About maximally localized states in quantum mechanics

We analyze the emergence of a minimal length for a large class of generalized commutation relations, preserving commutation of the position operators and translation invariance as well as rotation invariance (in dimension higher than one). We show that the construction of the maximally localized states based on squeezed states generally fails. Rather, one must resort to a constrained variational principle.Comment: accepted for publication in PR

Comment on "Quantum mechanics of smeared particles"

In a recent article, Sastry has proposed a quantum mechanics of smeared particles. We show that the effects induced by the modification of the Heisenberg algebra, proposed to take into account the delocalization of a particle defined via its Compton wavelength, are important enough to be excluded experimentally.Comment: 2 page

Spacetime could be simultaneously continuous and discrete in the same way that information can

There are competing schools of thought about the question of whether spacetime is fundamentally either continuous or discrete. Here, we consider the possibility that spacetime could be simultaneously continuous and discrete, in the same mathematical way that information can be simultaneously continuous and discrete. The equivalence of continuous and discrete information, which is of key importance in information theory, is established by Shannon sampling theory: of any bandlimited signal it suffices to record discrete samples to be able to perfectly reconstruct it everywhere, if the samples are taken at a rate of at least twice the bandlimit. It is known that physical fields on generic curved spaces obey a sampling theorem if they possess an ultraviolet cutoff. Most recently, methods of spectral geometry have been employed to show that also the very shape of a curved space (i.e., of a Riemannian manifold) can be discretely sampled and then reconstructed up to the cutoff scale. Here, we develop these results further, and we here also consider the generalization to curved spacetimes, i.e., to Lorentzian manifolds

Regional Debt in Monetary Unions: Is it Inflationary?

This paper studies the inflationary implications of interest bearing regional debt in a monetary union. Is this debt simply backed by future taxation with no inflationary consequences? Or will the circulation of region debt induce monetization by a central bank? We argue here that both outcomes can arise in equilibrium. In the model economy, there are multiple equilibria which reflect the perceptions of agents regarding the manner in which the debt obligations will be met. In one equilibrium, termed Ricardian, the future obligations are met with taxation by a regional government while in the other, termed Monetization, the central bank is induced to print money to finance the region's obligations. The multiplicity of equilibria reflects a commitment problem of the central bank. A key indicator of the selected equilibrium is the distribution of the holdings of the regional debt. We show that regional governments, anticipating central bank financing of their debt obligations, have an incentive to create excessively large deficits. We use the model to assess the impact of policy measures within a monetary union.Monetary Union ; Inflation tax ; Seigniorage ; Public debt.

Insulation impossible: monetary policy and regional fiscal spillovers in a federation

This paper studies the effects of monetary policy rules in a fiscal federation, such as the European Union. The focus of the analysis is the interaction between the fiscal policy of member countries (regions) and the monetary authority. Each of the countries structures its fiscal policy (spending and taxes) with the interests of its citizens in mind. Ricardian equivalence does not hold due to the presence of monetary frictions, modeled here as reserve requirements. When capital markets are integrated, the fiscal policy of one country influences equilibrium wages and interest rates. Under certain rules, monetary policy may respond to the price variations induced by regional fiscal policies. Depending on the type of rule it adopts, interventions by the monetary authority affect the magnitude and nature of the spillover from regional fiscal policy.Monetary Union, Inflation tax, Seigniorage, monetary rules, public debt.

Monetary rules and the spillover of regional fiscal policies in a federation.

This paper studies the effects of monetary policy rules in a fiscal federation, such as the European Union. The focus of the analysis is the interaction between the fiscal policy of member countries (regions) and the monetary authority. Each of the countries structures its fiscal policy (spending and taxes) with the interests of its citizens in mind. Ricardian equivalence does not hold due to the presence of monetary frictions, modelled here as reserve requirements. When capital markets are integrated, the fiscal policy of one country influences equilibrium wages and interest rates. Under certain rules, monetary policy may respond to the price variations induced by regional fiscal policies. Depending on the type of rule it adopts, interventions by the monetary authority affect the magnitude and nature of the spillover from regional fiscal policy.Monetary Union ; Inflation tax ; Seigniorage ; monetary rules ; public debt.