相关论文: General Formulation of Quantum Analysis

A rigid framework for the Cartan calculus of Lie derivatives, inner derivations, functions, and forms is proposed. The construction employs a semi-direct product of two graded Hopf algebras, the respective super-extensions of the deformed…

In this paper, a modified formulation of generalized probabilistic theories that will always give rise to the structure of Hilbert space of quantum mechanics, in any finite outcome space, is presented and the guidelines to how to extend…

This note presents a simple and unified formulation of the most fundamental structures used in quantum information with qubits, arbitrary dimension qudits, and quantum continuous variables. This \emph{general quantum variables} construction…

Recently, Lloyd and Montangero have made a brief research proposal on universal quantum computation in integrable systems. The main idea is to encode qubits into quantum action variables and build up quantum gates by the method of resonant…

We formulate quantum mechanics in spacetimes with real-order fractional geometry and more general factorizable measures. In spacetimes where coordinates and momenta span the whole real line, Heisenberg's principle is proven and the…

Generalizations of the three main equations of quantum physics, namely, the Schr\"odinger, Klein-Gordon, and Dirac equations, are proposed. Nonlinear terms, characterized by exponents depending on an index $q$, are considered in such a way…

In 1926, Dirac stated that quantum mechanics can be obtained from classical theory through a change in the only rule. In his view, classical mechanics is formulated through commutative quantities (c-numbers) while quantum mechanics requires…

The concept of polynomials in the sense of algebraic analysis, for a single right invertible linear operator, was introduced and studied originally by D. Przeworska-Rolewicz \cite{DPR}. One of the elegant results corresponding with that…

We present a model unifying general relativity and quantum mechanics. The model is based on the (noncommutative) algebra \mbox{{\cal A}} on the groupoid \Gamma = E \times G where E is the total space of the frame bundle over spacetime, and…

We will examine a particular mathematical derivation in a paper by P. Falkensteiner and H. Grosse (F&G) [1]. In [1] a quantity "delta(A)" is defined. This quantity is generated when the normal ordered generalized charge operator undergoes a…

A formalism is presented in which quantum particle dynamics can be developed on its own rather than `quantization' of an underlying classical theory. It is proposed that the unification of probability and dynamics should be considered as…

A universal formulation of the quantum uncertainty regarding quantum indeterminacy, quantum measurement, and its inevitable observer effect is presented with additional focus on the representability of quantum observables over a given…

A generalized canonical form of action of dynamic theories with higher derivatives is proposed, which does not require the introduction of additional dynamic variables. This form is the initial point for the construction of quantum theory,…

A unified framework for different formulations of quantum theoery is introduced specifying what is meant by a quantum mechanical theory in general.

Generators of spacetime translations and Lorentz group transformations form the Lie algebra of the Poincar\'e group and give rise to the Casimir invariants for a specification of elementary particle characteristics. Moreover quantum…

This investigation pertains to the construction of a class of generalised deformed derivative operators which furnish the familiar finite difference and the q-derivatives as special cases. The procedure involves the introduction of a linear…

A generalization of the classical Leibniz rule for the covariant derivative on a vector bundle is obtained.

Based on the operator representation on the module over Banach algebra $B(X)$, the Campbell-Baker-Hausdorff formula is generalized to the unbounded situations. In conclusion, by means of the logarithmic representation of generally-unbounded…

A key notion bridging the gap between {\it quantum operator algebras} \cite{LZ10} and {\it vertex operator algebras} \cite{Bor}\cite{FLM} is the definition of the commutativity of a pair of quantum operators (see section 2 below). This is…

Polynomials in differentiation operators are considered. The Darboux transformations covariance determines non-Abelian entries to form the coefficients of the polynomials. Joint covariance of a pair of such polynomials (Lax pair) as a…