相关论文: Eigenvalues as Dynamical Variables

Loop quantum gravity is an approach to quantum gravity that starts from the Hamiltonian formulation in terms of a connection and its canonical conjugate. Quantization proceeds in the spirit of Dirac: First one defines an algebra of basic…

In her recent work, Dittrich generalized Rovelli's idea of partial observables to construct Dirac observables for constrained systems to the general case of an arbitrary first class constraint algebra with structure functions rather than…

Finding diffeomorphism-invariant observables to characterize the properties of gravity and spacetime at the Planck scale is essential for making progress in quantum gravity. The holonomy and Wilson loop of the Levi-Civita connection are…

We define a number of natural (from geometric and combinatorial points of view) deformation spaces of valuations on finite graphs, and study functions over these deformation spaces. These functions include both direct metric invariants…

Natural human movements are stereotyped. They minimise cost functions that include energy, a natural candidate from mechanical and physiological points of view. In time-changing environments, however, motor strategies are modified since…

The relational formalism based on geometrical clocks and Dirac observables in linearized canonical cosmological perturbation theory is used to introduce an efficient method to find evolution equations for gauge invariant variables. Our…

We address the construction and interpretation of diffeomorphism-invariant observables in a low-energy effective theory of quantum gravity. The observables we consider are constructed as integrals over the space of coordinates, in analogy…

The application of the notion of `observable' from gauge theory to diffeomorphism-invariant theories -- most relevantly to general relativity -- has led to numerous conceptual and technical issues when interpreting classical theories with…

Observables 'are observed' whereas beables just 'are'. This gives beables more scope in the cosmological and quantum domains. Both observables and beables are entities that form 'brackets' with 'the constraints' that are 'equal to' zero. We…

We prove dynamical upper bounds for discrete one-dimensional Schroedinger operators in terms of various spacing properties of the eigenvalues of finite volume approximations. We demonstrate the applicability of our approach by a study of…

Physics in (canonical) quantum gravity needs to be manifestly diffeomorphism-invariant. Consequently, physical observables need to be formulated in terms of manifestly diffeomorphism-invariant operators, which are necessarily composite.…

It has recently been suggested that the gravitational dynamics could be obtained by requiring the action to be invariant under diffeomorphism transformations. We argue that the action constructed in usual way is automatically diffeomorphism…

We study how the problem of observables is fully resolved for background independent theories defined on finite graphs. We argue the correct analogue of coordinate independence is the invariance under changes of graph labels, a kind of…

We show in detail how the histories description of general relativity carries representations of both the spacetime diffeomorphisms group and the Dirac algebra of constraints. We show that the introduction of metric-dependent equivariant…

We analyze eigenvalues emerging from thresholds of the essential spectrum of one-dimensional Dirac operators perturbed by complex and non-symmetric potentials. In the general non-self-adjoint setting we establish the existence and…

Characterizations of all continuous, additive and $\mathrm{GL}(n)$-equivariant endomorphisms of the space of convex functions on a Euclidean space $\mathbb{R}^n$, of the subspace of convex functions that are finite in a neighborhood of the…

We derive for generally covariant theories the generic dependency of observables on the original fields, corresponding to coordinate-dependent gauge fixings. This gauge choice is equivalent to a choice of intrinsically defined coordinates…

In this article, we consider the Dirac operator with constant magnetic field in $\mathbb R^2$. Its spectrum consists of eigenvalues of infinite multiplicities, known as the Landau-Dirac levels. Under compactly supported perturbations, we…

A new variable in the Riemannian geometry is introduced by the tetrad and the Ricci's coefficients of rotation, the characters of curve of the Riemannian geometry are determined completely by the new variable; for general relativity, all…

We investigate the fate of diffeomorphisms when the radial gauge is imposed in canonical general relativity. As shown elsewhere, the radial gauge is closely related to the observer's observables. These observables are invariant under a…