Related papers: Quantum Jet Theory, Observer Dependence, and Multi…
I review the multi-dimensional generalizations of the Virasoro algebra, i.e. the non-central Lie algebra extensions of the algebra vect(N) of general vector fields in N dimensions, and its Fock representations. Being the Noether symmetry of…
Quantum Jet Theory (QJT) is a deformation of QFT where also the quantum dynamics of the observer is taken into account. This is achieved by introducing relative fields, labelled by locations measured by rods relative to the observer's…
The dimensional properties of fields in classical general relativity lead to a tangent tower structure which gives rise directly to quantum mechanical and quantum field theory structures without quantization. We derive all of the…
We postulate that the fundamental principles of Quantum Gravity are diffeomorphism symmetry, unitarity, and locality. Local observables are compatible with diffeomorphism symmetry in the presence of diff anomalies, which modify the symmetry…
The metric determines the casual structure of spacetime, but in quantum gravity it is also a dynamical field which must be quantized using this causal structure; this is the famous problem of time. A radical resolution of this paradox is…
One could begin a study like the present one by simply postulating that our universe is four-dimensional. There are ample reasons for doing this. Experience, observation and experiment all point to the fact that we inhabit a…
QJT (Quantum Jet Theory) is the quantum theory of jets, which can be canonically identified with truncated Taylor series. Ultralocality requires a novel quantization scheme, where dynamics is treated as a constraint in the history phase…
We investigate the quantum aspects of three-dimensional gravity with a positive cosmological constant. The reduced phase space of the three-dimensional de Sitter gravity is obtained as the space which consists of the Kerr-de Sitter…
In quantum mechanics the time dimension is treated as a parameter, while the three space dimensions are treated as observables. This assumption is both untested and inconsistent with relativity. From dimensional analysis, we expect quantum…
The geometrical description of Quantum Mechanics is reviewed and proposed as an alternative picture to the standard ones. The basic notions of observables, states, evolution and composition of systems are analised from this perspective, the…
Despite their diversity, many of the most prominent candidate theories of quantum gravity share the property to be effectively lower-dimensional at small scales. In particular, dimension two plays a fundamental role in the finiteness of…
The dimensional structure of space-time is investigated according to physical and mathematical methods. We show that ther are various empirical and theoretical restrictions on the number of independent dimensions of space-time, consequently…
In this paper, we studied the jet modules for the centerless Virasoro-like algebra which is the Lie algebra of the Lie group of the area-preserving diffeomorphisms of a $2$-torus. The jet modules are certain natural modules over the Lie…
The concept of a quantum structure underlying space has been proposed for quite some time, yet it has largely eluded direct observation. There is a prevailing notion that the minuscule effects stemming from quantum space could, under…
A purely geometrical relativity theory results from a construction that produces from three-dimensional space a happy unification of Kaluza's five-dimensional theory and Weyl's conformal theory. The theory can provide geometrical…
Canonical quantization of gravity requires knowledge about the representation theory of its constraint algebra, which is physically equivalent to the algebra of arbitrary 4-diffeomorphisms. All interesting lowest-energy representations are…
We argue that theories of quantum gravity constructed with the help of (Causal) Dynamical Triangulations have given us the most informative, quantitative models to date of quantum spacetime. Most importantly, these are derived dynamically…
In this review I summarise the status of observational research into relativistic jets from X-ray binaries, highlighting four areas in particular: (i) How relativistic are the jets ?, (ii) The disc : jet coupling, (iii) the nature of the…
We construct a mathematical version of quantum field theory. It assigns to a multidimensional variational principle an associative algebra which is a quantization of the Poisson algebra of classical field theory observables. For free scalar…
In this paper, we extend the quantum geometric tensor for parameter-dependent curved spaces to higher dimensions, and introduce an equivalent definition that generalizes the Zanardi, et al, formulation of the tensor. The parameter-dependent…