27,669 research outputs found

### Fubini vacua as a classical de Sitter vacua

The Fubini's idea to introduce a fundamental scale of hadron phenomena by
means of dilatation non-invariant vacuum state in the frame work of a scale
invariant Lagrangian field theory is recalled. The Fubini vacua is invariant
under the de Sitter subgroup of the full conformal group. We obtain a finite
entropy for the quantum state corresponding to the classical Fubini vacua in
Euclidean space-time resembeling the entropy of the de Sitter vacua. In
Minkowski space-time it is shown that the Fubini vacua is mainly a bath of
radiation with Rayleigh-Jeans distribution for the low energy radiation. In
four dimensions, the critical scalar theory is shown to be equivalent to the
Einstein field equation in the ansatz of conformally flat metrics and to the
SU(2) Yang-Mills theory in the 't Hooft ansatz. In D-dimensions, the Hitchin
formula for the information geometry metric of the moduli space of instantons
is used to obtain the information geometry of the free-parameter space of the
Fubini vacua which is shown to be a (D+1)-dimensional AdS space. Considering
the Fubini vacua as a de Sitter vacua, the corresponding cosmological constant
is shown to be given by the coupling constant of the critical scalar theory. In
Minkowski spacetime it is shown that the Fubini vacua is equivalent to an open
FRW universe.Comment: 15 pages, revtex4, to appear in Mod.Phys.Lett.

### Chai's Conjecture and Fubini properties of dimensional motivic integration

We prove that a conjecture of Chai on the additivity of the base change
conductor for semi-abelian varieties over a discretely valued field is
equivalent to a Fubini property for the dimensions of certain motivic
integrals. We prove this Fubini property when the valued field has
characteristic zero.Comment: 22 page

### The Structure of Equilibrium in an Asset Market with Variable Supply

This note presents new results on existence of rich Fubini extensions. The notion of a rich Fubini extension was recently introduced by Sun (2006) and shown by him to provide the proper framework to obtain an exact law of large numbers for a continuum of random variables. In contrast to the existence results for rich Fubini extensions established by Sun (2006), the arguments in this note don’t use constructions from nonstandard analysis.

### Forbidden rectangles in compacta

We establish negative results about "rectangular" local bases in compacta.
For example, there is no compactum where all points have local bases of cofinal
type \omega x \omega_2. For another, the compactum \beta\omega has no
nontrivially rectangular local bases, and the same is consistently true of
\beta\omega \ \omega: no local base in \beta\omega has cofinal type \kappa x c
if \kappa < m_{\sigma-n-linked} for some n in [1,\omega). Also, CH implies that
every local base in \beta\omega \ \omega has the same cofinal type as one in
\beta\omega.
We also answer a question of Dobrinen and Todorcevic about cofinal types of
ultrafilters: the Fubini square of a filter on \omega always has the same
cofinal type as its Fubini cube. Moreover, the Fubini product of nonprincipal
P-filters on \omega is commutative modulo cofinal equivalence.Comment: 15 page

### Generalized Fubini instantons

We show that $(1+2)$ nonlinear Klein-Gordon equation with negative coupling
admits an exact solution which appears to be the linear superposition of the
plane wave and the nonsingular rational soliton. We show that the same approach
allows to construct the solution of similar properties for the Euclidean
$\phi^4$ model with broken symmetry. Interestingly, this regular solution will
be of instanton type only in the $D\le 5$ Euclidean space.Comment: 10 page

- …