ﻻ يوجد ملخص باللغة العربية
Observable currents are locally defined gauge invariant conserved currents; physical observables may be calculated integrating them on appropriate hypersurfaces. Due to the conservation law the hypersurfaces become irrelevant up to homology, and the main objects of interest become the observable currents them selves. Gauge inequivalent solutions can be distinguished by means of observable currents. With the aim of modeling spacetime local physics, we work on spacetime domains $Usubset M$ which may have boundaries and corners. Hamiltonian observable currents are those satisfying ${sf d_v}F=-iota_VOmega_L+{sf d_h}sigma^F$ and a certain boundary condition. The family of Hamiltonian observable currents is endowed with a bracket that gives it a structure which generalizes a Lie algebra in which the Jacobi relation is modified by the presence of a boundary term. If the domain of interest has no boundaries the resulting algebra of observables is a Lie algebra. In the resulting framework algebras of observable currents are associated to bounded domains, and the local algebras obey interesting gluing properties. These results are due to considering currents that defined only locally in field space and to a revision of the concept of gauge invariance in bounded spacetime domains. A perturbation of the field on a bounded spacetime domain is regarded as gauge if: (i) the first order holographic imprint that it leaves in any hypersurface locally splitting a spacetime domain into two subdomains is negligible according to the linearized gluing field equation, and (ii) the perturbation vanishes at the boundary of the domain. A current is gauge invariant if the variation in them induced by any gauge perturbation vanishes up to boundary terms.
In a spacetime divided into two regions $U_1$ and $U_2$ by a hypersurface $Sigma$, a perturbation of the field in $U_1$ is coupled to perturbations in $U_2$ by means of the holographic imprint that it leaves on $Sigma$. The linearized gluing field eq
Using the fact that the algebra M(3,C) of 3 x 3 complex matrices can be taken as a reduced quantum plane, we build a differential calculus Omega(S) on the quantum space S defined by the algebra C^infty(M) otimes M(3,C), where M is a space-time manifo
We show that the Laplace-Beltrami equation $square_6 a =j$ in $(setR^6,eta)$, $eta := mathrm{diag}(+----+)$, leads under very moderate assumptions to both the Maxwell equations and the conformal Eastwood-Singer gauge condition on conformally flat spa
We discuss the construction of relational observables in time-reparametrization invariant quantum mechanics and we argue that their physical interpretation can be understood in terms of conditional probabilities, which are defined from the solutions
Taking up four model universes we study the behaviour and contribution of dark energy to the accelerated expansion of the universe, in the modified scale covariant theory of gravitation. Here, it is seen that though this modified theory may be a caus