相关论文: Comparative Theory of Background Independence

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…

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…

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…

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…

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…

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…

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…

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…

Since the main open problem of contemporary physics is to find a unified description of the four interactions, we present a possible scenario which, till now only at the classical level, is able to englobe experiments ranging from…

A recently proposed pregeometric auxiliary vector mediated gauge theory is studied in its canonical domain, by performing the Legendre transform on a curved background and by considering its covariant phase space, with further application…

The deformation theory of a Dirac structure is controlled by a differential graded Lie algebra which depends on the choice of an auxiliary transversal Dirac structure; if the transversal is not involutive, one obtains an $L_\infty$ algebra…

We show that a class of topological field theories are quantum duals of the harmonic oscillator. This is demonstrated by establishing a correspondence between the creation and annihilation operators and non-local gauge invariant observables…

This is primarily a survey of the way in which Hopf cyclic cohomology has emerged and evolved, in close relationship with the application of the noncommutative local index formula to transverse index theory on foliations. Being…

In this note, we describe how the study of backgrounds for general quantum systems can be formulated in terms of the representation theory of abstract $C^*$ algebras. We illustrate our general framework through two example systems:…

Classical background independence is reflected in Lagrangian general relativity through covariance under the full diffeomorphism group. We show how this independence can be maintained in a Hamilton-Jacobi approach that does not accord…

We present a pseudoclassical mechanics model which exhibits gauge symmetry and time-reparametrization invariance. As such, first- and second-class constraints restrict the phase space, and the Hamiltonian weakly vanishes. We show that the…

We consider two concepts often discussed as significant features of general relativity (particularly when contrasted with the other forces of the Standard Model): background independence and diffeomorphism invariance. We remind the reader…

The gauge symmetries of a general dynamical system can be systematically obtained following either a Hamiltonean or a Lagrangean approach. In the former case, these symmetries are generated, according to Dirac's conjecture, by the first…

Soon after the Yang-Mills work, the gauge invariance became one of the basic principles in the elementary particles theory. The gauge invariance idea is that Lagrangian has to be invariant not only with respect to the coordinates…