Related papers: Interpreting canonical tensor model in minisupersp…
Tensor models are the generalization of matrix models, and are studied as models of quantum gravity in general dimensions. In this paper, I discuss the algebraic structure in the fuzzy space interpretation of the tensor models which have a…
Minisuperpace Quantum Cosmology is an approach by which it is possible to infer initial conditions for dynamical systems which can suitably represent observable and non-observable universes. Here we discuss theories of gravity which, from…
In cosmology minisuperspace models are described by nonlinear time-reparametrization invariant systems with a finite number of degrees of freedom. Often these models are not explicitly integrable and cannot be quantized exactly. Having this…
The canonical tensor model (CTM) is a rank-three tensor model formulated as a totally constrained system in the canonical formalism. The constraint algebra of CTM has a similar structure as that of the ADM formalism of general relativity,…
This work is a continuation of our previous works concerning linear canonical transformations and phase space representation of quantum theory. It is mainly focused on the description of an approach which allows to establish spinorial…
The process of canonical quantization is redefined so that the classical and quantum theories coexist when \hbar>0, just as they do in the real world. This analysis not only supports conventional procedures, it also reveals new quantization…
Tensor models are measures for random tensors. They generalise matrix models and were developed to study random geometry in arbitrary dimension. Moreover, they are strongly connected to quantum gravity theories as additionally to the…
It has long been considered that conformal superspace is the natural configuration space for canonical general relativity. However, this was never definitively demonstrated. We have found that the standard conformal method of solving the…
Scalar-tensor theories are studied in the context of cosmological evolution, where the expansion history of the Universe is reconstructed. It is considered quintessence/phantom models, where inflation and cosmic acceleration are reproduced.…
Canonical variables for the Poisson algebra of quantum moments are introduced here, expressing semiclassical quantum mechanics as a canonical dynamical system that extends the classical phase space. New realizations for up to fourth order…
This article provides a basic introduction to some concepts of non-commutative geometry. The importance of quantum groups and quantum spaces is stressed. Canonical non-commutativity is understood as an approximation to the quantum group…
A generalized canonical form of multi-time dynamical theories is proposed. This form is a starting point for a modified canonical quantization procedure of theories based on a quantum version of the action principle. As an example, the…
Canonical correlation analysis is a family of multivariate statistical methods for the analysis of paired sets of variables. Since its proposition, canonical correlation analysis has for instance been extended to extract relations between…
A general framework for the description of the physical properties of matter by a canonical reduction procedure of tensors is presented; besides geometrical symmetries, this paper emphasizes the role of intrinsic symmetries which are due…
We present a study on linear canonical transformation in the framework of a phase space representation of quantum mechanics that we have introduced in our previous work [1]. We begin with a brief recall about the so called phase space…
This paper introduces a new object called the momentum tensor. Together with the velocity tensor it forms a basis for establishing the tensorial picture of classical and relativistic mechanics. Some properties of the momentum tensor are…
Causal Dynamical Triangulations is a background independent approach to quantum gravity. In this paper we introduce a phenomenological transfer matrix model, where at each time step a reduced set of quantum states is used. The states are…
Canonical correlation analysis (CCA) is a fundamental statistical tool for exploring the correlation structure between two sets of random variables. In this paper, motivated by recent success of applying CCA to learn low dimensional…
The rank-three tensor models, which have a rank-three tensor as their only dynamical variable, may be interpreted as models of dynamical fuzzy spaces. In this interpretation, the generalized Hermiticity condition on the rank-three tensor…
It is widely accepted that the fundamental geometrical law of nature should follow from an action principle. The particular subset of transformations of a system's dynamical variables that maintain the form of the action principle comprises…