Long Range Forces and Neutrino Mass

We explore the limits on neutrino mass which follow from a study of the long-range forces that arise from the exchange of massless or ultra-light neutrinos. Although the 2-body neutrino-exchange force is unobservably small, the many-body force can generate a very large energy density in neutron stars and white dwarfs. We discuss the novel features of neutrino-exchange forces which lead to large many-body effects, and present the formalism that allows these effects to be calculated explicitly in the Standard Model. After considering, and excluding, several possibilities for avoiding the unphysically large contributions from the exchange of massless neutrinos, we develop a formalism to describe the exchange of massive neutrinos. It is shown that the stability of both neutrons stars and white dwarfs in the presence of many-body neutrino-exchange forces implies a lower bound, $m \gtrsim 0.4$ eV/$c^{2}$ on the mass $m$ of any neutrino.Comment: 96 pages, 6 figures, 2 tables, requires revtex; to be published in Annals of Physic

Probability Distribution of Distance in a Uniform Ellipsoid: Theory and Applications to Physics

A number of authors have previously found the probability Pn(r) that two points uniformly distributed in an n-dimensional sphere are separated by a distance r. This result greatly facilitates the calculation of self-energies of spherically symmetric matter distributions interacting by means of an arbitrary radially symmetric two-body potential. We present here the analogous results for P2(r;ϵ) and P3(r;ϵ) which respectively describe an ellipse and an ellipsoid whose major and minor axes are 2a and 2b. It is shown that for ϵ = (1−b2/a2)1/2 ⩽ 1, P2(r;ϵ) and P3(r;ϵ) can be obtained as an expansion in powers of ϵ, and our results are valid through order ϵ4. As an application of these results we calculate the Coulomb energy of an ellipsoidal nucleus, and compare our result to an earlier result quoted in the literature

Neprijenosne kvantne igre

We present two alternative approaches to constructing 3 × 3 entangled quantum games, based on different formulations of mixed strategies in a quantum game. Although these formulations are quite similar in 2 × 2 games (2 players × 2 choices), their differences become pronounced in the 3 × 3 case. A 3 × 3 classical game is the simplest platform which allows for non-transitive strategies A, B, C, where A beats B, B beats C, and C beats A (A > B > C > A). We consider non-transitive strategies in both formulations of 3 × 3 quantum games, and show that non-transitivity survives in the quantum versions of the corresponding classical games. Some physical implications of these results are also considered.Predstavljamo dvije inačice pristupa za sastavljanje upletenih kvantnih igara, koji se zasnivaju na različitim obrascima miješanih strategija kvantne igre. Iako su ti obrasci u igrama 2 × 2 vrlo slični (2 igrača × 2 odabira), njihove razlike postaju istaknutije u slučaju 3×3. Klasična igra 3×3 je najjednostavnija osnova koja dozvoljava neprijenosne strategije A, B, C, gdje A nadjača B, B nadjača C, i C nadjača A (A > B > C > A). Razmatramo neprijenosne strategije za oba obrasca kvantnih igara 3 × 3, i pokazujemo kako se u kvantnim inačicama zadržava neprijenosnost odgovarajućih klasičnih igara. Razmatraju se fizičke posljedice tih ishoda