相关论文: Problem of Time and Background Independence: class…

This article introduces a novel "bootstrap domain-of-dependence" concept, according to which, for all time following a given illumination period of arbitrary duration, the wave field scattered by an obstacle is encoded in the history of…

Our paper illustrates how the theory of Lie systems allows recovering known results and provide new examples of piecewise deterministic processes with phase-type jumps for which the corresponding first-time passage problems may be solved…

Within the framework of classical field theory, the connection between the Dirac field as the field of matter and the spacetime metric is discussed. Polarization structure of the Dirac field is shown to be rich enough to determine the…

Lagrangian multiforms provide a variational framework for describing integrable hierarchies. This thesis presents two approaches for systematically constructing Lagrangian one-forms, which cover the case of finite-dimensional integrable…

Let $(G\rr P, \mathsf D_G)$ be a Dirac groupoid. We show that there are natural Lie algebroid structures on the units $\lie A(\mathsf D_G)$ and on the core $I^\tg(\mathsf D_G)$ of the multiplicative Dirac structure. In the Poisson case, the…

In this paper we present a theory of reduction of quantum systems in the presence of symmetries and constraints. The language used is that of Lie--Jordan Banach algebras, which are discussed in some detail together with spectrum properties…

We demonstrate that the Dirac representation theory can be effectively adjusted and applied to signal theory. The main emphasis is on orthogonality as the principal physical requirement. The particular role of the identity and projection…

In this paper, we describe a geometric setting for higher-order lagrangian problems on Lie groups. Using left-trivialization of the higher-order tangent bundle of a Lie group and an adaptation of the classical Skinner-Rusk formalism, we…

We study higher-order analogues of Dirac structures, extending the multisymplectic structures that arise in field theory. We define higher Dirac structures as involutive subbundles of $TM+\wedge^k TM^*$ satisfying a weak version of the…

In this work, resolutions will be given for commonly stated problems associated with a model that assumes that space and time are discretized (i.e., atomized). This model is in contrast to the continuous space-time model that is used in all…

Differential geomtrical methods for deriving the Dirac equation in Curved Spacetime are presented. Einstein's field equation is applied in a novel manner; in the most current standard reference, Birrell and Davies, 1994 [1], the suggestions…

We discuss mimetic gravity theories with direct couplings between the curvature and higher derivatives of the scalar field, up to the quintic order, which were proposed to solve the instability problem for linear perturbations around the…

In recent years much effort has been concentrated towards achieving polynomial time lower bounds on algorithms for solving various well-known problems. A useful technique for showing such lower bounds is to prove them conditionally based on…

The explicit semiclassical treatment of logarithmic perturbation theory for the bound-state problem within the framework of the Dirac equation is developed. Avoiding disadvantages of the standard approach in the description of exited…

Several situations of physical importance may be modelled by linear quantum fields propagating in fixed spacetime-dependent classical background fields. For example, the quantum Dirac field in a strong and/or time-dependent external…

Time boundary terms usually added to action principles are systematically handled in the framework of Dirac's canonical analysis. The procedure begins with the introduction of the boundary term into the integral Hamiltonian action and then…

In a series of papers, we will develop systematically the basic spectral theory of (self-adjoint) boundary value problems for operators of Dirac type. We begin in this paper with the characterization of (self-adjoint) boundary conditions…

I approach the Problem of Time and other foundations of Quantum Cosmology using a combined histories, timeless and semiclassical approach. This approach is along the lines pursued by Halliwell. It involves the timeless probabilities for…

The notion of rigidity of Lie algebra is linked to the following problem: when does a Lie brackets $\mu$ on a vector space g satisfy that every Lie bracket $\mu_1$ sufficiently close to $\mu$ is of the form $\mu_1 = P.\mu $ for some P in…

The ageing Lie algebra age(d) and especially its local representations for a dynamical exponent z=2 has played an important r\^ole in the description of systems undergoing simple ageing, after a quench from a disordered state to the…