Vacuum condensates, flavor mixing and spontaneous supersymmetry breaking

Spontaneous supersymmetry (SUSY) breaking is revealed in all phenomena in which vacuum condensates are physically relevant. The dynamical breakdown of SUSY is generated by the condensates themselves, which lift the zero point energy. Evidence is presented in the case of the Wess-Zuimino model, and the flavor mixing case is treated in detail.Comment: 5 page

Vacuum condensates as a mechanism of spontaneous supersymmetry breaking

A possible mechanism for the spontaneous breaking of SUSY, based on the presence of vacuum condensates, is reviewed. Such a mechanism could occur in many physical examples, both at the fundamental and emergent level, and would be formally analogous to spontaneous SUSY breaking at finite temperature in the TFD formalism, in which case it can be applied as well. A possible experimental setup for detecting such a breaking through measurement of the Anandan-Aharonov invariants associated with vacuum condensates in an optical lattice model is proposed.Comment: 6 pages, 2 figures, review article to appear in the special issue "Supersymmetry, Supergravity, and Superstring Phenomenology" of Advances in High Energy Physic

Spontaneous Supersymmetry Breaking Induced by Vacuum Condensates

We propose a novel mechanism of spontaneous supersymmetry breaking which relies upon an ubiquitous feature of Quantum Field Theory, vacuum condensates. Such condensates play a crucial r\^{o}le in many phenomena. Examples include Unruh effect, superconductors, particle mixing, and quantum dissipative systems. We argue that in all these phenomena supersymmetry, when present, is spontaneously broken. Evidence for our conjecture is given for the Wess--Zumino model, that can be considered an approximation to the supersymmetric extensions of the above mentioned systems. The magnitude of the effect is estimated for a recently proposed experimental setup based on an optical lattice.Comment: 5 page

Quasi-selective ultrafilters and asymptotic numerosities

We isolate a new class of ultrafilters on N, called "quasi-selective" because they are intermediate between selective ultrafilters and P-points. (Under the Continuum Hypothesis these three classes are distinct.) The existence of quasi-selective ultrafilters is equivalent to the existence of "asymptotic numerosities" for all sets of tuples of natural numbers. Such numerosities are hypernatural numbers that generalize finite cardinalities to countable point sets. Most notably, they maintain the structure of ordered semiring, and, in a precise sense, they allow for a natural extension of asymptotic density to all sequences of tuples of natural numbers.Comment: 27 page

Mixing-induced Spontaneous Supersymmetry Breaking

It is conjectured that flavor mixing furnishes a universal mechanism for the spontaneous breaking of supersymmetry. The conjecture is proved explicitly for the mixing of two Wess--Zumino $\mathcal{N}=1$ supermultiplets and arguments for its general validity are given. The mechanism relies on the fact that, despite mixing treats fermions and bosons symmetrically, both the fermionic and the bosonic zero point energies are shifted by a positive amount and this kind of shift does not respect supersymmetry.Comment: 5 pages, 1 figure, Eq(12) of V1 corrected to Eq(22), explicit off-shell formulation included, one reference adde

Key elements of global inflation

Against the background of large fluctuations in world commodity prices and global growth, combined with ongoing structural changes relating to globalization, this paper examines some of the key factors affecting global inflation. The paper empirically investigates various relative price and structural impacts on global inflation by: estimating a GVAR to examine how oil price shocks feed through to core and headline inflation; calculating the impact of increased imports from low-cost countries on manufacturing import prices; estimating Phillips curves in order to shed light on whether the inflationary process in the OECD countries has changed over time, particularly with respect to the roles of import prices, unit labour costs and the output gap. Overall, the paper finds that there seem to be various significant pressures on global trade prices and labour markets associated with structural factors possibly partly due to globalisation which, in addition to monetary policy, seem to be behind some of the changes in the inflation process over the period examined in this paper.Phillips Curve, inflation, output gap, import prices, unit labour costs, globalisation, monetary policy.

