Keynes’s missing axioms

Between Keynes’s verbalized theory and its formal basis persists a lacuna. The conceptual groundwork is too small and not general. The quest for a comprehensive formal basis is guided by the question: what is the minimum set of foundational propositions for a consistent reconstruction of the money economy? We start with three structural axioms. The claim of generality entails that it should be possible to prove that Keynes’s formalism is a subset of the structural axiom set. The axioms are applied to a central part of the General Theory in order to achieve consistency and generality

Casimir force in Schwarzschild metric: Progress report

In this paper I report progress on both theoretical and experimental aspects. I describe two approaches to calculating putative effects of gravitational curvature on the Casimir force. The work I describe continues the quest to answer the question: do virtual field excitations follow geodesics

Torsion-free, divisible, and Mittag-Leffler modules

We study (relative) K-Mittag-Leffler modules, with emphasis on the class K of absolutely pure modules. A final goal is to describe the K-Mittag-Leffler abelian groups as those that are, modulo their torsion part, aleph_1-free, Cor.6.12. Several more general results of independent interest are derived on the way. In particular, every flat K-Mittag-Leffler module (for K as before) is Mittag-Leffler, Thm.3.9. A question about the definable subcategories generated by the divisible modules and the torsion-free modules, resp., has been left open, Quest.4.6

Is There Unification in the 21st Century?

In the last 100 years, the most important equations in physics are Maxwell's equations for electrodynamics, Einstein's equation for gravity, Dirac's equation for the electron and Yang-Mills equation for elementary particles. Do these equations follow a common principle and come from a single theory? Despite intensive efforts to unify gravity and the particle interactions in the last 30 years, the goal is still to be achieved. Recent theories have not answered any question in physics. We examine the issues involved in this long quest to understand the ultimate nature of spacetime and matter.Comment: Lecture delievered in Conference in Honor of Murray Gell-Mann's 80th Birthday. February 24 - 26, 2010. Nanyang Executive Centre, Singapore. 10 page

Solar neutrino physics on the beginning of 2017

This writeup is a review of current hot topics on solar neutrinos. It is based on a talk at the conference "Neutrinos: the quest for a new physics scale", held at the CERN on March 2017, where the Organizers entrusted me with a discussion of the provocative question "whether solar neutrino physics is over". Rather than providing a straight (negative) answer, in view of an audience consisting mostly of colleagues working in theoretical particle physics, I deemed it more useful providing a description of what is the current activity of the physicists working in solar neutrinos, leaving the listener free of forming his/her own opinion apropos.Comment: LaTeX, 10 pages, 6 figures, 2 tables. Minor improvements, matches version published in "Nuclear Physics and Atomic Energy

Collider Searches for Extra Spatial Dimensions and Black Holes

Searches for extra spatial dimensions remain among the most popular new directions in our quest for physics beyond the Standard Model. High-energy collider experiments of the current decade should be able to find an ultimate answer to the question of their existence in a variety of models. We review these models and recent results from the Tevatron on searches for large, inverse-TeV-size, and Randall-Sundrum extra spatial dimensions. The most dramatic consequence of low-scale (~1 TeV) quantum gravity is copious production of mini-black holes at the LHC. We discuss selected topics in the mini-black-hole phenomenology.Comment: Invited talk given at the 13th Lomonosov International Conference on Elementary Particle Physics, Moscow, Russia, August 23-29, 200

Collider Searches for Extra Dimensions

Searches for extra spatial dimensions remain among the most popular new directions in our quest for physics beyond the Standard Model. High-energy collider experiments of the current decade should be able to find an ultimate answer to the question of their existence in a variety of models. Until the start of the LHC in a few years, the Tevatron will remain the key player in this quest. In this paper, we review the most recent results from the Tevatron on searches for large, 1/TeV-size, and Randall-Sundrum extra spatial dimensions, which have reached a new level of sensitivity and currently probe the parameter space beyond the existing constraints. While no evidence for the existence of extra dimensions has been found so far, an exciting discovery might be just steps away.Comment: To appear in Proceedings of SLAC Summer Institute, 2004. An extended version of the talk given on behalf of the CDF and D0 Collaboration

Testing locality and noncontextuality with the lowest moments

The quest for fundamental test of quantum mechanics is an ongoing effort. We here address the question of what are the lowest possible moments needed to prove quantum nonlocality and noncontextuality without any further assumption -- in particular without the often assumed dichotomy. We first show that second order correlations can always be explained by a classical noncontextual local-hidden-variable theory. Similar third-order correlations also cannot violate classical inequalities in general, except for a special state-dependent noncontextuality. However, we show that fourth-order correlations can violate locality and state-independent noncontextuality. Finally we obtain a fourth-order continuous-variable Bell inequality for position and momentum, which can be violated and might be useful in Bell tests closing all loopholes simultaneously.Comment: 12 pages, 1 figur