Ricci recurrent space times

The algebraic restrictions on the Ricci tensor in a Ricci-recurrent space-time are determined. The restrictions imposed on the Petrov type of the Weyl tensor are also given.     

On the renormalization problem of quantum gravity

Strong restrictions on possible counterterms are obtained using the Weyl gauge symmetrical form of the Einstein gravity. These restrictions are confirmed by the available one-loop calculations. Arguments in favor of the renormalizability of the quantum gravity are given.     

Manipulation of nonreciprocal unconventional photon blockade in a cavity-driven system composed of an asymmetrical cavity and two atoms with weak dipole-dipole interaction

We present a work of manipulating collective unconventional photon blockade (UCPB) and nonreciprocal UCPB (NUCPB) in a cavity-driven system composed of an asymmetrical single-mode cavity and two interacting identical two-level atoms (TLAs). When the atoms do not interact directly, the frequency and intensity restrictions of collective UCPB can be specified, and a giant NUCPB exists due to the splitting of optimal atom-cavity coupling strength in proper parameter regime. However, if a weak atom-atom interaction which provides a new and feeble quantum interference pathway to UCPB is taken into account, two restrictions of UCPB are combined complexly, which are rigorous to be matched simultaneously. Due to the push-and-pull effect induced by weak dipole-dipole interaction, the UCPB regime is compressed more or less. NUCPB is improved as a higher contrast is present when the two complex UCPB restrictions are matched, while it is suppressed when the restrictions are mismatched. In general, whether NUCPB is suppressed or promoted depends on its working parameters. Our findings show a prospective access to produce giant quantum nonreciprocity by a couple of weakly interacting atoms.     

Conformal Vector Fields and Conformal–Type Collineations in Space-Times

Some restrictions on the existence of homothetic and conformal vector fields in space-times which already admit some Killing symmetry are established. In particular, the behaviour of Weyl invariants and the nature of the Petrov type of the Weyl tensor along the integral curves of conformal vector fields are studied. This results in important restrictions between conformal vector fields and Killing orbits. A brief remark is made on Weyl collineations.     

The algebra of physical magnitudes

We define a physical magnitude as an equivalence class of measurement procedures and formulate sufficient restrictions on the equivalence relation to guarantee meaningful algebraic operations between magnitudes. These restrictions are not sufficient to let the Kochen and Specker argument go through. They are, however, stronger than mere statistical equivalence of measurement procedures and thus are relevant to the problem of the completeness of quantum mechanics. In fact, they give rise to a strong argument for the incompleteness of quantum mechanics.     

Instability of closed spaces in general relativity

There are strong restrictions on the solutions of the initial value constraints of General Relativity when the spatial hypersurface is closed. In particular, closed flat space is unstable: not all solutions of the linearized constraints correspond to nearby solutions of the constraints themselves. For example, no nearby solutions whatever exist which are time symmetric. Other restrictions, which limit perturbations of non-flat closed initial solutions, are also exhibited.Supported in part by the National Science Foundation and by the Humboldt-Foundation.Supported in part by Grant AFOSR 70-1864.     

Relativistic quantum logic

On the basis of the well-known quantum logic and quantum probability a formal language of relativistic quantum physics is developed. This language incorporates quantum logical as well as relativistic restrictions. It is shown that relativity imposes serious restrictions on the validity regions of propositions in space-time. By an additional postulate this relativistic quantum logic can be made consistent. The results of this paper are derived exclusively within the formal quantum language; they are, however, in accordance with well-known facts of relativistic quantum physics in Hilbert space.     

Global symmetries in four and higher dimensions

Knowing that a four-dimensional theory with gauge group G₀ is unified in theory with gauge group G puts restrictions on what global symmetries are possible in the low-energy world. Here we analyze those restrictions assuming that unification in G occurs inn four dimensions and assuming that unification occurs only in a higher-dimensional theory. There are possibilities for global symmetries which are not possible in the former case, so in principle indirect evidence for higher dimensions might be found by finding peculiar global symmetries in the low-energy world.     

Spatially integrable space-times

The topological and geometrical restrictions on spatially integrable space-times foliated by space-like hypersurfaces are investigated.     

例析运动学中的约束问题

通过例题探讨了约束的表述及其在求解运动学问题中的应用.     

On the logarithmic solutions of the WDVV equations

We consider restrictions and subsystems in the ∨-systems corresponding to the logarithmic solutions of the WDVV equations. We present certain solutions through restrictions of the Coxeter systems.     

Entanglement constrained by superselection rules

Bipartite entanglement may be reduced if there are restrictions on allowed local operations. We introduce the concept of a generalized superselection rule to describe such restrictions, and quantify the entanglement constrained by it. We show that ensemble quantum information processing, where elements in the ensemble are not individually addressable, is subject to the superselection rule associated with the symmetric group (the group of permutations of elements). We prove that even for an ensemble comprising many pairs of qubits, each pair described by a pure Bell state, the entanglement per element constrained by this superselection rule goes to zero for a large number of elements.     

Local properties of nonrenormalizable interactions

The possibility of constructing strictly localizable fields is considered, using generalized S-type spaces as spaces of basis functions. The restrictions imposed on the asymptotic behavior of the amplitudes coincide with the well-known restrictions found by Jaffe. Contrary to previous results, the spatial amplitudes and momenta are regular, and not singular functions, in the case considered. The possibility of formulating spectral conditions is investigated.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 76–81, August, 1971.     

北京机动车限行期间苯和甲苯的DOAS测量

基于差分光学吸收光谱(DOAS)技术在北京机动车限行期间8月7日到28日对苯和甲苯进行连续监测,获取苯、甲苯的变化特征,分析交通排放苯、甲苯和车流量关系. 监测结果表明,整个交通管制期间,监测点苯与甲苯相关系数为0.8,且二者比值为0.43～0.50,充分证明苯系物具有同源性. 限车时段苯的浓度下降11.4%,甲苯下降12.8%,而车流量下降11.8%,因此苯和甲苯是北京机动车排放的主要来源.     

Non-existence of trouser-worlds

Simple restrictions are derived on the global structure of normal hyperbolic Riemannian spaces. As a consequence, cosmological models of the trouser type are ruled out irrespective of field equations.     

Absence of preclassical solutions in Bianchi I loop quantum cosmology

Loop quantum cosmology, the symmetry reduction of quantum geometry for the study of various cosmological situations, leads to a difference equation for its quantum evolution equation. To ensure that solutions of this equation act in the expected classical manner far from singularities, additional restrictions are imposed on the solution. In this Letter, we consider the Bianchi I model, both the vacuum case and the addition of a cosmological constant, and show using generating function techniques that only the zero solution satisfies these constraints. This implies either that there are technical difficulties with the current method of quantizing the evolution equation, or else loop quantum gravity imposes strong restrictions on the physically allowed solutions.     

Exact solution of restricted cell model for hard parallel rectangles in a “brick-wall” configuration

The cell restrictions are defined, and it is shown that the model is essentially equivalent to a model presented in a previous paper.     

Remote two-time boundary conditions and special states in quantum mechanics

For an oscillating universe, the assumptions of wave-function localization and approximate symmetry for the initial and final states impose restrictions on the intermediate motion. We argue that one of these restrictions is the avoidance of superpositions of macroscopically distinct states.     

Lifshitz theory-— exact or approximate statistical mechanics?

We show that the Lifshitz and related theories of intermolecular interactions are equivalent to perturbation theory, and therefore subject to the usual restrictions of the latter.