相关论文: Quantum Mechanics in Curved Configurational Space

A strengthened canonical quantization scheme for the constrained motion on a curved hypersurface is proposed with introduction of the second category of fundamental commutation relations between Hamiltonian and positions/momenta, whereas…

Quantum deformations of sets of points of the real and the complexified projective line are constructed. These deformations depend on the deformation parameter q and certain further parameters \lambda_{ij}. The deformations for which the…

Relativistic quantum mechanics can be considered to have begun with a search for wave equations corresponding to each intrinsic spin. However, relativistic quantum physics differs fundamentally from the non-relativistic wave mechanics. It…

This paper presents the general theory of canonical transformations of coordinates in quantum mechanics. First, the theory is developed in the formalism of phase space quantum mechanics. It is shown that by transforming a star-product, when…

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…

In this paper we regard the dynamics obtained from Fermat principle as begin the classical theory of light. We (first-)quantize the action and show how close we can get to the Maxwell theory. We show that Quantum Geometric Optics is not a…

Perturbative quantum field theory usually uses second quantisation and Feynman diagrams. The worldline formalism provides an alternative approach based on first quantised particle path integrals, similar in spirit to string perturbation…

Starting from a real scalar quantum field theory with quartic self-interactions and non-minimal coupling to classical gravity, we define four equal-time, spatially covariant phase-space operators through a Wigner transformation of spatially…

These notes give an introduction to the quantization procedure called geometric quantization. It gives a definition of the mathematical background for its understanding and introductions to classical and quantum mechanics, to differentiable…

A reformulation of a physical theory in which measurements at the initial and final moments of time are treated independently is discussed, both on the classical and quantum levels. Methods of the standard quantum mechanics are used to…

We propose six principles as the fundamental principles of quantum mechanics: principle of space and time, Galilean principle of relativity, Hamilton's principle, wave principle, probability principle, and principle of indestructibility and…

Non-relativistic quantum mechanics is shown to emerge from classical mechanics through the requirement of a relativity principle based on special transformations acting on position and momentum uncertainties. These transformations keep the…

The quantum mechanical formalism for position and momentum of a particle in a one dimensional cyclic lattice is constructively developed. Some mathematical features characteristic of the finite dimensional Hilbert space are compared with…

Finite-dimensional Quantum Mechanics can be geometrically formulated as a proper classical-like Hamiltonian theory in a projective Hilbert space. The description of composite quantum systems within the geometric Hamiltonian framework is…

In this paper, the quantum corrections to the kinematics of geometry, specifically geodesics, are presented. This is done by employing the path integral over the geodesics. Interestingly, the geodesics do not see any modifications in this…

Till now, the foundation of quantum physics is still mysterious. To explore the mysteries in the foundation of quantum physics, people always take it for granted that quantum processes must be some types of fields/objects on a rigid space.…

Using tangent bundle geometry we construct an equivalent reformulation of classical field theory on flat spacetimes which simultaneously encodes the perspectives of multiple observers. Its generalization to curved spacetimes realizes a new…

The aim of these two papers (I and II) is to try to give fundamental concepts of quantum kinematics to q-deformed quantum spaces. Paper I introduces the relevant mathematical concepts. A short review of the basic ideas of q-deformed…

We show how to formulate physical theory taking as a starting point the set of states (geometric approach). We discuss the relation of this formulation to the conventional approach to classical and quantum mechanics and the theory of…

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…