Related papers: Classical Histories in Hamiltonian Systems
The hyperplane and proper time formalisms are discussed mainly for the spin-half particles in the quantum case. A connection between these covariant Hamiltonian formalisms is established. It is showed that choosing the space-like…
Mechanics is developed over a differentiable manifold as space of possible positions. Time is considered to fill a one--dimensional Riemannian manifold, so having the metric as lapse. Then the system is quantized with covariant instead of…
The key concept discussed in these lectures is the relation between the Hamiltonians of a quantum integrable system and the Casimir elements in the underlying hidden symmetry algebra. (In typical applications the latter is either the…
Recent developments in holographic gravity suggest that spacetime structure may be deeply related to quantum mechanics. In this work, from a different perspective, we demonstrate that wave-particle duality can be interpreted as the…
We review in simple terms the covariant approaches to the canonical formulation of classical relativistic field theories (in particular gauge field theories and general relativity) and we discuss the relationships between these approaches…
Working within the HPO (History Projection Operator) Consistent Histories formalism, we follow the work of Savvidou on (scalar) field theory and that of Savvidou and Anastopolous on (first-class) constrained systems to write a histories…
The consistent histories formulation of the quantum theory of a closed system with pure initial state defines an infinite number of incompatible consistent sets, each of which gives a possible description of the physics. We investigate the…
A covariant description of the canonical theory for interacting classical fields is developed on a space-like hypersurface. An identity invariant under the canonical transformations is obtained. The identity follows a canonical equation in…
It is expected that a quantum theory of gravity will radically alter our current notion of spacetime geometry. However, contrary to what was commonly assumed for many decades, quantum gravity effects could manifest in scales much larger…
If there exists a classical, i.e. deterministic theory underlying quantum mechanics, an explanation must be found of the fact that the Hamiltonian, which is defined to be the operator that generates evolution in time, is bounded from below.…
We investigate the possibility of assigning consistent probabilities to sets of histories characterized by whether they enter a particular subspace of the Hilbert space of a closed system during a given time interval. In particular we…
Time is absolute in standard quantum theory and dynamical in general relativity. The combination of both theories into a theory of quantum gravity leads therefore to a "problem of time". In my essay I shall investigate those consequences…
Quantum gravity aims to describe gravity in quantum mechanical terms. How exactly this needs to be done remains an open question. Various proposals have been put on the table, such as canonical quantum gravity, loop quantum gravity, string…
Understanding how classical physics emerges from quantum mechanics remains a central problem in the foundations of physics. Here we derive a classical limit from finite-resolution measurements, modeled by continuous coarse-grained POVMs.…
In this essay, we argue that the problem of time should not be regarded as an issue to be resolved within the prevailing framework for studying quantum gravity, but rather as an indication that there is an issue within the framework itself.…
While real Hamiltonian mechanics and Hermitian quantum mechanics can both be cast in the framework of complex canonical equations, their complex generalisations have hitherto been remained tangential. In this paper quaternionic and…
The method of decoherent histories allows probabilities to be assigned to sequences of quantum events in systems, such as the universe as a whole, where there is no external observer to make measurements. This paper applies the method of…
In this paper I raise a worry about the most extended resolutions of the problem of time of canonical quantizations of general relativity. The reason for this is that these resolutions are based on analogies with deparametrizable models for…
Any two infinite-dimensional (separable) Hilbert spaces are unitarily isomorphic. The sets of all their self-adjoint operators are also therefore unitarily equivalent. Thus if all self-adjoint operators can be observed, and if there is no…
Recent tremendous development of quantum information theory led to a number of quantum technological projects, e.g., quantum random generators. This development stimulates a new wave of interest in quantum foundations. One of the most…