Related papers: Non-associativity, supersymmetry and hidden variab…
We introduce an algebraic framework for interacting quantum systems that enables studying complex phenomena, characterized by the coexistence and competition of various broken symmetry states of matter. The approach unveils the hidden unity…
We study quantum mechanics in the stochastic formulation, using the functional integral approach. The noise term enters the classical action as a local contribution of anticommuting fields. The partition function is not invariant under…
Reduction is shown to be a possible consequence of the basic principles of quantum mechanics, involving no branching of the quantum state of the universe. The key feature of a measurement is attributed to the creation of macroscopic germs…
We consider in general terms dynamical systems with finite-dimensional, non-simply connected configuration-spaces. The fundamental group is assumed to be finite. We analyze in full detail those ambiguities in the quantization procedure that…
Collective phenomena arise from interactions within complex systems, leading to behaviors absent in individual components. Observing quantum collective phenomena with macroscopic mechanical oscillators has been impeded by the stringent…
Is quantum mechanics about 'states'? Or is it basically another kind of probability theory? It is argued that the elementary formalism of quantum mechanics operates as a well-justified alternative to 'classical' instantiations of a…
We examine the notion of symmetry in quantum field theory from a fundamental representation theoretic point of view. This leads us to a generalization expressed in terms of quantum groups and braided categories. It also unifies the…
Various topics concerning the entanglement of composite quantum systems are considered with particular emphasis concerning the strict relations of such a problem with the one of attributing objective properties to the constituents. Most of…
An introduction to some basic ideas of the author's "quantum cybernetics" is given, which depicts waves and "particles" as mutually dependent system components, thus defining "organizationally closed systems" characterized by a fundamental…
We report general properties of N-fold supersymmetry in one-dimensional quantum mechanics. N-fold supersymmetry is characterized by supercharges which are N-th polynomials of momentum. Relations between the anti-commutator of the…
In the quantum mechanics of collision problems we must consider scattering states of the system. For these states, the wave functions do not remain in Hilbert space, but they are expressible in terms of generalized functions of a Gel'fand…
The momentum operator representation of nonrelativistic anyons is developed in the Chern - Simons formulation of fractional statistics. The connection between anyons and the q-deformed bosonic algebra is established.
Why does the $i=\sqrt{-1}$ appear essentially in the quantum mechanics? Why are there operators and noncommutativity (the uncertainty relation) in the quantum mechanics? Why are these two aspects closely related and indivisible? In probing…
The review of modern study of algebraic, geometric and differential properties of quaternionic (Q) numbers with their applications. Traditional and "tensor" formulation of Q-units with their possible representations are discussed and groups…
The interaction between two parts in a compound quantum system may be reconsidered more completely than before and some new understandings and conclusions different from current quantum mechanics are obtained, including the conservation law…
This brief article gives an overview of quantum mechanics as a {\em quantum probability theory}. It begins with a review of the basic operator-algebraic elements that connect probability theory with quantum probability theory. Then quantum…
I examine quantum mechanical Hamiltonians with partial supersymmetry, and explore two main applications. First, I analyze a theory with a logarithmic spectrum, and show how to use partial supersymmetry to reveal the underlying structure of…
These five lectures collect elementary facts about 4D supersymmetric theories with emphasis on N=1 supersymmetry, as well as the basic notions of supersymmetric quantum mechanics. Contents: I. From symmetries to supersymmetry; II. Basic…
The basic framework for a systematic construction of a quantum theory of Riemannian geometry was introduced recently. The quantum versions of Riemannian structures --such as triad and area operators-- exhibit a non-commutativity. At first…
A vexing problem involving nonassociativity is resolved, allowing a generalization of the usual complex Mobius transformations to the octonions. This is accomplished by relating the octonionic Mobius transformations to the Lorentz group in…