ANTI-INTEGRAL AND ANTI HALF INTEGRAL FORMALISM FOR SPIN HALF TO SPIN FOUR ENTITIES and GRAVITON AND SPACE-TIME INTERACTION PRODUCTION OF PIONS, NEW GAMMAS AND THEIR ANTI-PARTICLES. by KLN

trusciencetrutechnology@blogspot.com

Volume 2015, Issue No.1, January 11^th, 2015, Time: 7h49m PM.

               

PREAMBLE

                Two papers are presented in Indian Science Congress held at Mumbai University, on 5^th January 2015, by me in the afternoon from 2h30mPM to 5h30mPM in the Physics Section.

            They are entitled 1. Anti-integral and Anti half integral formalism for spin half to spin four entities

and 2. GRAVITON AND SPACE-TIME INTERACTION PRODUCTION OF PIONS, NEW GAMMAS AND THEIR ANTI-PARTICLES.

            Details are presented below.

Anti-integral and Anti-half integral formalism

 for spin half to spin four entities

by

Professor Dr Kotcherlakota Lakshmi Narayana,

{Retd. Prof.of Physics, SU, Kolhapur} 17-11-10, Narasimha Ashram,

Official Colony, Maharanipeta.P.O. Visakhapatnam -530002,

Mobile No. 9491902867; Dt. 16 July 2014 at 10h15mAM

ABSTRACT

            An object of my work is that the anti-photon [1] series presents the possibility of higher spins and specifically the formalism and data presented in this paper on Anti-integral and Anti-half integral formalism specifically brings out the new mathematics for the spin-1/2 to spin 4 entities. The formalism extension to higher spins greater than spin 4 value referring to the anti-photon like particles is differed for publication at a later date.

INTRODUCTION  

Conceiving an anti-photon is a very bold venture by the author [1, 2, 3]. Having brought out a monograph book December 2013 on this subject matter the author now feels to extend the concept to higher spins.

 My Presentation

SPIN ½

Imaginary

           (S_μν )² +1/4 =  S²_μν  + 1/4=0  or   S²_μν  =   -¼  --------------(1)

giving                                       

                                    S_μν =±i/2. ---------------------(2)

Realistic

t²_μν -  1/4 = 0 giving t_μν   = ±1/2 -----------(3)

with t_μν = ∓ i S_μν------------------------(4)

SPIN 1

Imaginary

 [(S_μν )²+1]* (S_μν ) = (S_μν )³ + (S_μν )= (S_μν )³ + S_μν  =0 ---------(5)

With S_μν   =   ±i ,  0.-------------(6)

Realistic

We have t³_μν -  t_μν = 0. ----------------(7)

Surprisingly it yields t_μν = ∓ 1,  0,   ±1 ----------------(8)

With t²_μν    = - S² _μν -----------------------(9)

SPIN 3/2

Imaginary

We have   S²_μν = ±3/2 i   ,    ± i / 2 --------(10)

Interestingly yields S⁴_μν + 5/2 * S²_μν +9/16 = 0-----------(11)

Realistic

t⁴_μν - 5/2* t²_μν + 9/16  =0 .-------------------(12)

but it gives t_μν = ∓ 3/2,    ∓ 1/2,    ±1/2,    ±3/2----------------(13)

with t⁴_μν = S⁴_μν------------------------(14)

For spin 3/2 we have

(t_μν +3/2)* (t_μν +1/2)* (t_μν -1/2) (t_μν -3/2)=0 ---(15)

SPIN 2

Imaginary

S_μν   =   ± 2i,   ±i ,  0.-------------(16)

Surprisingly it gives S⁵_μν + 5* S³_μν + 4 * S_μν  =0-----(17)

For spin 2 we have (S_μν -2i)* (S_μν -i)* (S_μν )* (S_μν + i)( (S_μν + 2i)=0 -----(18)

Realistic

The expressions for (t_μν +2)* (t_μν +1)* (t_μν )* (t_μν -1)( (t_μν -2)=0---------------(19)

yields t⁵_μν  -  5 * t³_μν + 4 * t_μν =0 . -------------------------(20)

solve(t⁵_μν    -  5 * t³_μν+ 4 * t_μν)--------------------------(21)

ans =  ∓ 2 ;   ∓ 1;    0 ;    ±1;  ±2 . -------------------------(22)

These are the explicit values for Spin 2.

