Related papers: Quantum periods: A census of \phi^4-transcendental…
A noncommutative geometric generalisation of the quantum field theoretical framework is developed by generalising the Heisenberg commutation relations. There appear nonzero minimal uncertainties in positions and in momenta. As the main…
We quantize graphs (networks) which consist of a finite number of bonds and vertices. We show that the spectral statistics of fully connected graphs is well reproduced by random matrix theory. We also define a classical phase space for the…
Quantum gauge theories with finite-dimensional representation spaces are constructed that can have canonical gauge field theories as singular limits. They describe nature as a recursive quantum assembly by iterating Fermi-Dirac…
In contrast to the usual quantum systems which have at most a finite number of open spectral gaps if they are periodic in more than one direction, periodic quantum graphs may have gaps arbitrarily high in the spectrum. This property of…
A fundamental problem with attempting to quantize general relativity is its perturbative non-renormalizability. However, this fact does not rule out the possibility that non-perturbative effects can be computed, at least in some…
We give a review of concepts related to connection of classical and quantum theories, from the phase space perspective. Quantum theory is described by non-commutative operators of coordinates and momenta, results in values having a certain…
It is shown that loop divergences emerging in the Green functions in quantum field theory originate from correspondence of the Green functions to {\em unmeasurable} (and hence unphysical) quantities. This is because no physical quantity can…
We describe quantum theories for massless (p,q)-forms living on Kaehler spaces. In particular we consider four different types of quantum theories: two types involve gauge symmetries and two types are simpler theories without gauge…
An analytic theory is developed for the density of states oscillations in quantum wells in a magnetic field which is tilted with respect to the barrier planes. The main oscillations are found to come from the simplest one or two-bounce…
After giving an overview of the existing theory regarding the periods of sequences defined by linear recurrences over finite fields, we give explicit descriptions of the sets of periods that arise if one considers all sequences over…
We provide a mechanism by which, from a background independent model with no quantum mechanics, quantum theory arises in the same limit in which spatial properties appear. Starting with an arbitrary abstract graph as the microscopic model…
Quantum mechanics for a four-state-system is derived from classical statistics. Entanglement, interference, the difference between identical fermions or bosons and the unitary time evolution find an interpretation within a classical…
We introduce a new model of background independent physics in which the degrees of freedom live on a complete graph and the physics is invariant under the permutations of all the points. We argue that the model has a low energy phase in…
We pursue the view that quantum theory may be an emergent structure related to large space-time scales. In particular, we consider classical Hamiltonian systems in which the intrinsic proper time evolution parameter is related through a…
We argue that quantum theory is a low-energy effective theory which emerges from some sub-quantum level theory which is of an undulatory and translocal character. We show the close connection of quantum theory with both gravity and the…
The real time evolution of quantum field theory models can be calculated order by order in perturbation theory. For $\lambda \phi^4$ models, the perturbative series have a zero radius of convergence which in part motivated the design of…
There is accumulating evidence in lattice QCD that attempts to locate confining fields in vacuum configurations bring results explicitly depending on tha lattice spacing (that is, ultraviolet cut off). Generically, one deals with…
Quantum fields are shown to provide an example of infinite-dimensional quantum groups. A dictionary is established between quantum field and quantum group concepts: the expectation value over the vacuum is the counit, Wick's theorem is the…
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…
Quantum graphity is a background independent model for emergent locality, spatial geometry and matter. The states of the system correspond to dynamical graphs on N vertices. At high energy, the graph describing the system is highly…