相关论文: Nambu variant of Local Resolution of Problem of Ti…

In a major advance and simplification of this field, we show that A Local Resolution of the Problem of Time - also viewable as A Local Theory of Background Independence - can at the classical level be described solely by of Lie's…

A local resolution of the Problem of Time has recently been given, alongside reformulation as a local theory of Background Independence. The classical part of this can be viewed as requiring just Lie's Mathematics, albeit entrenched in…

A local resolution of the Problem of Time has recently been given, alongside reformulation as a local theory of Background Independence. The classical part of this requires just Lie's Mathematics, much of which is basic: i) Lie derivatives…

We introduce nine further local facets of the classical Problem of Time, and underlying Background Independence aspects, the previous two Articles having covered one further facet-and-aspect each for a total of eleven. I.e. 1) Constraint…

This Series of Articles provides a local resolution of this major longstanding foundational problem between QM and GR, or, more generally, between Background Dependent and Background Independent Physics. We focus on the classical version;…

Given a state space, Assignment of Observables involves Taking Function spaces Thereover. At the classical level, the state space in question is phase space or configuration space. This assignment picks up nontrivialities when whichever…

In this final piecemeal treatment of local Problem of Time facets, and underlying Background Independence aspects, we first reconsider the ten local facets and aspects considered so far at the quantum level. This is essential both to…

Background Independence is the modern form of the relational side of the Absolute versus Relational Debate. Difficulties with its implementation form the Problem of Time. Its 9 facets - Isham and Kucha\v{r}'s conceptual classification -…

This paper concerns what Background Independence itself is (as opposed to some particular physical theory that is background independent). The notions presented mostly arose from a layer-by-layer analysis of the facets of the Problem of…

We establish a classical analog of the Nambu-Goldstone theorem for spontaneous breaking of spacetime symmetries. It provides a counting rule for independent Nambu-Goldstone fields and states which of them are gapped. We demonstrate that…

The Lie claw digraph controls Background Independence and thus the Problem of Time and indeed the Fundamental Nature of Physical Law. This has been established in the realms of Flat and Differential Geometry with varying amounts of extra…

Yang-Mills theories supplemented by an additional coordinate constraint, which is solved and substituted in the original Lagrangian, provide examples of the so called Nambu models, in the case where such constraints arise from spontaneous…

I lay out the problem of time facets as arising piecemeal from a number of aspects of background independence. Almost all of these already have simpler classical counterparts. This approach can be viewed as a facet by facet completion of…

The Lie claw digraph has recently been shown to control Background Independence and thus both the Problem of Time and the nature of Physical Law. This is established for Flat and Differential Geometry with varying amounts of extra…

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,…

We review some aspects of Nambu mechanics on the basis of the works previously published separately by the present author. Main focuses are on three themes, its various symmetry structures, their possible relevance to string/M theory, and a…

We present several non-trivial examples of the three-dimensional quantum Nambu bracket which involve square matrices or three-index objects. Our examples satisfy two fundamental properties of the classical Nambu bracket: they are…

Nambu proposed an extension of dynamical system through the introduction of a new bracket (Nambu bracket) in 1973. This article is a short review of the developments after his paper. Some emphasis are put on a viewpoint that the Nambu…

M-branes are related to theories on function spaces $\cal{A}$ involving M-linear non-commutative maps from $\cal{A} \times \cdots \times \cal{A}$ to $\cal{A}$. While the Lie-symmetry-algebra of volume preserving diffeomorphisms of $T^M$…

We propose a variant formulation of Hamiltonian systems by the use of variables including redundant degrees of freedom. We show that Hamiltonian systems can be described by extended dynamics whose master equation is the Nambu equation or…