This is the desired expressive values of Spin 2 projections from +2 to -2.

Next we extend the formalism to study the higher spins explicitly:

SPIN 5/2

Imaginary

S _μν = ∓5/2*i; ∓3/2*i;∓i/2---------------(23)

Similarly evaluated for spin 5/2  

(iS_μν +5/2)* (iS_μν +3/2)* (iS_μν +1/2)* (iS_μν-1/2)* (iS_μν-3/2)*( iS_μν-5/2) =0 ---(24)

gives S⁶_μν + 35/4 * S⁴_μν + 259/16 * S²_μν + 225/64=0------------------(25)

         MATHLAB gives just:  ans =  5/2;   ½;  3/2; -1/2; -3/2; -5/2---(26)

Actually it should be S= ∓5/2*i; ∓3/2*i;∓i/2 a result obtained by explicit evaluation.

Realistic

((t_μν +3)* (t_μν +2)* (t_μν +1)* (t_μν )* (t_μν -1)( (t_μν -2)*( t_μν -3)=0---------------(27)

       yields t_μν^6-35/4*t_μν^4+259/16*t_μν^2-225/64==0-------------------------------(28)

              solve(t_μν^6-35/4*t_μν^4+259/16*t_μν^2-225/64==0)---------------------------(29)

                       yields the ans =  5/2;  ½;  3/2; -1/2; -3/2; -5/2----------------------------(30)

a result obtained by explicit evaluation.

SPIN 3

Imaginary

: S _μν =∓3*i, ∓2*i,∓i,0--------(31)

(S _μν -3*i)*(S _μν -2*i)*(S _μν -i)*S _μν *(S _μν +i)*(S _μν +2*i)*(S _μν +3*i)=0------------------(32)

                                     yields S⁷_μν + 14 * S⁵_μν + 49 * S³_μν + 36* S_μν =0----------------------(33)

                                          MATHLAB gives again ans: 3, 1, 2, 0, -1, -2, -3------------------(34)

Realistic

 We get the equation  

 ±t _μν ^7 ∓14*t _μν ^5   ±  49*t _μν ^3 ∓ 36*t _μν =0---(35)

              solve(t^7-14*t^5+49*t^3-36*t==0)---------------------------------(36)

MATHLAB gives again ans =   3;   1;  2;   0;  -1;  -2;  -3 -------(37)

t _μν= ∓i*S _μν; t³ _μν= ±i*S³ _μν; t⁵ _μν= ∓i*S⁵ _μν; t⁷ _μν= ±i*S⁷ _μν;----------(38)

SPIN 7/2

Imaginary

S _μν =∓7/2*i,  ∓5/2*i,    ∓3/2*i,   ∓i/2-------------------(39)

S _μν ^8+(84/4)*S _μν ^6+(1974/16)*S _μν ^4+(12916/64)*S _μν ^2+(11025/256)==0-------(40)

Realistic

 We get the equation  

t _μν ^8 ∓84/4*t _μν ^6   ± 1974/16*t _μν ^4 ∓ 12916/64*t _μν ^2+ 11025/256=0---(41)

solving we obtain

                                     t _μν=  ±7/2,     ±5/2,    ±3/2,    ±1/2------------------------------------(42)

SPIN 4

Imaginary

S _μν =   ∓ 9/2*i,   ∓7/2*i,  ∓5/2*i,    ∓3/2*i,   ∓i/2-------------------(43)

Yields the expression for spin 4 as

S ⁹_μν +30*S⁷ _μν + 273*S⁵ _μν + 820*S³ _μν + 576* S _μν ==0-------(44)

Realistic

 We get the equation  

± t ⁹_μν ∓ 30*t⁷ _μν  ± 273*t⁵ _μν ∓ 820*t³ _μν ± 576* t _μν ==0-------(45)

Yielding

t _μν=  ± 4,   ± 3,   ± 2,     ± 1,  0.------------------(46)

Conclusions

        The t_μν = ∓ i S_μν yields the realistic and as well the imaginary quantum numbers for the spins ½ to 4 explicitly presented above.   

