Related papers: Classical approximations of relativistic quantum p…
Quantum computers can be used to simulate nonlinear non-Hamiltonian classical dynamics on phase space by using the generalized Koopman-von Neumann formulation of classical mechanics. The Koopman-von Neumann formulation implies that the…
We study how meaningful physical predictions can arise in nonperturbative quantum gravity in a closed Lorentzian universe. In such settings, recent developments suggest that the quantum gravitational Hilbert space is one-dimensional and…
We show that quantum mechanics can be represented as an asymptotic projection of statistical mechanics of classical fields. Thus our approach does not contradict to a rather common opinion that quantum mechanics could not be reduced to…
In this talk I briefly review recent developments in quantum field theories on a noncommutative Euclidean space, with Heisenberg-like commutation relations between coordinates. I will be concentrated on new physics learned from this…
This work deals with the new, relativistic direction in quantum econophysics, within the bounds of which a change of the classical paradigms in mathematical modelling of socio-economic system is offered. Classical physics proceeds from the…
This paper reviews the histories approach to quantum mechanics. This discussion is then applied to theories of quantum gravity. It is argued that some of the quantum histories must approximate (in a suitable sense) to classical histories,…
This study investigates pseudo-Hermitian quantum mechanics, where the Hamiltonian satisfies a modified Hermiticity condition. We extend the uncertainty relation for such systems, demonstrating its equivalence to the standard Hermitian case…
Intuitively, the more powerful a theory is, the greater the variety and quantity of ideas can be expressed through its formal language. Therefore, when comparing two theories concerning the same subject, it seems only reasonable to compare…
We describe quantum and classical Hamiltonian dynamics in a common Hilbert space framework, that allows the treatment of mixed quantum-classical systems. The analysis of some examples illustrates the possibility of entanglement between…
We generalize the Hamiltonian picture of General Relativity coupled to classical matter, known as geometrodynamics, to the case where such matter is described by a Quantum Field Theory in Curved Spacetime, but gravity is still described by…
Non-relativistic quantum mechanics for a free particle is shown to emerge from classical mechanics through an invariance principle under transformations that preserve the Heisenberg position-momentum inequality. These transformations are…
After analyzing Dirac's equation, one can suggest that a well-known quantum-mechanical momentum operator is associated with relativistic momentum, rather than with non-relativistic one. Consideration of relativistic energy and momentum…
Based on the Bohr's correspondence principle it is shown that relativistic mechanics and quantum mechanics may be considered as generalizations of classical mechanics. A comparative description of relativistic and classical mechanics is…
We study time dependent correlation functions in hot quantum and classical field theory for the $\lambda\phi^4$ case. We set up the classical analogue of thermal field theory and make a direct comparison between the quantum and classical…
A quantum field theory is described which is a supersymmetric classical model. -- Supersymmetry generators of the system are used to split its Liouville operator into two contributions, with positive and negative spectrum, respectively. The…
Relativistic quantum mechanics can be considered to have begun with a search for wave equations corresponding to each intrinsic spin. However, relativistic quantum physics differs fundamentally from the non-relativistic wave mechanics. It…
We show that for the Lindblad evolution defined using (at most) quadratically growing classical Hamiltonians and (at most) linearly growing classical jump functions (quantized into jump operators assumed to satisfy certain ellipticity…
We start with a discussion of the use of mathematics to model the real world then justify the role of Hilbert space formalism for such modelling in the general context of quantum logic. Following this, the incompleteness of the…
The relational version of the modal interpretation offers both a consistent quantum ontology and solution for quantum paradoxes within the framework of nonrelativistic quantum mechanics. In the present paper this approach is generalized for…
In this first of a series of four articles, it is shown how a hamiltonian quantum dynamics can be formulated based on a generalization of classical probability theory using the notion of quasi-invariant measures on the classical phase space…