Related papers: Quantization on space-like surfaces
Dynamical evolution is described as a parallel section on an infinite dimensional Hilbert bundle over the base manifold of all frames of reference. The parallel section is defined by an operator-valued connection whose components are the…
Quantum field theory (QFT) in classical spacetime has revealed interesting and puzzling aspects about gravitational systems, in particular black hole thermodynamics and its information processing. Although quantum gravitational effects may…
In quantum mechanics, one can express the evolution operator and other quantities in terms of functional integrals. The main goal of this paper is to prove corresponding results in the geometric approach to quantum theory. We apply these…
Quantum cosmology describes universe as a relativistic object with an evolution defined by an equation for the energy density corresponding to the least action principle: (Taganov, 2008). In quantum cosmology this equation plays the same…
The formulation of quantum mechanics within the framework of entropic dynamics is extended to the domain of relativistic quantum fields. The result is a non-dissipative relativistic diffusion in the infinite dimensional space of field…
We consider a Schr\"odinger quantum dynamics for the gravitational field associated to a FRW spacetime and then we solve the corresponding eigenvalue problem. We show that, from a phenomenological point of view, an Evolutionary Quantum…
Simulating key static and dynamic properties of matter -- from creation in the Big Bang to evolution into sub-atomic and astrophysical environments -- arising from the underlying fundamental quantum fields of the Standard Model and their…
The recently proposed probability representation of quantum mechanics is generalized to quantum field theory. We introduce a probability distribution functional for field configurations and find an evolution equation for such a…
Over the past five years, there has been significant progress on the problem of quantization of diffeomorphism covariant field theories with {\it local} degrees of freedom. The absence of a background space-time metric in these theories…
The logical structure of Quantum Mechanics (QM) and its relation to other fundamental principles of Nature has been for decades a subject of intensive research. In particular, the question whether the dynamical axiom of QM can be derived…
This thesis, explores the quantum entanglement and evolution through both a geometric and dynamical perspective. The first part focuses on classical phase space and its central role in Hamiltonian mechanics, emphasizing the importance of…
Deterministic dynamical models are discussed which can be described in quantum mechanical terms. -- In particular, a local quantum field theory is presented which is a supersymmetric classical model. The Hilbert space approach of Koopman…
It is known that quantum field theories in curved spacetime suffer from a number of pathologies, including the inability to relate states on different spatial slices by proper unitary time-evolution operators. In this article, we illustrate…
Invariance under translation is exploited to efficiently simulate one-dimensional quantum lattice systems in the limit of an infinite lattice. Both the computation of the ground state and the simulation of time evolution are considered.
Using general features of recent quantizations of the Hamiltonian constraint in loop quantum gravity and loop quantum cosmology, a dynamical interpretation of the constraint equation as evolution equation is presented. This involves a…
We describe a $q$-deformed dynamical system corresponding to the quantum free particle moving along the circle. The algebra of observables is constructed and discussed. We construct and classify irreducible representations of the system.
Process of formation of the universe with its further expansion in the first evolution stage is investigated in the framework of Friedmann-Robertson-Walker metrics on the basis of quantum model, where a new type of matter is introduced,…
Noncommutative field theory (NCFT) is an extension of quantum field theory (QFT) that redefines spacetime, replacing commuting coordinates with a noncommutative structure. This shift fundamentally alters the way fields, interactions, and…
We present a gravitational quantum dynamics theory that combines quantum field theory for particle dynamics in space-time with classical Einstein's general relativity in a non-Riemannian Finsler space. This approach is based on the…
This letter serves as the generalization of the work 2505.16436, where we investigated the quantum field theory in Klein space which has two time directions. We extend studies to the general spacetime $\mathbb{R}^{n,d-n}\,(n,d-n\geq2)$ in a…