Related papers: Generalized imaginary units in quantum mechanics
We discuss the problems of quantum theory (QT) complicating its merging with general relativity (GR). QT is treated as a general theory of micro-phenomena - a bunch of models. Quantum mechanics (QM) and quantum field theory (QFT) are the…
In it's usual presentation, classical mechanics appears to give time a very special role. But it is well known that mechanics can be formulated so as to treat the time variable on the same footing as the other variables in the extended…
The Fourier transform, known in classical analysis, and generalized in abstract harmonic analysis, can also be considered in the theory of locally compact quantum groups. In this note, I discuss some aspects of this more general Fourier…
Machine learning is a fascinating and exciting field within computer science. Recently, this excitement has been transferred to the quantum information realm. Currently, all proposals for the quantum version of machine learning utilize the…
Group representations play a central role in theoretical physics. In particular, in quantum mechanics unitary --- or, in general, projective unitary --- representations implement the action of an abstract symmetry group on physical states…
Quantum computers promise a highly efficient approach to investigate quantum phase transitions, which describe abrupt changes between different ground states of many-body systems. At quantum critical points, the divergent correlation length…
A nonlocal generalization of quantum field theory in which momentum space is the space of continuous maps of a circle into $\mathbf{R}^4$ is proposed. Functional integrals in this theory are proved to exist. Renormalized quantum field model…
How should we interpret physical theories, and especially quantum theory, if we drop the assumption that we should treat it as an exact description of the whole Universe? I expound and develop the claim that physics is about the study of…
The geometric form of standard quantum mechanics is compatible with the two postulates: 1) The laws of physics are invariant under the choice of experimental setup and 2) Every quantum observation or event is intrinsically statistical.…
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…
The structure of covariant instruments is studied and a general structure theorem is derived. A detailed characterization is given to covariant instruments in the case of an irreducible representation of a locally compact group.
Complex numbers are widely used in both classical and quantum physics, and play an important role in describing quantum systems and their dynamical behavior. In this paper we study several measures of imaginarity of quantum states in the…
Quantum physics involves an ensemble of quantum systems, usually one thinks of a large ensemble of identical quantum systems at one single time. In single ion experiments one has a single quantum system at an ensemble of different times.…
In the work it is shown that the principles "the objective local theory" and corollaries of the standard quantum mechanics are not in such antagonistic inconsistency as it is usually supposed. In the framework of algebraic approach, the…
We put forward a possible new interpretation and explanatory framework for quantum theory. The basic hypothesis underlying this new framework is that quantum particles are conceptual entities. More concretely, we propose that quantum…
This study examines Quaternion Dirac solutions for an infinite square well. The quaternion result does not recover the complex result within a particular limit. This raises the possibility that quaternionic quantum mechanics may not be…
This article presents a novel interpretation of quantum mechanics. It extends the meaning of ``measurement'' to include all property-indicating facts. Intrinsically space is undifferentiated: there are no points on which a world of locally…
We point out a fundamental problem that hinders the quantization of general relativity: quantum mechanics is formulated in terms of systems, typically limited in space but infinitely extended in time, while general relativity is formulated…
Recently, we presented a unified way of analysing classical cosmological perturbation in generalized gravity theories. In this paper, we derive the perturbation spectrums generated from quantum fluctuations again in unified forms. We…
It is a fundamental question that why quantum mechanics uses complex numbers instead of only real numbers. To address this topic, recently, a rigorous resource theory for the imaginarity of quantum states were established, and several…