相关论文: Geometry, stochastic calculus and quantum fields i…

The relativistic quantum phase space (QPS) formalism extends classical phase space by incorporating both mean values and variance-covariance matrices of quantum states, thereby providing a unified setting where the uncertainty principle and…

This talk is an introduction to ideas of non-commutative geometry and star products. We will discuss consequences for physics in two different settings: quantum field theories and astrophysics. In case of quantum field theory, we will…

Non commutative geometry is creating new possibilities for physics. Quantum spacetime geometry and post inflationary models of the universe with matter creation have an enormous range of scales of time, distance and energy in between. There…

If quantum gravity respects the principles of quantum mechanics, suitably generalized, it may be that a more viable approach to the theory is through identifying the relevant quantum structures rather than by quantizing classical spacetime.…

In a recent paper (arXiv:1412.6000) a general mechanism for emergence of cosmological space-time geometry from a quantum gravity setting was devised and departure from standard dispersion relations for elementary particle were predicted. We…

Quantum groups lead to an algebraic structure that can be realized on quantum spaces. These are noncommutative spaces that inherit a well defined mathematical structure from the quantum group symmetry. In turn such quantum spaces can be…

We study a class of theories in which space-time is treated classically, while interacting with quantum fields. These circumvent various no-go theorems and the pathologies of semi-classical gravity, by being linear in the density matrix and…

Perturbative deformations of symmetry structures on noncommutative spaces are studied in view of noncommutative quantum field theories. The rigidity of enveloping algebras of semi-simple Lie algebras with respect to formal deformations is…

A century after the advent of Quantum Mechanics and General Relativity, both theories enjoy incredible empirical success, constituting the cornerstones of modern physics. Yet, paradoxically, they suffer from deep-rooted, so-far intractable,…

The different roles and natures of spacetime appearing in a quantum field theory and in classical physics are analyzed implying that a quantum theory of gravitation is not necessarily a quantum theory of curved spacetime. Developing an…

Background independence is often emphasized as an important property of a quantum theory of gravity that takes seriously the geometrical nature of general relativity. In a background-independent formulation, quantum gravity should determine…

The existence of a fundamental length (or fundamental time) has been conjecture in many contexts. Here one discusses some consequences of a fundamental constant of this type, which emerges as a consequence of deformation-stability…

All existing experimental results are currently interpreted using classical geometry. However, there are theoretical reasons to suspect that at a deeper level, geometry emerges as an approximate macroscopic behavior of a quantum system at…

We briefly review ideas about ``noncommutativity of space-time'' and approaches toward a corresponding theory of gravity.

Relativistic deformed kinematics leads to a loss of the absolute locality of interactions. In previous studies, some models of noncommutative spacetimes in a two-particle system that implements locality were considered. In this work, we…

It has earlier been argued that there should exist a formulation of quantum mechanics which does not refer to a background spacetime. In this paper we propose that, for a relativistic particle, such a formulation is provided by a…

We present a mathematical framework for quantum mechanics in which the basic entities and operations have physical significance. In this framework the primitive concepts are states and effects and the resulting mathematical structure is a…

Noncommutative or `quantum' differential geometry has emerged in recent years as a process for quantizing not only a classical space into a noncommutative algebra (as familiar in quantum mechanics) but also differential forms, bundles and…

Familiar formulations of classical and quantum mechanics are shown to follow from a general theory of mechanics based on pure states with an intrinsic probability structure. This theory is developed to the stage where theorems from quantum…

A perturbative formulation of algebraic field theory is presented, both for the classical and for the quantum case, and it is shown that the relation between them may be understood in terms of deformation quantization.