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Research during the last decade demonstrates that effects originating on the Planck scale are currently being tested in multiple observational contexts. In this review we discuss quantum gravity phenomenological models and their possible…
We look at non-classical negations and their corresponding adjustment connectives from a modal viewpoint, over complete distributive lattices, and apply a very general mechanism in order to offer adequate analytic proof systems to logics…
Quantum complementarity is a fundamental feature of quantum systems and has captivated the physics research community for nearly a century, with significant advancements emerging in recent decades. This review traces the historical…
We present an operational reconstruction of the well-known two-to-one homomorphism between the groups $SU(2)$ and $SO(3)$, grounded in the physical description of quantum state preparation and evolution. Starting from the connection between…
An algebraic formulation of general relativity is proposed. The formulation is applicable to quantum gravity and noncommutative space. To investigate quantum gravity we develop the canonical formalism of operator geometry, after…
Over the last three years, a number of fundamental physical issues were addressed in loop quantum gravity. These include: A statistical mechanical derivation of the horizon entropy, encompassing astrophysically interesting black holes as…
Gravity theory based on current algebra is formulated. The gauge principle rather than the general covariance combined with the equivalence principle plays the pivotal role in the formalism, and the latter principles are derived as a…
This paper is the fourth in a series whose goal is to develop a fundamentally new way of building theories of physics. The motivation comes from a desire to address certain deep issues that arise in the quantum theory of gravity. Our basic…
Gravity theories with non-minimally coupled scalar fields are used as characteristic examples in order to demonstrate the challenges, pitfalls and future perspectives of considering alternatives to general relativity. These lecture notes…
The semiclassical interaction of the gravitational with a quantum scalar field is considered, in view of the renormalizability of the associated energy-momentum tensor in a n-dimensional curved spacetime resulting from a quadratic…
A fully consistent linear perturbation theory for cosmology is derived in the presence of quantum corrections as they are suggested by properties of inverse volume operators in loop quantum gravity. The underlying constraints present a…
The causal structure of space-time offers a natural notion of an opposite or orthogonal in the logical sense, where the opposite of a set is formed by all points non time-like related with it. We show that for a general space-time the…
The Ahtekar-Isham C*-algebra known from Loop Quantum Gravity is the algebra of continuous functions on the space of (generalized) connections with a compact structure Lie group. The algebra can be constructed by some inductive techniques…
The scalar-tensor theory of gravitation has been and still is one of the most widely discussed "alternative theories" to General Relativity (GR). Despite nearly half a century of its age, it continues to attract renewed interests of not…
A new model of self-organized criticality is proposed. An algebra of operators is introduced which is similar to that used for the Abelian sandpile model. The structure of the configurational space is determined and the number of recurrent…
This chapter provides a review of the frameworks developed for cosmological perturbation theory in loop quantum cosmology, and applications to various models of the early universe including inflation, ekpyrosis and the matter bounce, with…
We use the method of embedding a subsystem (i.e. its observable algebra) into a larger quantum system to extract a cosmological sector from full Loop Quantum Gravity. The application of this method provides a setting for a systematic study…
A local conception is proposed to reconcile quantum theory with general relativity, which allows one to avoid some difficulties --- as e.g. vacuum catastrophe --- of the global approach.
Assuming the von Neumann algebra associated with a generic de Sitter observer is properly infinite (type III) we use Connes cocycle to identify the unique ( up to unitary equivalence) background independent dominant weight on an extended…
In quantum cosmology, one applies quantum physics to the whole universe. While no unique version and no completely well-defined theory is available yet, the framework gives rise to interesting conceptual, mathematical and physical…