Related papers: Quantum Dimensions and Quantum Galois Theory
Quantum theory (QT) has been confirmed by numerous experiments, yet we still cannot fully grasp the meaning of the theory. As a consequence, the quantum world appears to us paradoxical. Here we shed new light on QT by being based on two…
The geometry of Quantum Mechanics in the context of uncertainty and complementarity, and probability is explored. We extend the discussion of geometry of uncertainty relations in wider perspective. Also, we discuss the geometry of…
The applications of geometric control theory methods on Lie groups and homogeneous spaces to the theory of quantum computations are investigated. These methods are shown to be very useful for the problem of constructing an universal set of…
We consider some simple examples of supersymmetric quantum mechanical systems and explore their possible geometric interpretation with the help of geometric aspects of real Clifford algebras. This leads to natural extensions of the…
We propose quantum-mechanical systems in which the number of spatial dimensions is promoted to a dynamical quantum variable, making the effective dimension state-dependent. Interestingly, systems of this form can exhibit enhanced symmetries…
A superfield formalism for quantum fields with N-extended superconformal symmetry is developed using vertex algebra techniques in four dimensions.
The $n$-point amplitudes of gauge and gravity theory are given as a series in the coupling. The recursive derivative expansion is used to find all of the coupling coefficients. Initial conditions to any bare Lagrangian, or of an improved…
A theory of quasi modules at infinity for (weak) quantum vertex algebras including vertex algebras was previously developed in \cite{li-infinity}. In this current paper, quasi modules at infinity for vertex algebras are revisited. Among the…
A rigorous mathematical theory of dimensional analysis, systematically accounting for the use of physical quantities in science and engineering, perhaps surprisingly, was not developed until relatively recently. We claim that this has…
The paper reviews and discusses four ideas scattered in previous papers of the author. First, objective properties of quantum systems are not associated with observables but are defined by preparations. Second, measurable results of…
I discuss a set of strong, but probabilistically intelligible, axioms from which one can {\em almost} derive the appratus of finite dimensional quantum theory. Stated informally, these require that systems appear completely classical as…
We attempt to contribute some novel points of view to the "foundations of quantum mechanics", using mathematical tools from "quantum probability theory" (such as the theory of operator algebras). We first introduce an abstract algebraic…
Quantum measurement is universal for quantum computation. This universality allows alternative schemes to the traditional three-step organisation of quantum computation: initial state preparation, unitary transformation, measurement. In…
The analysis of mathematical structure of the method of operator manifold guides our discussion. The latter is a still wider generalization of the method of secondary quantization with appropriate expansion over the geometric objects. The…
For theoretical approach of quantum measurements it is proposed a set of reconsidered conjectures. The proposed approach implies linear functional transformations for probability density and current but preserves the expressions for…
We present a quantum theory of distances along a curve, based on a linear line element that is equal to the operator square root of the quadratic metric of Riemannian geometry. Since the linear line element is an operator, we treat it…
A very elementary introduction to quantum algebras is presented and a few examples of their physical applications are mentioned.
We explain that a bulk with arbitrary dimensions can be added to the space over which a quantum field theory is defined. This gives a TQFT such that its correlation functions in a slice are the same as those of the original quantum field…
Let $V$ be a simple vertex operator superalgebra and $G$ a finite automorphism group of $V$ containing the canonical automorphism $\sigma$ such that $V^G$ is regular. It is proved that every irreducible $V^G$-module occurs in an irreducible…
We define and study the notion of quantum polarity, which is a kind of geometric Fourier transform between sets of positions and sets of momenta. Extending previous work of ours, we show that the orthogonal projections of the covariance…