# DIMENSIONAL REDUCTION AXIAL UNIVERSES (AxU) P. P. Fiziev ...

DIMENSIONAL REDUCTION AXIAL UNIVERSES (AxU) P. P. Fiziev ...

DIMENSIONAL REDUCTION AXIAL UNIVERSES (AxU) P. P. Fiziev ...

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**DIMENSIONAL** **REDUCTION**in (1+2)-dimensional**AXIAL** **UNIVERSES** (**AxU**)andKLEIN-GORDON WAVESP. P. **Fiziev**,D.V. ShirkovBLThPh, JINR, DubnaTalk at the Seminar ofthe Faculty of PhysicsSofia University ,May 09, 2011

The basic problem of the standardapproach to quantum gravity is causedby the very classical Einstein-Hilbertaction in D = 1 + d :The same in theStandard ModelwithoutHiggs bosonfor dimension D > 2A New Idea:D. V. Shirkov, Particles and Nuclei (PEPAN), Lett. No 6 (162), 2010

Great Unification by dimensionalreduction instead of leptoquarks:

Greg (Grigoriy) Landsberg, Paris, July 2010

Relation of the above (relativistic) examples withthe modern solid state physics of two-dimensional crystalsgraphene, fulerene,carbon nanotubes,carbon nanobuds,etc: Nobel Prize in Physics 2010

Examples of 2-dim manifolds withvariable geometries(surfaces of bottles)D. V. Shirkov,,Good problem:Solvethe Klei n-Gordoneq.,the Dirac eq.the heat eq.,e.t.c.,on that kind ofvariable geometries.

KGEq for TEST PARTICLES:10 80baryons -EddingtonIn the STATIC case we assume (at least locally)numberTheKleinGordonEquationonManifoldswithvariabletopologicaldimensionWe consider the toy models in whichthe physical space is a continuousmerger :and THE TIME IS GLOBAL !Then we have local solutions:With common frequency:

Wave Equation in (1+2)-dim Static **AxU**Shape function:Standard anzatz:Simple problems:The only nontrivial problem: Z-equation centrifugalThe basicTheorem:Using proper changes of variables we can transformthe Z-equation in the Schrodinger-like form:

Some Explicit ExamplesTwo Cylinders of Constant Radii R and r < R,Connected Continuously by a Part of Cone:The shapefunction:

ContinuousspectrumstatesExact Solutions and the limit *

The resonant states:M = 0S – matrix polesA nontrivial dependence on the mass M:

Real forSchrodinger-type ODEqwith potentialThe solution:

Expansion: 5% for 10 9 yearsWhat was thereBEFORE the Big Bang?Is the Big Bang actuallya transition from aLOWER **DIMENSIONAL**world to theFOUR**DIMENSIONAL**ONE??? HST2011 New ideaP.F., D.Shirkov:

(1+2)-dim Time Dependent **AxU**Inconsider

**DIMENSIONAL** **REDUCTION** POINTSand**DIMENSIONAL** TRANSITION POINTSSymbolically:

Einstein eqs for time dependent (1+2) –dim **AxU**=>Determinant:Field equations:Matter equations:

There vacuum solutions of Einstein eqs :1.- expanding cylinder2.- static coneMOVIE3.- moving coneLorentz transform

Solutions for the (1+2) **AxU** filled with “dust”=>=>omogeneous Monge(1784)-Ampere(1820) equation:Implicit general solution:=>Godograph of the velocity v(t,z)General solution of the Cauchy problem:

Three classes of special solutionsinvolving one arbitrary functionLorentz transformwhereare arbitrary constants.

whereNew restriction:

1. Creation and annihilation of pairs of DRPs is possible.2.Lorentz transform3. Forzeros ofRelative velocities:4. For

1.2.3.

Solutions of KGEq on (1+2)-dim**AxU** with positive termDiscretespectra:

Solutions to the KGEq on (1+2)-dim**AxU** filled with “dust”

CONCLUDING REMARKS1. A signal, related to degree of freedom specificfor the higher-dim part does not penetrateinto the smaller-dim part,the inertial forces at the junction.2. The specific spectrum of scalarexcitations characterizes the junctiongeometry. A new idea: To explain thebecause ofobserved particles spectra by geometry of thejunction between domains of the space-timewith different topological dimension.

3. The set of the dimensional reduction point -DPR may have complicated structure anddynamics:4. Critical behavior of the solutions for testparticles around DPR exist and depends bothon geometry and motion.

5. The parity violation, due to the asymmetryof space geometry could yield the CP- and T-violation.This gives a hope to discover a simple natural basis forexplanation of the real situation, concerningC, P, and T properties of the particles.6. Barion-antibarion asymmetry versusasymmetry of the space-time ???7. The Big Bang = ? = time transformation ofspace dimensions ???

?Weare stilllookingfor theMASTERKEY !Thank You foryour attention