String Theory: A Model Beyond Popular Physics. Kenny Wunder Mississippi State University TAMU Cyclotron

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1 Sing Theo: A Model Beond Popula Phsics Kenn Wunde Mississippi Sae Univesi TAMU Ccloon

2 Tpes of sing heo Bosonic sing heo Tpe I sing heo Tpe II A sing heo Tpe II B sing heo Heeoic sing heo

3 The big ideas (in bosonic sing heo) On geome Idenificaion Compacificaion D banes Evoluion of he acion Paameeizing made eas The ligh cone gauge Becoming paicles

4 Some hings abou geome: Idenificaion

5 Some hings abou geome: Idenificaion

6 Some hings abou geome: Idenificaion π

7 Some hings abou geome: Compacificaion

8 Some hings abou geome: Compacificaion

9 Some hings abou geome: Compacificaion

10 Some hings abou geome: Compacificaion

11 Some hings abou geome: Compacificaion

12 Some hings abou geome: Compacificaion

14 Bounda condiions and D banes Neumann bounda condiions (, ) (, a) Diichle bounda condiions (, ) (, a)

15 Bounda condiions and D banes

16 Bounda condiions and D banes

17 Bounda condiions and D banes

18 The classical acion The classical poin paicle L( ) m V ( ) ; ( ) d( ) d f S[ ] m i V ( ) d δs ( m V ( ) ) f δ d i m V ( )

19 The classical acion The classical sing ( ) d T L a ) ( ( ) f i f i a T d d d L S ) ( + + a T T d d S f i δ δ δ δ δ

20 The classical acion The classical sing ( ), T L L P T L P

21 The classical acion The classical sing + + a T T d d S f i δ δ δ δ δ [ ] + a d d S f i δ δ δ P P

22 The classical acion The classical sing P P + he wave equaion!!

23 The elaivisic acion The elaivisic poin paicle ( ) ( ) ( 3 ds c d + d + d + d ) ds c d - S mc ds mc P f S d - i v c c v So, L mc v c

24 The elaivisic acion The elaivisic poin paicle ds η ν d d ν d d ( d ) S mc i f d η ν d d d d d d d d ν d d S mc d d d d ν f d η i ν

25 The elaivisic acion The elaivisic sing ef: Zwiebach, p..

26 The elaivisic acion The elaivisic sing ( ) ( ) ( ) ( ) ( ) 3,,,,,,, d dv d dv ef: Zwiebach, p..

27 The elaivisic acion The elaivisic sing da dv dv sin dv θ dv cos θ dv dv dv dv cos θ da ( dv dv )( dv dv ) ( dv ) dv

28 The elaivisic acion The elaivisic sing d d da d d A

29 The elaivisic acion The elaivisic sing ( d ),,..., (,σ ) ( ( ) ( ) ( )), σ,, σ,..., d, σ

30 The elaivisic acion The elaivisic sing σ σ σ σ d d A σ σ σ d d A

31 The elaivisic acion The elaivisic sing Nambu Goo sing acion S T c σ ( ) ( ) ( ) d dσ i f

32 The elaivisic acion The elaivisic sing ( ) ( ) ( ) ( ) ( ), c T L ( ) ( ) ( ) ( ) ( ) c T L P ( ) ( ) ( ) ( ) ( ) ' c T σ L P

33 The elaivisic acion The elaivisic sing δs + σ P P σ T c π α l s α

34 The elaivisic acion The elaivisic sing ( ) ( ) ( ) ( ) ( ), c T L ( ) ( ) ( ) ( ) ( ) c T L P ( ) ( ) ( ) ( ) ( ) ' c T σ L P

35 The elaivisic acion The elaivisic sing δs + σ P P σ T c π α l s α

36 Effecive paameeizaion: The ligh cone gauge π β ( n p) σ dσ n σ ~ P n (, σ ) βα ( n p) (, ~ σ ) : σ gauge : gauge +

37 Effecive paameeizaion: The ligh cone gauge P πα P σ π α ' P P + σ σ ''

38 Solving he wave equaion ( ) ( ) ( ) ( ) σ σ σ + + g f, + cos ), ( n in n n e n i σ α α α α σ α α p n a n n α

39 Becoming paicles M α n na I* a I n n

40 Closed sings and open sings Closed sings Gavions Open sings Ohe bosons

41 Acknowledgemens Thank You: D. Melanie Becke D. She Yennello La Ma Sean Downes

42 Acknowledgemens

43 Bibliogaph Zwiebach. A Fis Couse in Sing Theo. Cambidge Univesi Pess, 4. Zwiebach. A Fis Couse in Sing Theo. nd Ediion. Cambidge Univesi Pess, 9. Becke, Becke, and Schwaz. Sing Theo and M-heo: A Moden Inoducion. Cambidge Univesi Pess, 7. McMahon, David. Sing Theo Demsified. McGaw-Hill, 9. Ka, David. Schaum s Oulines: Tenso Calculus. McGaw- Hill, 988.

45 The elaivisic acion The elaivisic poin paicle S d δ f δ ( ) i dp d δs dp d dp d d d d ν d ν ( p ) ( η p ) η ( p ) d ν ν d d ds d p mc ds

MATHEMATICAL FOUNDATIONS FOR APPROXIMATING PARTICLE BEHAVIOUR AT RADIUS OF THE PLANCK LENGTH

Fundamenal Jounal of Mahemaical Phsics Vol 3 Issue 013 Pages 55-6 Published online a hp://wwwfdincom/ MATHEMATICAL FOUNDATIONS FOR APPROXIMATING PARTICLE BEHAVIOUR AT RADIUS OF THE PLANCK LENGTH Univesias