相关论文: Noncommutative Spacetime and Quantum Mechanics

We will highlight that despite there being various approaches to quantum gravity, there are universal approach-independent features of quantum gravity. The geometry of spacetime becomes an emergent structure, which emerges from some purely…

A quantum theory of asymptotically flat space-times is presented using the solutions of the Null Surface Formulation (NSF) field equations in a perturbative scheme. Free-field commutation relations are given for the null free data of NSF at…

Quantum field theory (QFT) is supposed to be gauge invariant. However it has been well established that a direct calculation of the vacuum polarization tensor produces a non-gauge invariant result. In this paper it will be shown that this…

The quantum version of the free fall problem is a topic often skipped in undergraduate quantum mechanics courses because its discussion usually requires wavepackets built on the Airy functions -- a difficult computation. Here, on the…

Treating the gravitational force on the same footing as the electroweak and strong forces, we present a quantum field theory of gravity based on spin and scaling gauge symmetries. A biframe spacetime is initiated to describe such a quantum…

Free scalar field theory on 2 dimensional flat spacetime, cast in diffeomorphism invariant guise by treating the inertial coordinates of the spacetime as dynamical variables, is quantized using LQG type `polymer' representations for the…

An adapted representation of quantum mechanics sheds new light on the relationship between quantum states and classical states. In this approach the space of quantum states splits into a product of the state space of classical mechanics and…

This article provides a basic introduction to some concepts of non-commutative geometry. The importance of quantum groups and quantum spaces is stressed. Canonical non-commutativity is understood as an approximation to the quantum group…

The conflict between the locality of general relativity, reflected in its space-time description, and the non-locality of quantum mechanics, contained in its Hilbert space description, is discussed. Gauge covariant non-local observables…

We consider the nature of quantum properties in non-relativistic quantum mechanics (QM) and relativistic QFTs, and examine the connection between formal quantization schemes and intuitive notions of wave-particle duality. Based on the map…

The canonical answer to the question posed is "Yes." -- tacitly assuming that quantum theory and the concept of spacetime are to be unified by `quantizing' a theory of gravitation. Yet, instead, one may ponder: Could quantum mechanics arise…

We consider the evolution of quantum fields on a classical background space-time, formulated in the language of differential geometry. Time evolution along the worldlines of observers is described by parallel transport operators in an…

Beginning with ordinary quantum mechanics for spinless particles, together with the hypothesis that all experimental measurements consist of positional measurements at different times, we characterize directly a class of nonlinear quantum…

We reconsider perturbative unitarity in quantum field theory and upgrade several arguments and results. The minimum assumptions that lead to the largest time equation, the cutting equations and the unitarity equation are identified. Using…

A very simple field theory in noncommutative phase space X^{M},P^{M} in d+2 dimensions, with a gauge symmetry based on noncommutative u*(1,1), furnishes the foundation for the field theoretic formulation of Two-Time Physics. This leads to a…

In this work quantum physics in noncommutative spacetime is developed. It is based on the work of Doplicher et al. which allows for time-space noncommutativity. The Moyal plane is treated in detail. In the context of noncommutative quantum…

We introduce a framework for non-linear time evolution in quantum mechanics as a natural non-linear generalization of the Schrodinger equation. Within our framework, we derive simple toy models of dynamical geometry on finite graphs. Along…

In this paper we consider the observables describing fundamental spatiotemporal properties and relations in the context of Quantum Gravity (QG). As we will show, in both Loop Quantum Gravity and in String Theory, these observables are…

We describe a theory amalgamating quantum theory and general relativity through the identification of a continuous 4-dimensional spacetime arena constructed from the substructures of a generalised multi-dimensional form for proper time. In…

Non-invertible symmetries in quantum field theory (QFT) generalize the familiar product rule of groups to a more general fusion rule. In many cases, gauged versions of these symmetries can be regarded as dual descriptions of invertible…