Euclidean integers, Euclidean ultrafilters, and Euclidean numerosities

We introduce a "Euclidean" notion of size (numerosity) for "Punktmengen", i.e. sets of points of Euclidean (finitely dimensional) spaces over any "line" L, namely one that maintains the Cantorian defiitions of order, addition and multiplication, while preserving the ancient principle that "the whole is greater than the part" (a set is (strictly) larger than its proper subsets). These numerosities satisfy the five Euclid's common notions, thus enjoying a very good arithmetic, since they constitute the nonnegative part of the ordered ring of the Euclidean integers, here introduced by suitably assigning a transfinite sum to (ordinally indexed) kappa-sequences of integers (so generating a semiring of nonstandard natural numbers). Most relevant is the natural set theoretic definition of the set-preordering <: given any two sets X, Y of any cardinality, one has X<Y if and only if there exists a proper superset of X that is equinumerous to Y . Extending this "superset property" from countable to uncountable sets has been one of the main open question in this area from the beginning of the century

Introducing the basic concepts of general relativity in high schools

INTRODUCTION Unlike the case of quantum mechanics, the teaching at the high school level of general relativity (GR) has been the target of relatively minor efforts by researchers in physics education (Kersting, Henriksen, Boe &amp; Angell 2018), despite both subjects being included in the curricula in many countries. Although its foundations are not as controversial as those of quantum mechanics, GR also rests on some subtle conceptual steps, and, moreover, it cannot be probed using real experiments. Hence, teaching it at the high school level presents important challenges. However, the conceptual steps needed for GR are firmly founded in classical mechanics, electromagnetism, and special relativity (Sciama 1969), and when suitably presented and supported by adequate material, they can be within grasp of final year pupils. In this presentation, we outline and discuss a proposal in which these basic concepts are gradually introduced as natural extensions of those that physics pupils know, in a simple yet nontrivial way, which goes beyond the current textbook approaches. The latter, indeed, usually present little more than a popular level account. Typically, they rely on the famous elastic sheet analogy, which in turn is based on the iconic fact that GR geometrizes the gravitational field. However, such a statement takes quite a long route to be established, hence without adequate motivation, usually results in students getting the impression that the theory comes out of the blue. Also, the analogy is not very accurate, failing to highlight the role of time in the theory. FROM CLASSICAL MECHANICS TO GR: A PROPOSAL Our proposal starts from a critical rethinking of the principles of Newtonian mechanics, focusing on the role of inertia and of inertial forces, and on the principle of equivalence of gravitational and inertial mass. This part can be supplemented by real experiments and simulations. The next step involves special relativity, discussing the apparently unrelated problems of extending the relativity principle to non-inertial frames, and of reconciling gravity with the universal speed limit. Then, the way in which the equivalence principle allows to extend the special relativity principle is discussed with the help of Einstein’s elevator thought experiment. Crucial here is the discussion of how the equivalence principle is elevated from mechanics to all physical phenomena and how it is reconciled with the fact that special relativity teaches us that inertial mass is a form of energy. By means of some thought experiments, in fact, it is possible to quantitatively show that the same is true for the gravitational mass (Einstein, 1911). Then, by further thought experiments and simple calculations, some consequences of this principle can be explored: the gravitational redshift and time-dilation, the application to the Global Positioning System, and the gravitational bending of light. At this point, students should be invited to reflect on the special features that a theory based on special relativity and on Einstein’s equivalence principle should have, in comparison with electromagnetism, and the consequences should be explored. Finally, the thought experiment of the rotating disc (Janssen, 2014) can provide a way of motivating the well-known geometric picture. REFERENCES Einstein A. (1911). Einfluss der Schwerkraft auf die Ausbreitung des Lichtes. Ann. Phys. (Ser.4), 35, 898. Janssen M. (2014). “No success like failure…”. Einstein’s quest for general relativity, 1907-1920. In M.Janssen &amp; C. Lehner (Eds.), The Cambridge companion to Einstein (pp. 167-227). Cambridge: Cambridge University Press. Kersting, M., Henriksen, E. K., Boe, M.V., &amp; Angell. C. (2018). General relativity in upper secondary school: Design and evaluation of an online environment using the model of educational reconstruction. Phys. Rev. Phys. Educ. Res. 14, 010130. Sciama, D. (1969). The physical foundations of general relativity, New. York: Doubleday

Extended LaSalle's invariance principle for full-range cellular neural networks

In several relevant applications to the solution of signal processing tasks in real time, a cellular neural network (CNN) is required to be convergent, that is, each solution should tend toward some equilibrium point. The paper develops a Lyapunov method, which is based on a generalized version of LaSalle's invariance principle, for studying convergence and stability of the differential inclusions modeling the dynamics of the full-range (FR) model of CNNs. The applicability of the method is demonstrated by obtaining a rigorous proof of convergence for symmetric FR-CNNs. The proof, which is a direct consequence of the fact that a symmetric FR-CNN admits a strict Lyapunov function, is much more simple than the corresponding proof of convergence for symmetric standard CNNs