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A new look at some

general puzzles of

Universe

Our

Goal: To

Open the

Padlocks

of

Nature!

Plamen Fiziev, Dmitrii Shirkov

BLTF, JINR, Dubna

FIFTEENTH LOMONOSOV CONFERENCE ON

ELEMENTARY PARTICLE PHYSICS

Moscow, 18 of August 2011


Alternatives to/for the Higgs

mechanism

Quantum Gravity

What was there




BEFORE the Big Bang

Physics on manifolds with

variable topological dimension

and

reduction of space dimensions


CP, T violation (discovered in 1956-1964)

=> Nobel Price in Physics (1980)

1. LEFT and RIGHT are not equivalent

2. the TIME is not reversible




Baryon-Antibaryon asymmetry

In the visible universe we have only barions:

#ANTIBARIONS = 10 -18 #BARIONS

Problem:

still NO convincing theoretical explanation

P.F., D.Shirkov 2011

New idea: asymmetric SPACE-TIME


The QFT g '4 model in 4D and 2D dimensions

D. V. Shirkov, Particles and Nuclei (PEPAN), Lett. No 6 (162), 2010

The coupling running here is defined by the only diagram

the 1st one-loop contribution to 4-vertex function.

It behaves quite differently in the “low-Q, 4-dim” region and in the

“high-Q, 2-dim” one. Explicitly:


Grand Unification by Dimensional Reduction

UV fixed point for g and Grand Unification

by Dimensional Reduction

New brave Great Unification by

Dimensional Reduction instead of Leptoquarks


The basic problem of the standard approach to

quantum gravity is caused by the very classical

Einstein-Hilbert action in D = 1 + d :

The quantum gravity is not

renormalizable for dimension D > 2 since

The same in the

Standard Model

without

Higgs boson

A New Idea: lower topological dimension at small distances

D. V. Shirkov, Particles and Nuclei (PEPAN), Lett. No 6 (162), 2010


Greg Landsberg, Paris, July 2010


Jonas Mureika and Dejan Stojkovic

Lower dimensionality at higher energies has manifold theoretical advantages as

recently pointed out by Anchordoqui et al. [arXiv:1003.5914]. Moreover, it

appears that experimental evidence may already exist for it: A statistically

significant planar alignment of events with energies higher

than TeV has been observed in some earlier cosmic ray

experiments. We propose a robust and independent test for this new

paradigm. Since (2 + 1)-dimensional spacetimes have no gravitational degrees of

freedom, gravity waves cannot be produced in that epoch. This places a universal

maximum frequency at which primordial waves can propagate, marked by the

transition between dimensions. We show that this cutoff frequency may be

accessible to future gravitational wave detectors such as the Laser Interferometer

Space Antenna.

Detecting Vanishing Dimensions via Primordial

Gravitational Wave Astronomy

PRL 106, 101101 (April, 2011)


Relation of the above (relativistic) examples with

the modern solid state physics of two-dimensional crystals

graphene, fulerene,

carbon nanotubes,

carbon nanobuds, etc:

Nobel Prize in Physics 2010


Examples of 2-dim manifolds with

variable geometries

(surfaces of buttles)

D. V. Shirkov,

A new scientific area

Good problems:

Solve

the Klein-Gordon

eq.,

the Dirac eq.

the heat eq.,

e.t.c.,

on that kind of

variable geometries.


KGEq for TEST PARTICLES: 10 90

baryons -

Eddington

number

In the STATIC case we assume (at least locally)

The

Klein

Gordon

Equation

on

Manifolds

with

variable

topological

dimension

We consider the toy models in which the

physical space is a continuous merger :

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 centrifugal term

The basic

Theorem:

Using proper changes of variables we can transform

the Z-equation in the Schrodinger-like form:


Some Explicit Examples

Two Cylinders of Constant Radii R and r < R,

Connected Continuously by a Part of Cone:


Continuous spectrum of states

Exact Solutions

In terms of the Bessel Functions

In the limit

one obtains the S-matrix

No signals with m ≠ 0

from 2D into 1D part

due to the centrifugal

force


M = 0

The resonant states

- S–matrix poles

A nontrivial dependence on the mass M:


According to our basic theorem we reduce the problem to

Schrodinger-type ODEq

with potential

The exact solution can be written in terms

of the

HYPERGEOMETRIC FUNCTIONS.

