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In general relativity, the causal structure between events is dynamical, but it is definite and observer-independent; events are point-like and the membership of an event A in the future or past light-cone of an event B is an…
In these proceedings we summarize previous work where we formalize a general concept of algebraic field theories using operads. After giving a gentle reminder of algebraic quantum field theory, operads and their algebras, we construct field…
The influence of additional information on the decision making of agents, who are interacting members of a society, is analyzed within the mathematical framework based on the use of quantum probabilities. The introduction of social…
We propose a modification of a recently introduced generalized translation operator, by including a $q$-exponential factor, which implies in the definition of a Hermitian deformed linear momentum operator $\hat{p}_q$, and its canonically…
We quantise the new connection formulation of D+1 dimensional General Relativity developed in our companion papers by Loop Quantum Gravity (LQG) methods. It turns out that all the tools prepared for LQG straightforwardly generalise to the…
Quantum gravity is expected to introduce quantum aspects into the description of reference frames. Here we set the stage for exploring how quantum gravity induced deformations of classical symmetries could modify the transformation laws…
We develop and defend the thesis that the Hilbert space formalism of quantum mechanics is a new theory of probability. The theory, like its classical counterpart, consists of an algebra of events, and the probability measures defined on it.…
We consider the domain of applicability of general relativity (GR), as a classical theory of gravity, by considering its applications to a variety of settings of physical interest as well as its relationship with real observations. We argue…
In quantum mechanics time usually appears as classical parameter which means that it is treated as being essentially different from spatial coordinates that are represented by operators. On the other hand, relativity theory demands to treat…
Theories of quantum gravity generically presuppose or predict that the reality underlying relativistic spacetimes they are describing is significantly non-spatiotemporal. On pain of empirical incoherence, approaches to quantum gravity must…
We consider a number of aspects of the problem of defining time observables in quantum theory. Time observables are interesting quantities in quantum theory because they often cannot be associated with self-adjoint operators. Their…
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…
A universal formulation of the quantum uncertainty regarding quantum indeterminacy, quantum measurement, and its inevitable observer effect is presented with additional focus on the representability of quantum observables over a given…
Considering a fluctuating scalar field on momentum space, some relativistic statistical field theories are constructed. A Hilbert space of observables is then constructed from functionals of the fluctuating scalar field with an inner…
The classical procedures which define the relativistic notion of space-time can be implemented in the framework of Quantum Field Theory. Only relying on the conformal symmetries of field propagation, time-frequency transfer and localization…
The standard formalism of quantum theory is enhanced and definite meaning is given to the concepts of experiment, measurement and event. Within this approach one obtains a uniquely defined piecewise deterministic algorithm generating…
To admit a canonically conjugate time operator, the Hamiltonian has to be a generator of translations (like the momentum operator generates translations in space), so its spectrum must be unbounded. But the Hamiltonian governing our world…
Quantum mechanics is formulated as a geometric theory on a Hilbert manifold. Images of charts on the manifold are allowed to belong to arbitrary Hilbert spaces of functions including spaces of generalized functions. Tensor equations in this…
Preliminary results on a canonical formulation of general relativity based on an analogy with the string model of elementary particles are presented. Rather than the metric components, the basic fields of the formalism are taken to be the…
I briefly summarized some recent work which uses the techniques of effective field theory to make quantum predictions in general relativity. In contrast to conventional expectations, these are in fact well behaved. The leading quantum…