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

On Quantum Field Theory with Nonzero Minimal Uncertainties in Positions and Momenta

We continue studies on quantum field theories on noncommutative geometric spaces, focusing on classes of noncommutative geometries which imply ultraviolet and infrared modifications in the form of nonzero minimal uncertainties in positions and momenta. The case of the ultraviolet modified uncertainty relation which has appeared from string theory and quantum gravity is covered. The example of euclidean $\phi^4$-theory is studied in detail and in this example we can now show ultraviolet and infrared regularisation of all graphs.Comment: LaTex, 32 page

Maximal Localisation in the Presence of Minimal Uncertainties in Positions and Momenta

Small corrections to the uncertainty relations, with effects in the ultraviolet and/or infrared, have been discussed in the context of string theory and quantum gravity. Such corrections lead to small but finite minimal uncertainties in position and/or momentum measurements. It has been shown that these effects could indeed provide natural cutoffs in quantum field theory. The corresponding underlying quantum theoretical framework includes small `noncommutative geometric' corrections to the canonical commutation relations. In order to study the full implications on the concept of locality it is crucial to find the physical states of then maximal localisation. These states and their properties have been calculated for the case with minimal uncertainties in positions only. Here we extend this treatment, though still in one dimension, to the general situation with minimal uncertainties both in positions and in momenta.Comment: Latex, 21 pages, 2 postscript figure

Does Inflation Targeting decrease Exchange Rate Pass-through in Emerging Countries?

In this paper, we empirically examine the effect of inflation targeting on the exchange rate pass-through to prices in emerging countries. We use a panel VAR that allows us to use a large dataset on twenty-seven emerging countries (fifteen inflation targeters and twelve inflation nontargeters). Our evidence suggests that inflation targeting in emerging countries contributed to a reduction in the pass-through to various price indexes (import prices, producer prices and consumer prices) from a higher level to a new level that is significantly different from zero. The variance decomposition shows that the contribution of exchange rate shocks to price fluctuations is more important in emerging targeters compared to nontargeters, and the contribution of exchange rate shocks to price fluctuations in emerging targeters declines after adopting inflation targeting.Inflation Targeting, Exchange Rate Pass-Through, panel VAR.

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

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.

Quantum Field Theory with Nonzero Minimal Uncertainties in Positions and Momenta

A noncommutative geometric generalisation of the quantum field theoretical framework is developed by generalising the Heisenberg commutation relations. There appear nonzero minimal uncertainties in positions and in momenta. As the main result it is shown with the example of a quadratically ultraviolet divergent graph in $\phi^4$ theory that nonzero minimal uncertainties in positions do have the power to regularise. These studies are motivated with the ansatz that nonzero minimal uncertainties in positions and in momenta arise from gravity. Algebraic techniques are used that have been developed in the field of quantum groups.Comment: 52 pages LATEX, DAMTP/93-33. Revised version now includes a chapter on the Poincare algebra and curvature as noncommutativity of momentum spac

Unsharp Degrees of Freedom and the Generating of Symmetries

In quantum theory, real degrees of freedom are usually described by operators which are self-adjoint. There are, however, exceptions to the rule. This is because, in infinite dimensional Hilbert spaces, an operator is not necessarily self-adjoint even if its expectation values are real. Instead, the operator may be merely symmetric. Such operators are not diagonalizable - and as a consequence they describe real degrees of freedom which display a form of "unsharpness" or "fuzzyness". For example, there are indications that this type of operators could arise with the description of space-time at the string or at the Planck scale, where some form of unsharpness or fuzzyness has long been conjectured. A priori, however, a potential problem with merely symmetric operators is the fact that, unlike self-adjoint operators, they do not generate unitaries - at least not straightforwardly. Here, we show for a large class of these operators that they do generate unitaries in a well defined way, and that these operators even generate the entire unitary group of the Hilbert space. This shows that merely symmetric operators, in addition to describing unsharp physical entities, may indeed also play a r{\^o}le in the generation of symmetries, e.g. within a fundamental theory of quantum gravity.Comment: 23 pages, LaTe