ACKNOWLEDGMENT

                   The author is fully expressive of his gratitude to Late Professor K. R. Rao D.Sc. (Madras) D.Sc. (London), whose D.Sc. Thesis of Madras University submitted in 1927, was an inspiration to formulate the New Spin considerations of the present paper as they describe the possible Anti-integral and Anti-half integral formalism for spin half to spin four entities.

REFERENCES

1.           Antigravity-like event competes marveling with the visible Universe yet times! ”.  Visakhapatnam City Observation of a possible DARK Matter Event. What  constitutes  the  observed  Dark  Matter  visible brilliance  of  light  by  the  present  author,   on  that  fateful  evening  of  rain  and  thunder  shower  that  lashed  almost  one  and  half hours  at  the  outskirts of  Visakhapatnam  city![Ref. No.18a].  On  August 14 , 2011, trusciencetrutechnology@blogspot.com, published,  Saturday,  August 18,  2012  the  observation  of  a  up-going  positron,   in  the flash  lightning  at  Visakhapatnam photographed  luckily by the  author,  fol lowed  by  a  mild  earthquake  in  that  region  of observation  supports  the  idea  that  they  could  be  colliding particles of  Dark Matter.  The lightning  was very  furious during the  actual   Earth  tremors  happening  seen  brilliantly  in Visakhapatnam  near  the  Bus  stand  area  of  Gajuvaka.  A photograph  of  the  observed  lightning  has  already  been published  by  the present  author  in  a previous  publication of  the  trusciencetrutechnology@blogspot.com. It  is  probably  a  wild  wind  of  radiation  from  the Earth’ s  tremor!   I   quote  that  “I   don’ t  think  it  makes  you  believe  it  must be  Dark  Matter,   nor do  I   think  it makes  you  believe  it  cannot  be”  a  remark  of  particle  theorist  from New  York  University,   report  published  in  Phys.  Review Lett. on Friday!   Whether  the  emitted  positrons  are  an astonishing  and  puzzling  signals  of  the  Dark  Matter observed,   photographed  by  the  present  author  and reviewed  in  a previous publication of  this blogspot! . Refer: trusciencetrutechnology@blogspot.com, Prof K Lakshmi Narayana, Visakhapatnam.

2.      The author has the pleasure to bring out the significant work on the discovery, observation and analysis of Anti-Photon. It is fortuitous observation by the author on the eve of 14 August 2013 at a place near Visakhapatnam. See the Book on Anti-Photon by the present author.

 3.      PHYSICS SECTION.  ISCA 2013 held in Kolkata Jan 3^rd to 7^th, 2013.  “Analysis of the Thunderbolt Lightning at Visakhapatnam during the onset of a mild Earth Tremor on 14 August”    Author: Professor Dr Kotcherlakota Lakshmi Narayana, {Retd. Prof. of Phys, SU} 17-11-10, Narasimha Ashram, Official Colony, Maharanipeta. P. O, Visakhapatnam-530002.Mobile No: 9491902867.

 *********************************************************************************

The Indian Science Congress Association

Session to be held Mumbai in Jan 3-7, 2015.

