trusciencetrutechnology@blogspot.com
Volume 2016, Issue No. 1b, Dated: 12 January 2016, Time: 17:54 PM
Indian Science Congress Association
Mysure PHYSICS Paper
5 January, 2016 between 3 to 6 PM display.
Indian Science Congress Association
Mysure PHYSICS Paper
5 January, 2016 between 3 to 6 PM display.
Professor Dr. Kotcherlakota Lakshmi Narayana,
(Retd. Prof. of Physics, Shivaji University, Kolhapur - 416004)
Res: 17-11-10, Narasimha Ashram, Official Colony,
Maharanipeta. P. O., Visakhapatnam-530002, A.P.
Mobile: 09491902867.
kotcherlakoa_l_n@hotmail.com
lakshminarayana.kotcherlakota@gmail.com
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INDIAN SCIENCE CONGRESS ASSOCIATION,
14 Biresh Guha Street, Kolkata-700017.
ISCA, MYSURE UNIVERSITY, 2016 January 3 to 7,
Physics Session Paper. Displayed on 5 January 2016 at
Physics Department between 3 to 6 PM.
Professor Dr. Kotcherlakota Lakshmi Narayana,
trusciencetrutechnology@blogspot.com
{Retd.Prof. of Physics, SU, Kolhapur-416004}
17-11-10, Narasimha Ashram, Official Colony,
Maharanaipeta. P.O., Visakhapatnam – 530002. AP.
Mobile: 9491902867;16 July 2014 at 10h15mAM
lakshminarayana.kotcherlakota@gmail.com
=================================================================
ABSTRACT
An object of my work is that the Anti-Photon [Ref. Physics Section ISCA
2015, held at Mumbai Univ., Jan 5th] series presents the possibility
of higher fractional spins, the formalism and data presented in this paper on Anti-fractional
integral formalism specifically brings out the new mathematics for the spin
±1/8 to spin ±31/8 entities. The formalism extension to higher spins is also
worked out.
INDIAN SCIENCE CONGRESS SESSION, PHYSICS SECTION, CRAWFORD HALL, MYSORE,
2016.
==================================================================
Anti-fractional integral formalism to bring out New Physics
for the Spin
±1/8 to Spin ±31/8 in steps of ±1/8th devoid of integrals.
Professor Dr. Kotcherlakota Lakshmi Narayana, {Retd.Prof. of Physics, SU, Kolhapur-416004}
17-11-10,
Narasimha Ashram, Official Colony,
Maharanaipeta. P.O., Visakhapatnam – 530002. A.P
Mobile: 9491902867;16 July 2014 at 10h15mAM.
PREAMBLE
Paper presented in the Indian Science Congress session held at Mysore
University, on 5 January 2016, in the Physics Section. Sequel to my paper
presented on the 5th January 2015, at University of Mumbai. There
the integral Spins were considered and present version for the Mysore
University, ISCA session, of year 2016, the Anti-fractional integral formalism
that brings out NEW PHYSICS is given. The possibility of higher spins,
specifically the formalism presented in this paper on Anti-fractional
integral formalism brings out the new Physics, for the spin ±1/8 to spin ±31/8 entities.
INTRODUCTION
Conceiving an anti-photon is a very bold endeavour by the author [1, 2 and
3]. Having brought out a monograph book December 2013 on this subject matter
the author now feels to extend the concept to Anti-fractional integral
formalism for higher spins.
