Related papers: Indefinite probabilities in quantum spacetime: A d…
The relativistic conception of space and time is challenged by the quantum nature of physical observables. It has been known for a long time that Poincar\'e symmetry of field theory can be extended to the larger conformal symmetry. We use…
We consider a massive particle of arbitrary spin and the basis vectors that carry the unitary, irreducible representations of the Poincar\'e group. From the complex coefficients in normalizable superpositions of these basis vectors, we…
We propose a mathematical structure, based on a noncommutative geometry, which combines essential aspects of general relativity and quantum mechanics, and leads to correct "limiting cases" of both these theories. We quantize a groupoid…
A unified conceptual foundation of classical and quantum physics is given, free of undefined terms. Ensembles are defined by extending the `probability via expectation' approach of Whittle to noncommuting quantities. This approach carries…
In quantum mechanics, the Heisenberg uncertainty relation presents an ultimate limit to the precision by which one can predict the outcome of position and momentum measurements on a particle. Heisenberg explicitly stated this relation for…
The fundamental dynamics of quantum particles is neutral with respect to the arrow of time. And yet, our experiments are not: we observe quantum systems evolving from the past to the future, but not the other way round. A fundamental…
Quantum uncertainty relations have deep-rooted significance on the formalism of quantum mechanics. Heisenberg's uncertainty relations attracted a renewed interest for its applications in quantum information science. Robertson derived a…
We adapt the axioms of the quantum mechanics to the quantum Minkowski space-time coordinates and their transformations under the quantum Lorentz group to show how we can formulate the noncommutative special relativity and its quantum…
I discuss the indefinite metrical structure of the time-space translations as realized in the indefinite inner products for relativistic quantum fields, familiar in the example of quantum gauge fields. The arising indefinite unitary…
The role of quantum universal enveloping algebras of symmetries in constructing a noncommutative geometry of space-time and corresponding field theory is discussed. It is shown that in the framework of the twist theory of quantum groups,…
An analysis of quantum measurement is presented that relies on an information-theoretic description of quantum entanglement. In a consistent quantum information theory of entanglement, entropies (uncertainties) conditional on measurement…
A nonrelativistic proof of the spin-statistics theorem is given in terms of the field operators satisfying commutation and anticommutation relations, which are introduced here in the coordinate space as a means to build the permutation…
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…
The formulation of a consistent measurement theory for relativistic quantum fields has become a problem of growing foundational and practical significance. Standard non-relativistic measurement models fail to incorporate the essential…
Researchers have long been aiming to understand how the characteristics of Quantum Theory and General Relativity combine to account for regimes in their interface. One reason why this is a hard task is how differently the theories approach…
Quantum theory does not provide a unique definition for the joint probability of two non-commuting observables, which is the next important question after the Born's probability for a single observable. Instead, various definitions were…
Quantum gravity may modify the fundamental symmetries that govern identical particles. In particular, noncommutative spacetime frameworks predict deformations of Bose and Fermi statistics. Here we develop a relativistic quantum field theory…
Geometrical structures of quantum mechanics provide us with new insightful results about the nature of quantum theory. In this work we consider mixed quantum states represented by finite rank density operators. We review our geometrical…
The measurement processes that are traditionally described within the realm of non-relativistic quantum mechanics are transcribed into the covariant framework of Cartan's space, the four-valued representation space of the restricted…
It is known that non-commuting observables in quantum mechanics do not have joint probability. This statement refers to the precise (additive) probability model. I show that the joint distribution of any non-commuting pair of variables can…