GRAVITON AND SPACE-TIME INTERACTION PRODUCTION OF PIONS, NEW GAMMAS AND THEIR ANTI-PARTICLES

Professor Dr Kotcherlakota Lakshmi Narayana,

trusciencetrutechnology@blogspot.com

{Retd. Prof.of Physics, SU, Kolhapur} 

17-11-10, Narasimha Ashram, Official Colony, 

Maharanipeta.P.O.   Visakhapatnam -530002,

Mobile No. 09491902867

ABSTRACT

             An object of the present work is to present the new findings by the author about the Graviton, Space-Time interaction production of Pions, new Photons and new Anti-Photons [Ref: see the book on Anti-Photons by the author 1993]. A completely new view of the space-time structure its involvement with the Gravitons is envisaged and presented to account for terrestrial atmosphere presence of Pions, new Photons and new Anti-Photons. The diagrammatic approach to evaluate the matrix elements is given. The new current matrix elements of the  graviton, with one - Pion state ⊞ (sum) new gamma, yields new 

mathematics of new Algebra,  

                                            

                            

with novel sum ⊞ of the right hand side. The new photons have five projections to go with the similar Pions to match the Graviton of five projections +2, +1, 0, -1, -2. Similar expressions for the Anti-Graviton, Anti-Photon and the Anti-Pion are suggested and explicitly formulated by me. The effect of Gravity on virtual Pion-Gamma pairs as they propagate through space lead to a violation of Einstein’s equivalence principle while the effect is difficult to be measured being virtual its effects on creation of Muon-neutrino pairs and virtual Photons seems to be manageable. The analogous matrix element for the Anti-Photon γ’_ν  is possible. Obviously the formalism developed helps to easily write down the corresponding matrix elements for the π ^–_μ.

 The Indian Science Congress Association

Session to be held Mumbai in Jan 3-7,  2015.

GRAVITON AND SPACE-TIME INTERACTION PRODUCTION OF PIONS, NEW GAMMAS AND THEIR ANTI-PARTICLES

Professor Dr Kotcherlakota Lakshmi Narayana,

trusciencetrutechnology@blogspot.com

{Retd. Prof.of Physics, SU, Kolhapur} 17-11-10, Narasimha Ashram,

Official Colony, Maharanipeta.P.O. Visakhapatnam -530002,

Mobile No. 09491902867

INTRODUCTION   

   

            The author has succeeded to formulate a new theory of Graviton, and Space-Time interaction production of Pions, new gammas and their anti-particles. An important struggle in Elementary Particle Physics is to involve Graviton with the other particles. The object of present paper is to enumerate a significant and a novel approach to unify the particles adopting a new mathematics. The success goes with the definition of new Sum designated by the operator ⊞. This helps to sum the components of Pion (with five components) and a new photon (with again five components). The idea being simply to match, the five components of a spin-2 particle, like the Graviton. It is well known to have spin-2 graviton of a single spin-2 instead of all the five projections of it as envisaged in this paper. The effect of Gravity on virtual Pion-Gamma pairs as they propagate through space lead to a violation of Einstein’s equivalence principle. While the effect is difficult to be measured being virtual its effects on creation of muon-neutrino pairs and virtual Photons seems to be manageable. The analogous matrix element for the Anti-Photon γ’_ν is possible. Obviously the formalism developed helps to easily write down the corresponding matrix elements for the π ^–_μ.

MATHEMATICS DETAILS

           The new current matrix elements of the Graviton, with one - Pion state ⊞ (sum) new gamma, yields new mathematics of present  new Algebra,  

                      

with novel sum of the right hand side. The new photons have five projection to go with the similar Pions to match the Graviton of five projections +2, +1, 0, -1, -2.

(a)  A_μν (x) expressions

          The sum on the right hand side adds up the components of the Pion and the new gamma particles. We have explicitly the expressions for these sums as follows;

(1⊞1), (1⊞0), (0⊞0), (-1⊞0), (-1⊞-1)

yielding the five sets to match the five components of a 
spin-2 Graviton 
                                           viz., +2, +1, 0, -1, -2.

          The A_μν (x) components are

[A₂₂, A₂₁, A₂₀, A _2-1, A_2-2; A₁₂, A₁₁, A₁₀, A_1-1, A_1-2;

    A₀₂, A₀₁, A₀₀, A _0-1, A_0-2; A_-12, A_-11, A_-10, A_-1-1, A_-1-2;

     A_-22, A _-21,  A _-20, A_-2-1,  A _-2-2; A_-22, A_-21, A_-20, A_-2-1, A_-2-2]

                

                

The five components of a spin-2 Graviton                                           

 viz., +2, +1, 0, -1, -2.