My Presentation
SPINS
(±1/8, ±1/4, ±3/8)
Imaginary
(Sμν
–i/8)( Sμν + i/8) = (Sμν)2 +1/8 = S2μν +
1/8=0
Or S2μν =
- 1/8 --------------(1)
Giving
Sμν = ± i/(2√2) ---------------------(2)
Realistic
t2μν - 1/8 = 0 giving tμν =
±1/(2√2) -----------(3)
with tμν = ∓ i Sμν------------------------(4)
Imaginary
(Sμν
–i/4)(Sμν + i/4) = (Sμν )2 +1/16 = S2μν
+ 1/16=0
Or S2μν
= - 1/16 --------------(1a)
Giving
Sμν = ± 1/4
---------------------(2a)
Realistic
t2μν - 1/16 = 0 giving tμν =
± 1/4 -----------(3a)
with tμν = ∓ i Sμν------------------------(4a)
Imaginary
(Sμν
–3i/8)(Sμν + 3i/8) = (Sμν)2 +9/64 = S2μν
+ 9/64=0
Or S2μν
= - 9/64 --------------(1b)
Giving
Sμν = ± i 3/8 ---------------------(2b)
Realistic
t2μν - 9/64 = 0 giving tμν =
± 3/8 -----------(3b)
with tμν = ∓ i Sμν------------------------(4b)
SPIN
(±5/8, ±3/4,±7/8)
±5/8
Imaginary
(Sμν
–i5/8)(Sμν + i5/8) = ((Sμν)2 +25/64) Sμν = S3μν +
25/64 Sμν =0
Or S3μν
= - Sμν 25/64
--------------(5)
Giving
Sμν = ± i5/8
---------------------(6)
Realistic
t2μν = - S2μν = 25/64 giving tμν = 5/8
-----------(7)
with tμν = ∓ i Sμν------------------------(8)
±3/4
Imaginary
(Sμν
–
3i/4) Sμν (Sμν + 3i/4) = (Sμν )2
+1/16 = (S2μν + 9/16) Sμν =0
or S2μν
= - 9/16; Sμν = ±i3/4; --------------(5a)
Giving
Sμν = ± i3/4 ---------------------(6a)
Realistic
t3μν - 27/64 = 0 giving tμν = ± 3/4
-----------(7a)
with tμν = ∓ i Sμν------------------------(8a)
±7/8
Imaginary
(Sμν
–7i/8) Sμν (Sμν + 7i/8) = ((Sμν )2
+49/64) Sμν = S3μν
+ 49/64 Sμν4 =0
Or S2μν
= - 49/64 --------------(5b)
Giving
Sμν = ± i 7/8 ---------------------(6b)
Realistic
tμν = 7/8; t2μν= 49/64; t3μν =
343/512
with tμν = ∓ i Sμν------------------------(8b)
SPIN (±9/8, ±5/4, ±11/8)
±9/8
Imaginary
Sμν =
±i1/8; Sμν = ±i9/8;
[(S2
μν + 81/64]* (Sμν + 1/64) = (Sμν)4 + 82/64
S2 μν + 81/(64) 2; ---------(5)
(Sμν)4 + 41/32 S2
μν + 81/(64) 2;------------------(6)
Realistic
(tμν)4 -
41/32 t2 μν + 81/(64) 2 =0…………….(7)
tμν =
±9/√64 or tμν
= ±1/8;…………(8)
With tμν = ∓ i Sμν -----------------------(9)
±5/4
Imaginary
[(S2 μν +
25/64]* (Sμν + 1/16) = (Sμν)4 + 26/16 S2
μν + 25/(16) 2; …..(5a)
(Sμν)4
+ 13/8 S2 μν + 25/(16) 2 = 0; ………….(6a)
Realistic
(tμν)4 –
26/16 t2 μν + 25/(16) 2 =
0…………….(7a)
t2μν =
±25/8 or t2μν =
±1/8;…………(8a)
With t2μν =
S2 μν
-----------------------(9a)
±11/8
Imaginary
[(S2 μν +121/64]*( S2μν + 9/64) = (Sμν)4 +
65/32 S2 μν +1089/(64) 2 = 0;-----(5b)
Realistic
(tμν)4
– 130/64 t2 μν + 1089/(64) 2 =
0---------------(7b)
t2μν =
±9/64 or t2μν =
±121/64;…………(8b)
With tμν
= ∓ i Sμν -----------------------(9b)
SPIN
(±15/8, ±7/4, ±13/8)
±15/8
Imaginary
[(S2
μν + 225/64]* (S2 μν + 49/64) Sμν
= ((Sμν)4
+ 274/64 S2 μν + 225x49/(64) 2 ) Sμν
; …..(5)
((Sμν)4 + 274/64
S2 μν + 11025/(64) 2 ) S μν= 0;
…..(6)
