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There has been recent interest in identifying entanglement as the fundamental concept from which space may emerge. We note that the particular way that a Hilbert space is decomposed into tensor factors is important in what the resulting…
Recent studies show that deformations in quantum mechanics are inevitable. In this contribution, we consider a relativistic quantum mechanical differential equation in the presence of Dunkl operator-based deformation and we investigate…
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…
The article summarizes and consolidates investigations on hyperbolic complex numbers with respect to the Klein-Gordon equation for fermions and bosons. The hyperbolic complex numbers are applied in the sense that complex extensions of…
Consider the quotient of a Hilbert space by a subgroup of its automorphisms. We study whether this orbit space can be embedded into a Hilbert space by a bilipschitz map, and we identify constraints on such embeddings.
Studies of geometrical theories suggest that fundmental problems of quantization arise from the disparate usage of displacement operators. These may be the source of a concealed inconsistency in the accepted formalism of quantum physics.…
We discuss a time-splitting spectral method for the solution of the Klein--Gordon--Maxwell system in quantum electrodynamics. The convergence in Hilbert space is proven theoretically and charge conservation is established. The theoretical…
Single-valuedness of the eigenfunctions of the quantised Hitchin Hamiltonians is proposed as a natural quantisation condition. Separation of Variables can be used to relate the classification of eigenstates to the classification of…
A detailed consideration of the Klein-Gordon equation in relativistic quantum mechanics is presented in order to offer more clarity than many standard approaches. The equation is frequently employed in the research literature, even though…
We can obtain one solution of the Hamiltonian constraint equation in the local sense. The form of the state is suggested from the up-to-down method in our previous work. The up-to-down method works for different way in treating the general…
An extension of the Dirac procedure for the quantization of constrained systems is necessary to address certain issues that are left open in Dirac's original proposal. These issues play an important role especially in the context of…
A possible way for the consistent probability interpretation of the Klein-Gordon equation is proposed. It is assumed that some states of a scalar charged particle cannot be physically realized. The rest of quantum states are proven to have…
We present a general approach to quantum entanglement and entropy that is based on algebras of observables and states thereon. In contrast to more standard treatments, Hilbert space is an emergent concept, appearing as a representation…
We show that the Segal quantization of an arbitrary system of decoupled harmonic oscillators is unique in the sense that the one particle Hilbert space is completely determined by the requests of being a naturally complex symplectic space…
We develop a systematic procedure for constructing quantum many-body problems whose spectrum can be partially or totally computed by purely algebraic means. The exactly-solvable models include rational and hyperbolic potentials related to…
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…
On logarithmic paper some real algebraic curves look like smoothed broken lines. Moreover, the broken lines can be obtained as limits of those curves. The corresponding deformation can be viewed as a quantization, in which the broken line…
A longstanding question in quantum gravity regards the localization of quantum information; one way to formulate this question is to ask how subsystems can be defined in quantum-gravitational systems. The gauge symmetry and necessity of…
We investigate modifications of quantum mechanics (QM) that replace the unitary group in a finite dimensional Hilbert space with a finite group and determine the minimal sequence of subgroups necessary to approximate QM arbitrarily closely…
A number of arguments purport to show that quantum field theory cannot be given an interpretation in terms of localizable particles. We show, in light of such arguments, that the classical $\hbar\to 0$ limit can aid our understanding of the…