相关论文: Infinite dimensional covariance and non relativist…

This is a survey on the finite basis problem for varieties of algebraic systems. Our exposition is in two directions: (i) We give numerous examples of varieties which are not finitely based. (ii) We give examples of important varieties with…

The algebra of observables associated with a quantum field theory is invariant under the connected component of the Lorentz group and under parity reversal, but it is not invariant under time reversal. If we take general covariance…

The article provides an introduction to infinite-dimensional differential calculus over topological fields and surveys some of its applications, notably in the areas of infinite-dimensional Lie groups and dynamical systems.

Solutions of matrix quantum mechanics have been shown to describe time dependent backgrounds in the holographically dual two dimensional closed string theory. We review some recent work dealing with non-trivial space-times which arise in…

It is pointed out that affine Lie algebras appear to be the natural mathematical structure underlying the notion of integrability for two-dimensional systems. Their role in the construction and classification of 2D integrable systems is…

The main purpose of part (III) is to give explicit geodesics and billiard orbits in polysquares that exhibit time-quantitative density. In many instances, we can even establish a best possible form of time-quantitative density called…

Quantum reference frames have attracted renewed interest recently, as their exploration is relevant and instructive in many areas of quantum theory. Among the different types, position and time reference frames have captivated special…

An approach to infinite dimensional integration which unifies the case of oscillatory integrals and the case of probabilistic type integrals is presented. It provides a truly infinite dimensional construction of integrals as linear…

Use of certain non-commuting variables is considered in first-order differential equations. Superspace variables are discussed within the setting of first-order ordinary differential equations and n-ary algebras. Results on quadratic…

Study of time series data often involves measuring the strength of temporal dependence, on which statistical properties like consistency and central limit theorem are built. Historically, various dependence measures have been proposed. In…

We discuss representing and reasoning with knowledge about the time-dependent utility of an agent's actions. Time-dependent utility plays a crucial role in the interaction between computation and action under bounded resources. We present a…

A modification of the covariant theory is proposed in which the self-energy of the system, corresponding to time-like degrees of freedom in the configuration space, preserves the classical law of change in quantum theory. As a result,…

The paper investigates, in the framework of branching space-times, whether an infinite EPR-like correlation which does not involve finite EPR-like correlations is possible.

An extension of the finite and infinite Lie groups properties of complex numbers and functions of complex variable is proposed. This extension is performed exploiting hypercomplex number systems that follow the elementary algebra rules. In…

We review some of the recent developments in two dimensional statistical mechanics in which corner transfer matrices provide the vital link between the physical system and the representation theory of quantum affine algebras. This opens…

In this paper we define infinite-dimensional algebra and its representation, whose basis is naturally identified with semi-infinite configurations of the square ladder model. We also extrapolate the ideas for the cyclic 3-leg triangular…

Uncertainty relations are fundamental in quantum mechanics. Here I propose state-independent variance-based uncertainty relations for two or more arbitrary observables in finite dimensional spaces. The uncertainty relations provide…

In this lecture, we survey a number of recent results and developments regarding the representation theory of infinite-dimensional quantum groups (quantum affine algebras and related algebras), as well as their connections with cluster…

We show existence and uniqueness results for nonlinear parabolic equations in noncylindrical domains with possible jumps in the time variable

Vertex algebras in higher dimensions correspond to models of quantum field theory with global conformal invariance. Any vertex algebra in dimension D admits a restriction to a vertex algebra in any lower dimension and, in particular, to…