Related papers: A local diagnostic program for unitary evolution i…
In this second part of the `essay on the completion of quantum theory' we define the {\em unitary setting of completed quantum mechanics}, by adding as intrinsic data to those from Part I (arXiv:1711.08643) the choice of a north pole N and…
Discrete canonical evolution is a key tool for understanding the dynamics in discrete models of spacetime, in particular those represented by a triangular Regge lattice. We consider a finite-dimensional system whose evolution is realized by…
We calculate the power spectrum of density fluctuations in the statistical non-equilibrium field theory for classical, microscopic degrees of freedom to first order in the interaction potential. We specialise our result to cosmology by…
An effective operational approach to quantum mechanics is to focus on the evolution of wave-packets, for which the wave-function can be seen in the semi-classical regime as representing a classical motion dressed with extra degrees of…
In quantum mechanics the unitary evolution is most often described in a pre-selected Hilbert space ${\cal H}^{(textbook)}$ in which, due to the Stone theorem, the Schr\"odinger-picture Hamiltonian is self-adjoint,…
Loop quantum cosmology was shown to interpolate between de Sitter and FLRW Universe phases through a bounce by including Euclidean and Lorentzian terms of the Hamiltonian constraint with weight one -that corresponding to classical General…
We derive the effective equations for the out of equilibrium time evolution of the order parameter and the fluctuations of a scalar field theory in spatially flat FRW cosmologies. After setting the problem in general we propose a…
The quantization of unimodular gravity in minisuperspace leads to a time evolution of states generated by the Hamiltonian, as in usual quantum mechanics. We revisit the analysis made in Ref. \cite{unruh}, extending it to phantom scalar…
We use the non-equlibrium statistical field theory for classical particles, recently developed by Mazenko and Das and Mazenko, together with the free generating functional we have previously derived for point sets initially correlated in…
In math.RT/0302174 we developed a framework to study representations of groups of the form $G((t))$, where $G$ is an algebraic group over a local field $K$. The main feature of this theory is that natural representations of groups of this…
We expand our group classification of quasilinear evolution equations (Acta Appl.Math., v.69, 2001) to the case of general evolution equation in one spatial variable. This enables obtaining several new classes of evolution equations with…
We give a path integral formulation of the time evolution of qudits of odd dimension. This allows us to consider semiclassical evolution of discrete systems in terms of an expansion of the propagator in powers of $\hbar$. The largest power…
An approach to the simulation of locally interacting systems is demonstrated and assayed. The proposal is built upon the concept of folding of bosonic modes previously introduced in the context of linear dynamics and can be seen as an…
We investigate fermionic quantum field theories using functional renormalisation. In the limit of many fermion flavours $N$, we demonstrate that theories have exact solutions for their quantum effective actions given by quasi-local…
Several quantum gravity scenarios lead to physics below the Planck scale characterised by nonlocal, Lorentz invariant equations of motion. We show that such non-local effective field theories lead to a modified Schr\"odinger evolution in…
We derive a well-behaved nonlinear extension of the non-relativistic Liouville-von Neumann dynamics driven by maximal entropy production with conservation of energy and probability. The pure state limit reduces to the usual Schroedinger…
We investigate quantum effects in the evolution of general systems. For studying such temporal quantum phenomena, it is paramount to have a rigorous concept and profound understanding of the classical dynamics in such a system in the first…
In this series of works, we study exactly solvable non-unitary time evolutions in one-dimensional quantum critical systems ranging from quantum quenches to time-dependent drivings. In this part I, we are motivated by the recent works of…
We study the implications of a noncommutative geometry of the minisuperspace variables for the FRW universe with a conformally coupled scalar field. The investigation is carried out by means of a comparative study of the universe evolution…
In the geometry of quantum-mechanical processes, the time-varying curvature coefficient of a quantum evolution is specified by the magnitude squared of the covariant derivative of the tangent vector to the state vector. In particular, the…