Related papers: von Neumann Lattices in Finite Dimensions Hilbert …

The holographic principle and the thermodynamics of de Sitter space suggest that the total number of fundamental degrees of freedom associated with any finite-volume region of space may be finite. The naive picture of a short distance…

Field theories place one or more degrees of freedom at every point in space. Hilbert spaces describing quantum field theories, or their finite-dimensional discretizations on lattices, therefore have large amounts of structure: they are…

The quantum mechanical formalism for position and momentum of a particle in a one dimensional cyclic lattice is constructively developed. Some mathematical features characteristic of the finite dimensional Hilbert space are compared with…

A composite quantum system comprising a finite number k of subsystems which are described with position and momentum variables in Z_{n_{i}}, i=1,...,k, is considered. Its Hilbert space is given by a k-fold tensor product of Hilbert spaces…

We study the Hilbert space structure of gauge-invariant operators emergent in large-$N$ multi-matrix quantum mechanics. Building on the framework of \cite{deMelloKoch:2025ngs}, we identify a class of light single-trace operators that behave…

We argue in a model-independent way that the Hilbert space of quantum gravity is locally finite-dimensional. In other words, the density operator describing the state corresponding to a small region of space, when such a notion makes sense,…

We consider many-body quantum systems on a finite lattice, where the Hilbert space is the tensor product of finite-dimensional Hilbert spaces associated with each site, and where the Hamiltonian of the system is a sum of local terms. We are…

The classical phase of the matrix model of 11-dimensional M-theory is complex, infinite-dimensional Hilbert space. As a complex manifold, the latter admits a continuum of nonequivalent, complex-differentiable structures that can be placed…

This paper begins the study of infinite-dimensional modules defined on bicomplex numbers. It generalizes a number of results obtained with finite-dimensional bicomplex modules. The central concept introduced is the one of a bicomplex…

This paper is a detailed study of finite-dimensional modules defined on bicomplex numbers. A number of results are proved on bicomplex square matrices, linear operators, orthogonal bases, self-adjoint operators and Hilbert spaces, including…

In physics, experiments ultimately inform us as to what constitutes a good theoretical model of any physical concept: physical space should be no exception. The best picture of physical space in Newtonian physics is given by the…

We compute the vacuum local modular Hamiltonian associated with a space ball region in the free scalar massless Quantum Field Theory. We give an explicit expression on the one particle Hilbert space in terms of the higher dimensional…

The concepts of independence and totalness of subspaces are introduced in the context of quasi-probability distributions in phase space, for quantum systems with finite-dimensional Hilbert space. It is shown that due to the…

An adapted representation of quantum mechanics sheds new light on the relationship between quantum states and classical states. In this approach the space of quantum states splits into a product of the state space of classical mechanics and…

A Hilbert space in M dimensions is shown explicitly to accommodate representations that reflect the prime numbers decomposition of M. Representations that exhibit the factorization of M into two relatively prime numbers: the kq…

The quantum states or Hilbert spaces for the quantum field theory in de Sitter space-time are studied on ambient space formalism. In this formalism, the quantum states are only depended $(1)$ on the topological character of the de Sitter…

First a description of 2+1 dimensional non-commutative(NC) phase space is presented, where the deformation of the planck constant is given. We find that in this new formulation, generalized Bopp's shift has a symmetric representation and…

We construct two Hilbert spaces over the set of all metrics of arbitrary but fixed signature, defined on a manifold. Every state in one of the Hilbert spaces is built of an uncountable number of wave functions representing some elementary…

We present a N-dimensional quantization a la Berezin-Klauder or frame quantization of the complex plane based on overcomplete families of states (coherent states) generated by the N first harmonic oscillator eigenstates. The spectra of…

We obtain solutions of the Wheeler-DeWitt equation with positive cosmological constant for a closed universe in the large-volume limit. We argue that this space of solutions provides a complete basis for the Hilbert space of quantum gravity…