Realistic
(tμν)4 – 274/64
t2 μν + 11025/(64)2 ) t μν = 0…………….(7)
Imaginary
[(S2
μν + 49/16]* (S2 μν
+ 9/16) Sμν ---------------------(5a)
= ((Sμν)4
+ 58/16 S2 μν + 441/256 ) Sμν = 0 ;
…..(6a)
Realistic
(tμν)4 –
58/16 t2 μν + 441/256) t μν = 0--------------(7a)
Imaginary
[(S2 μν +
13/8.13/8]* (S2 μν
+ 25/64) Sμν ---------------------(5b)
= ((Sμν)4
+ 194/64 S2 μν +169/64. 25/64 ) Sμν
= 0 ; ……….(6b)
Realistic
(tμν)4
– 194/64 t2 μν + 169/64. 25/ 64 ) t μν = 0--------------(7b)
SPIN (±19/8,
± 9/4, ±17/8)
±19/8
Imaginary
(S2 μν + 19*19/64)* (S2
μν + 11*11/64)* (S2
μν + 9/64)-------------(5)
((Sμν)6 + 482/64 S4
μν +4338/4096 S2μν
+ 3948129/262144)=0;--------(6)
Realistic
((tμν)6 - 491/64 t4 μν + 4338/4096
t2μν –
3948129/262144)=0-------(7)
± 9/4
Imaginary
(S2 μν +
81/16)* (S2 μν +
25/16)* (S2 μν + 1/16)---------(5a)
((Sμν)6
+ 107/16S4 μν +2132/256 S2μν +
2025/(16*16*16))=0;------(6a)
Realistic
((tμν)6 - 107/16
t4 μν + 2132/256 t2μν -
2025/(16*16*16))=0;----(7a)
±17/3
Imaginary
(S2 μν +
289/64)* (S2μν +
81/64)* (S2μν + 1/64)---------(5b)
((Sμν)6
+ 371/64 S4 μν + 23779/256 S2μν +
23409/(64*64*64))=0;--------(6b)
Realistic
((tμν)6
- 971/64 t4 μν + 23779/256 t2μν -
23409/(64*64*64))=0;---(7b)
SPIN ( ±23/8,
±11/4, ±21/8)
±23/8
Imaginary
(S2 μν + 529/64)* (S2μν + 225/64)* (S2μν +
49/64)---------------(5)
((Sμν)6
+ 803/64 S4 μν + 155971/256 S2μν +
119025x49 / (64*64*64))=0;----(6)
Realistic
((tμν)6 - 803/64 t4
μν + 155971/256 t2μν - 5832225/(64*64*64))=0;---(7)
±11/4
Imaginary
(S2 μν + 121/16)*
(S2μν + 49/16)* (S2μν
+ 9/16)---------------(5a)
((Sμν)6
+ 179/16 S4 μν + 7459 / 256 S2μν +
53361 / (16*16*16))=0;----(6a)
Realistic
((tμν)6 -
174/16 t4 μν + 7459 / 256 t2μν -
53361/(16*16*16))=0;------(7a)
±21/8
Imaginary
(S2 μν + 441/64)* (S2μν + 169/64)* (S2μν +
25/64)---------------(5b)
((Sμν)6 + 635/64 S4
μν + 89479 / 4096 S2μν + 74529x25 /
(64*64*64))=0;---(6b)
Realistic
((tμν)6 - 635/64 t4
μν + 89479 /4096 t2μν -
1863225/(64*64*64))=0;------(7b)
SPIN (
±27/8, ±13/4, ±25/8)
±27/8
Imaginary
(S2 μν + 276/64)* (S2μν + 196/64)* (S2μν +
121/64)*( S2μν + 9/64)------(5)
(Sμν)8
+ 602/64 S6 μν + 116545 / 4096 S4μν
+ 75464882 / (643)
S2μν + 58910544/644=0;-----------(6)
Realistic
(tμν)8
- 602/64 t6 μν + 116545 / 4096 t4μν
- 75464882 / (643)
t2μν + 58910544/644=0;-----------(7)
±13/4
Imaginary
(S2 μν + 169/16)*
(S2μν + 81/16)* (S2μν
+ 25/16)*( S2μν + 1/16)------(5a)
(Sμν)8
+ 276/16 S6 μν + 20214 / 256 S4μν
+ 6250 / (163)
S2μν + 342225 / 164=0;-----------(6a)
Realistic
(tμν)8
– 276/16 t6 μν + 20214 / 162 t4μν
- 6250 / (163)
t2μν + 342225 /164
= 0;-----------(7a)
±25/8
Imaginary
(S2 μν + 625
/64)* (S2μν + 289/64)*(S2μν +
81/64)*(S2μν + 1/64)------(5a)
(Sμν)8
+ 996/64 S6 μν + 255654 / 642 S4μν
