Related papers: Physical Interpretations of Nilpotent Quantum Mech…
We present a construction of the formalism where fundamental variables are nilpotent, but in contrast to the supermathematics, commutative. This gives another possibility to realize classically the Pauli exclusion principle. We sketch the…
The formalism of nilpotent mechanics is introduced in the Lagrangian and Hamiltonian form. Systems are described using nilpotent, commuting coordinates $\eta$. Necessary geometrical notions and elements of generalized differential…
Quantum mechanics is more than the derivation of straightforward theorems about vector spaces, Hilbert spaces and functional analysis. In order to be applicable to experiment and technology, those theorems need interpretation and meaning.…
Standard quantum mechanics unquestionably violates the separability principle that classical physics (be it point-like analytic, statistical, or field-theoretic) accustomed us to consider as valid. In this paper, quantum nonseparability is…
It is shown that quantum mechanics on noncommutative spaces (NQM) can be obtained by the canonical quantization of some underlying second class constrained system formulated in extended configuration space. It leads, in particular, to an…
For the Becchi-Rouet-Stora-Tyutin (BRST) invariant extended action for any gauge theory, there exists another off-shell nilpotent symmetry. For linear gauges, it can be elevated to a symmetry of the quantum theory and used in the…
The discussion of the foundations of quantum mechanics is complicated by the fact that a number of different issues are closely entangled. Three of these issues are i) the interpretation of probability, ii) the choice between realist and…
The classical and quantum features of Nambu mechanics are analyzed and fundamental issues are resolved. The classical theory is reviewed and developed utilizing varied examples. The quantum theory is discussed in a parallel presentation,…
The interpretation of quantum mechanics has been a problem since its founding days. A large contribution to the discussion of possible interpretations of quantum mechanics is given by the so-called impossibility proofs for hidden variable…
In analogy with conventional quantum mechanics, non-commutative quantum mechanics is formulated as a quantum system on the Hilbert space of Hilbert-Schmidt operators acting on non-commutative configuration space. It is argued that the…
Incompatibility between conjugate variables and complementary pictures comes in two kinds, exclusive of one another. The first kind is unconditional, and the second conditional on quantum's indivisibility. We employ this distinction to…
The non-individuals interpretation of quantum mechanics is presented with the aim of clarifying it and highflying some of its salient features. Alternative formulations of it are proposed and examined.
We introduce specific type of hyperbolic spaces. It is not a general linear covariant object, but of use in constructing nilpotent systems. In the present work necessary definitions and relevant properties of configuration and phase spaces…
The Hilbert space formalism of quantum mechanics is reviewed with emphasis on applications to quantum computing. Standard interferomeric techniques are used to construct a physical device capable of universal quantum computation. Some…
In this paper we attempt to provide a physical representation of quantum superpositions. For this purpose we discuss the constraints of the quantum formalism to the notion of possibility and the necessity to consider a potential realm…
We point out that some of the proposed generalized/modified uncertainty principles originate from solvable, or nilpotent at appropriate limits, "deformations" of Lie algebras. We briefly comment on formal aspects related to the…
Quantum mechanics is formulated as a geometric theory on a Hilbert manifold. Images of charts on the manifold are allowed to belong to arbitrary Hilbert spaces of functions including spaces of generalized functions. Tensor equations in this…
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…
Here I explore a novel no-collapse interpretation of quantum mechanics which combines aspects of two familiar and well-developed alternatives, Bohmian mechanics and the many-worlds interpretation. Despite reproducing the empirical…
It is shown that quantum mechanics on noncommutative (NC) spaces can be obtained by canonical quantization of some underlying constrained systems. Noncommutative geometry arises after taking into account the second class constraints…