate a characterization of Quantum Mechanics by two physical principles based on general probabilistic theories. We first give the operationally motivated definition of the physical equivalence of states and…

We develop a novel approach to Quantum Mechanics that we call Curved Quantum Mechanics. We introduce an infinite-dimensional K\"ahler manifold ${\cal M}$, that we call the state manifold, such that the cotangent space $T_z^*{\cal M}$ is a…

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…

Quantum mechanics can emerge from classical statistics. A typical quantum system describes an isolated subsystem of a classical statistical ensemble with infinitely many classical states. The state of this subsystem can be characterized by…

The properties which give quantum mechanics its unique character - unitarity, complementarity, non-commutativity, uncertainty, nonlocality - derive from the algebraic structure of Hermitian operators acting on the wavefunction in complex…