+ 14885284 / (643)
S2μν + 14630625 / 644 = 0;-----------(6a)
Realistic
(tμν)8 - 996/64 t6
μν + 255654 / 642 t4μν
- 14885284 / (643)
t2μν + 14630625 / 644 = 0;---------(7a)
SPIN
(±31/8, ±15/4,±27/8)
±31/8
Imaginary
(S2
μν + 961 /64)* (S2μν + 529/64)*(S2μν
+ 225/64)*(S2μν + 49/64) Sμν -----(5)
i.e. Sμν [(Sμν)8
+ 1764/64 S6 μν + 4605654 / 642 S4μν
+ 20513570 / (643)
S2μν + 5604768225 / 644] = 0;------(6)
Realistic
±i.tμν [(tμν)8
- 1764/64 t6 μν + 4605654 / 642 t4μν
- 20513570 / (643)
t2μν + 5604768225 / 644] =
0;------(7)
±15/4
Imaginary
(S2 μν + 225 /16)* (S2μν
+ 121/16)*(S2μν + 49/16)*(S2μν +
9/16) Sμν -----(5a)
i.e. Sμν [(Sμν)8
+ 404/16 S6 μν + 477348 / 162 S4μν
+ 3104912 / (163)
S2μν + 12006225 / 164] = 0;------(6a)
Realistic
±i.tμν [(tμν)8
- 404/16 t6 μν + 47734 / 162 t4μν
- 3104912 / (163)
t2μν + 12006225 / 164] =
0;------(7a)
±29/8
Imaginary
(S2 μν + 841 /64)* (S2μν
+ 441/64)*(S2μν +169/64)*(S2μν +
25/64) Sμν -----(5b)
i.e.
Sμν [(Sμν)8 + 1476/64 S6
μν + 623814 / 642 S4μν
+ 77367364 / (643)
S2μν + 1566972225 / 644] =
0;------(6b)
Realistic
±i.tμν [(tμν)8
– 1476 /64 t6 μν + 623814 / 642 t4μν
- 77367364 / (643)
t2μν + 1566972225 / 644] =
0;------(7b)
Conclusions
The tμν
= ∓ i Sμν yields the
realistic and as well the imaginary quantum numbers for the spins ±1/8 to spin ±31/8 entities to 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 fractional integral spins
for ±1/8 to spin ±31/8 entities.
REFERENCES
A. Indian
Science Congress, Physical Sciences Session, 2015 at Mumbai University, Physics
Department,
at 2h30mPM, on 5th January, 2015.
1. Antigravity-like
event competes marvelling 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 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 to 7,
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. trusciencetrutechnology@blogspot.com, Volume 2015, Issue No.7, July 23rd, 2015,
Time: 7h00m A.M.
ISCA 2016 ON 5 January 2016 between 3 to 6 PM.
PHYSICS DEPARTMENT
PHYSICS DEPARTMENT
A Special note:
One person from Netherlands visited the Mathematics Displays at Mathematics Department and I found him interested in my Paper entitled "GALACTIC
GRAVITON INTERACTION WITH DARK ENTITY" by Professor Dr. K. L. Narayana, trusciencetrutechnology@blogspot.com. Given
to ISCA, MYSURE UNIVERSITY, 2016 January 3rd to 8th,
MATHEMATICS SECTION. I presume, he is M. K. Richardson, Leiden University. I am grateful to him for the visit on 5 Jan 2016 around 3.30 PM on 5 Jan 2016.
ACKNOWLEDGEMENT
The author is deeply indebted to Late Prof. K. R. Rao,
D.Sc. (Madras) D.Sc. (London) for his interest and encouragement to publish the articles for the benefit world intellectual readers and the academicians.
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