The spectrum is real for some


Expansion: 5% for 10 9 years

What was there

BEFORE the Big Bang

Is the Big Bang actually

a transition from a

LOWER DIMENSIONAL

world to the

FOUR

DIMENSIONAL

ONE

HST

2011 New idea

P.F., n D.Shirkov:


How to find

the physically admissible

solutions and their dynamics

The answer:

SOLVING EINSTEN EQUATIONS

A remarkable result:

Many of the needed exact solutions

for (1+2)-dim static AxU

(axial symmetric universes)

were pointed out in arXiv 10041510.


According to the Hawking & Penrose theorems

the GR dynamics in general physical conditions

unavoidable leads to singularities of space-time.

What happens after we reach such singularity

“The end of time …”A new look at the problem:

For the simple example - E. Kasner (1921) solution around

the singularity the very dimension of the space

changes in two different ways:

2d

3d

cube

1d


(1+2)-dim Time Dependent AxU

Consider

and

with variable

compactification

radius


Einstein eqs for time dependent (1+2) –dim AxU

Determinant:

Field equations:

Axial symmetry

Conservation of the momentum:


DIMENSIONAL REDUCTION POINTS

and

DIMENSIONAL TRANSITION POINTS

Symbolically:


Three vacuum solutions of Einstein eqs

1.

In

- expanding thread to a cylinder

Related by Lorentz transformations:

2.

- a static cone:

3.

- moving cone


Solutions of KGEq on (1+2)-dim

AxU with positive term can

be described in the Legendre

functions.


Solutions for the (1+2) AxU filled with “dust”

Homogeneous 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 solutions

involving one arbitrary function :

are arbitrary constants.


Dynamics of DRPs in (1+2) AxU with “dust”

1. Creaton and anihilation of pairs of DRPs is possible.

2. Dynamics of DRPs for the three types of functions :

are the zeros of


The solutions of matter equations

where

under a new restriction::


CONCLUDING REMARKS

1. A signal, related to degree of freedom

specific for the higher-dim part does not

penetrate into the smaller-dimensional part,

because of the inertial forces at the junction.

Such forces exist inevitably in curved space times

and in spaces with variable dimension.


CONCLUDING REMARKS

2. The specific spectrum of scalar excitations

characterizes the junction geometry.

A new idea:

To explain the observed particles spectra by

geometry of the junction between domains of the

space-time with different topological dimension.


CONCLUDING REMARKS

3. Instead of fixing the radii of

compactification ρ(t, z) ≥ 0 of the

compactified dimensions we let them to be

space-time functions, obtained solving Einstein

equations.

If ρ(t, z) → ∞ , we have a flat space.

In the opposite case, when ρ(t, z) → 0

the topological dimension of the

space-time reduces.

For (1+d)-case see

P.P.F. arXiv:1012.3520 [math-ph].


CONCLUDING REMARKS

4. The set of the dimensional reduction point -

DPR may have complicated structure and

dynamics:

5. Critical behavior of the solutions for test

particles around DPR exist and depends both

on geometry and motion.


CONCLUDING REMARKS

6. The parity violation, due to the asymmetry

of space geometry could yield the CP- and T

violation.

This gives a hope to recover a simple and natural

reason on a basic level for explanation of the real

situation with C, P, and T properties of the

particles relating these properties to the

global properties of the Universe.

Another recent attempt, based on local properties of the

space-time: see paper: arXiv:1107.1575

Mark J Hadley “The asymmetric Kerr metric as a source of

CP violation”.


CONCLUDING REMARKS

7. Baryon-antibaryon asymmetry

versus asymmetry of the space-time


Can it be related with asymmetry of

the very space-time


CONCLUDING REMARKS

8. The Big Bang = = time transformation of space

dimensions 1 2 3 MOVIE 3


Thank You for

your

attention

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