        The matrix element can easily set up by expanding the

        The essential difference of the usual algebra and present formulation is in the extended states of π_μ and γ_ν are respectively given by (1, 1, 0, -1, -1) and (1, 0, 0, 0, -1) to account for the five projections of spin-2 Graviton. 

        The formalism has only additional (1,-1) for the new Pion and (0, 0) for the new Photon.

(b)    A^’_μν (x) expressions

        The new current matrix elements of the Graviton, with one - Pion state, ⊞ (sum), new Anti-gamma, yields new mathematics of Algebra,  

with novel sum of the right hand side. The new dashed Anti-photons  γ’_ν have also five projections (1, 0, 0, 0, -1)  to go with the similar 

                          Pions (1, 1, 0, -1, -1)  to match the Graviton 

                           of five projections +2, +1, 0, -1, -2.

The A’_μν (x) components are

[A’₂₂, A’₂₁, A’₂₀, A’_2-1, A’_2-2; A’₁₂, A’₁₁, A’₁₀, A’_1-1, A’_1-2;

A’₀₂, A’₀₁, A’₀₀, A’_0-1, A’_0-2; A’_-12, A’_-11, A’_-10, A’_-1-1, A’_-1-2;

A’_-22, A’_-21,  A’_-20, A’_-2-1,  A’_-2-2; A’_-22, A’_-21, A’_-20, A’_-2-1, A’_-2-2]

               

                 The five components of a spin-2 Graviton 
                                        
                               viz., +2, +1, 0, -1, -2.

                     

                   

        The essential difference is that the new dashed Anti-photons γ’_ν describe the Physics, as envisaged by the author in his publication viz., 

[Ref: see the book on Anti-Photons by the author 1993].

        Present work relies on the ideas presented in my publications 

and the recent literature listed below [Ref. 1, 2, 3, 4, 5 and 6].

CONCLUSIONS

        Association of these Anti-Photons with the 

Pion to form the matrix element with Graviton is 

of paramount significance. Obviously the 

formalism developed helps to easily write down 

the corresponding matrix elements for the π ^–_μ.

ACKNOWLEDGMENT

                   The author is fully expressive of his gratitude to Late Professor K. R. Rao D.Sc. (Madras) D.Sc. (London), whose D.Sc. Thesis of Madras University submitted in 1927, was an inspiration to formulate the New Spin considerations of the present paper as they describe the the Graviton, Space-Time interaction production of new Pions, new Photons and new Anti-Photons.

REFERENCES

1.         Antigravity-like event competes marveling with the visible Universe yet times!  Visakhapatnam City Observation of a possible DARK Matter Event. What  constitutes  the  observed  Dark  Matter  visible brilliance  of  light  by  the  present  author,   on  that  fateful  evening  of  rain  and  thunder  shower  that  lashed  almost  one  and  half hours  at  the  outskirts of  Visakhapatnam  city![Ref. No.18a].  On  August 14 , 2011, trusciencetrutechnology@blogspot.com, published,  Saturday,  August 18,  2012  the  observation  of  a  up-going  positron,   in  the flash  lightning  at  Visakhapatnam photographed  luckily by the  author,  followed  by  a  mild  earthquake  in  that  region  of observation  supports  the  idea  that  they  could  be  colliding particles of  Dark Matter.  The lightning  was very  furious during the  actual   Earth  tremors  happening  seen  brilliantly  in Visakhapatnam  near  the  Bus  stand  area  of  Gajuvaka. 

