相关论文: Generally covariant Quantum Mechanics

The framework of generalized probabilistic theories is a powerful tool for studying the foundations of quantum physics. It provides the basis for a variety of recent findings that significantly improve our understanding of the rich physical…

We develop general theory of equivariant quantum cohomology for ample Kahler manifolds and prove the mirror conjecture for projective complete intersections.

Conventional relativistic quantum mechanics, based on the Klein-Gordon equation, does not possess a natural probabilistic interpretation in configuration space. The Bohmian interpretation, in which probabilities play a secondary role,…

In this work, we study the magnetic effects of gravity in the framework of special relativity. Imposing covariance of the gravitational force with respect to the Lorentz transformations, we show from a thought experiment that a…

This paper is the first of two papers devoted to formulation of quantum mechanics of a particle in a normal geodesic frame of reference in the general Riemannian space-time. Here canonical quantization of geodesic motion in the…

We carry out a generalization of quantum group co-representations in order to encode in this structure those cases where non-commutativity between endomorphism matrix entries and quantum space coordinates happens.

We propose a new formalism of quantum subsystems which allows to unify the existing and new methods of reduced description of quantum systems. The main mathematical ingredients are completely positive maps and correlation functions. In this…

In this paper, we give random matrix theory approach to the quantum mechanics using the quantum Hamilton-Jacobi formalism. We show that the bound state problems in quantum mechanics are analogous to solving Gaussian unitary ensemble of…

A non-relativistic quantum mechanical theory is proposed that describes the universe as a continuum of worlds whose mutual interference gives rise to quantum phenomena. A logical framework is introduced to properly deal with propositions…

Inspired by classical ("actual") Quantum Theory over $\mathbb{C}$ and Modal Quantum Theory (MQT), which is a model of Quantum Theory over certain finite fields, we introduce General Quantum Theory as a Quantum Theory -- in the K{\o}benhavn…

General covariance is a crucial notion in the study of field theories in curved spacetime. A field theory defined with respect to a semi-Riemannian metric is generally covariant if two metrics which are related by a diffeomorphism produce…

We propose a fibre bundle formulation of the mathematical base of relativistic quantum mechanics. At the present stage the bundle form of the theory is equivalent to its conventional one, but it admits new types of generalizations in…

A new formulation of quantum mechanics based on differential commutator brackets is developed. We have found a wave equation representing the fermionic particle. In this formalism, the continuity equation mixes the Klein-Gordon and…

The question of general covariance in quantum gravity is considered in the first post-Newtonian approximation. Transformation properties of observable quantities under deformations of a reference frame, induced by variations of the gauge…

Based on the de Broglie-Bohm relativistic quantum theory of motion we show that the conformal formulation of general relativity, being linked with a Weyl-integrable geometry, may implicitly contain the quantum effects of matter. In this…

This paper provides theorems aimed at shedding light on issues in the foundations of quantum mechanics. These theorems can be used to propose new interpretations to the theory, or to better understand, evaluate and improve current…

In all nontrivial cases renormalization, as it is usually formulated, is not a change of integration variables in the functional integral, plus parameter redefinitions, but a set of replacements, of actions and/or field variables and…

The algebraic formulation of the quantum group gauge models in the framework of the $R$-matrix approach to the theory of quantum groups is given. We consider gauge groups taking values in the quantum groups and noncommutative gauge fields…

The relation between continuous functions and random vectors is revealed in the paper that the main meaning is described as, for any given continuous function, there must be a sequence of probability spaces and a sequence of random vectors…

The suggested theory is the new quantum mechanics (QM) interpretation.The research proves that QM represents the electrodynamics of the curvilinear closed (non-linear) waves. It is entirely according to the modern interpretation and…