1 / 20

The 26 dimensions of string theory

Delve into the intricate world of string theory, a comprehensive theory that unifies quantum mechanics and gravity. Discover why string theory postulates 26 dimensions, merging general relativity, special relativity, particle physics, and more. Explore the profound implications of quantum gravity, gauge symmetries, and anomalies in this all-encompassing theory. Join us in deciphering the mysteries of the cosmos through the lens of string theory.

michelel
Download Presentation

The 26 dimensions of string theory

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. The 26 dimensions of string theory • Why string theory? • What is string theory? • Why 26 dimensions?

  2. General relativity Special relativity Newtonian mechanics Statistical mechanics Particle physics Non linear dynamics Solid state physics Biology A theory of everything Quantum Gravity ? Quantum mechanics

  3. Quantum particle Quantization Classical particle:  p(t), x(t)  <P(t)>, <X(t)>

  4. <j(X,t)> For a point source at origin For a constant electric field Quantization of fields  <P(t)>, <X(t)> Maxwell equations: <r> j

  5. m0c2 <j(X,t)> + E = e- a m0c2 = + mrc2 = Quantum Electro Dynamics The self energy problem.

  6. <G> Quantum gravity G = T G <T> Self energy problem

  7. Free particles t0 t

  8. Symmetries Galilean group Boosts: Rotations: X → X - Vt X → Cos(q)X + Sin(q)Y K1,K2,K3 [Ki,Kj]=0 R1,R2,R3 [Ri,Rj]=eijkRk Translations: X → X + a [Pi,Pj]=0 P1,P2,P3

  9. Relativistic particle l0 l x Xm(l) y t

  10. Symmetries Poincare group +Diffeomorphism Boosts: Rotations: X → g(X – Vt) X → Cos(q)X + Sin(q)Y K1,K2,K3 [Ki,Kj]= eijkKk R1,R2,R3 [Ri,Rj]=eijkRk Diffeomorphism: Translations: l → f(l) X → X + a [Pi,Pj]=0 P1,P2,P3

  11. t s Free string Free string: Free particle: Xm(t,s0) Xm(t0,s) Xm(t0,s0) t y x

  12. Symmetries Poincare group +Diffeomorphism +Weyl Rotations Translations Boosts Diffeomorphism Weyl

  13. Quantum String (light cone gauge)  Xm(s,t) <Xm(s,t)>   <E> E  J <J>

  14. M2 a†1|0> = 0 S2 a†1|0> = 0 String theory Tachyon Tachyon Photon Graviton Massive particle a†2|0> or a†1a†1|0> M2 a†2|0> = 1 a†1|0> |0> M2 |0> = -1 b†1|0> M2 b†1|0> = 0 S2 b†1|0> = 2

  15. Quantum String (light cone gauge) [Pi,Pj]=0  [Ji,H]=0  [Ki,Kj]=ifijkJk  [Pi,H]=0 [Ki,Pj]=-iHdij [Ji,Jj]=ifijkJk  [Ji,Kj]=ifijkKk [Ji,Pj]=ifijkPk  [Ki,H]=-iPi [H,H]=0 

  16. Gauge symmetries Maxwell equations Gauge symmetries Gauge fixing (Lorentz gauge) (Coulomb gauge) String equations Gauge fixing X0+X1=t (Light cone gauge)

  17. S→S’ = S Dx(t)→Dx(t)’ = Dx(t) Anomalies Feynmans approach: ~ħ t=tf t=t0 ?

  18. String theory • String theory is a consistent theory of gravitons. • The dimension of space time is fixed by a quantum anomaly. D=26

  19. Possibilities • String theory is incorrect. • 26 (10) dimensions • ???

  20. Fin

More Related