             A photograph  of  the  observed  lightning  has  already  been published  by  the present  author  in  a previous  publication of  the  trusciencetrutechnology@blogspot.com. It  is  probably  a  wild  wind  of  radiation  from  the Earth’ s  tremor!   I   quote  that  “I   don’ t  think  it  makes  you  believe  it  must be  Dark  Matter,   nor do  I   think  it makes  you  believe  it  cannot  be”  a  remark  of  particle  theorist  from New  York  University,   report  published  in  Phys.  Review Lett. on Friday!   Whether  the  emitted  positrons  are  an astonishing  and  puzzling  signals  of  the  Dark  Matter observed,   photographed  by  the  present  author  and reviewed  in  a previous publication of  this blogspot! . Refer: trusciencetrutechnology@blogspot.com, Prof K Lakshmi Narayana, Visakhapatnam.

2. The author has the pleasure to bring out the significant work on the discovery, observation and analysis of Anti-Photon. It is fortuitous observation by the author on the eve of 14 August 2013 at a place near Visakhapatnam. See the Book on Anti-Photon by the present author.

 3. PHYSICS SECTION.  ISCA 2013 held in Kolkata Jan 3^rd to 7^th, 2013.  “Analysis of the Thunderbolt Lightning at Visakhapatnam during the onset of a mild Earth Tremor on 14 August”    Author: Professor Dr Kotcherlakota Lakshmi Narayana, {Retd. Prof. of Phys, SU} 17-11-10, Narasimha Ashram, Official Colony, Maharanipeta. P. O, Visakhapatnam-530002.Mobile No: 9491902867.

            4.  K. L. Narayana & S. B. Patil, ”A Physical model from the Mass empirics

              of  two-particle Baryon  Resonance States and a postulation of medium and

              low  strong  interactions”, Indian Journal of Physics Vol. 50,

              pages 993-1002, 1976,  and  Ind. Sci. Cong. Waltair, 1976.

           5.  D S Hajdukovk, Astrophysics Space Sci. vol.326, p3-5, 2010.

                 The surprise that the geometrical mean of the Pion mass and baryonic    

                  mass of a galaxy, divided by the Compton wavelength of a Pion,

                 has the same order of magnitude as the radial dark matter (dm) density

                 i.e. ρ_r =  dM_dm/dr = 1/ B . 1/λ_π √m_π √M_b

                 Dimension less constant B may vary from galaxy to galaxy but close

                 to  B=2. So this leads to M_dm = ρ_r(r-a)= 1/B . (r-a)/ λ_π√m_π √M_b  where

                 the constant ‘a’ depends on Galaxy in question.  In our galaxy

                 M_b= 3E+41Kg    and  a= 8 kpc

                  m³_π= ħ²/ (cG) . HΩ_Λ/ √(Ω-1)   R₀/R -----(8)   and

                   m³_π = ħ²/ (cG) . HΩ_Λ/ √(Ω-1)  =  M²_P m_χ

                 ` m³_π = ħ²/ (cG) . H-----(9)

                  which is known to Dirac 1937,1938 and Weinberg 1972.

                  Plausible alternative is  m³_π=4π ħ²/ (cG) . H√Ω_Λ -----(10)

                   8, 9 and 10 may be written as m³_π= M²_P m_χ where

                  M²_P= √( ħc)/G is Planck’s constant.

                  And m_π = m³_π/ M²_P= ħ/c²  . HΩ_v/ √(Ω-1) =3.25E-68 Kg.

                  Planck mass is close to geometrical mean of minimum mass m_π

              and present mass of Universe M_u i.e. M_P~√( M_u m_π).

             6.  trusciencetrutechnology@blogspot.com, Vol.2012, Issue No.10, dt: 30 October

                  2012, Time: 17h16m P.M, “A FIVE DIMENSIONAL THEORY OF GENERAL

                  RELATIVITY AND PRODUCTION OF ELECTRON AND POSITRON PAIR”.

                  Professor Dr Kotcherlakota Lakshmi Narayana,

DATA PRESENTED AT THE Indian Science Congress Session held at Mumbai University, Mumbai on 5th January 2015,  
at 2h 30m PM to 5h 30m PM at the Physics Session. 
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