Download presentation

Presentation is loading. Please wait.

Published byHaley Rooke Modified over 2 years ago

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

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

3
Quantization p(t), x(t) Classical particle:, Quantum particle

4
Quantization of fields, For a point source at origin For a constant electric field Maxwell equations: <><>

5
Quantum Electro Dynamics The self energy problem. e-e- + m0c2m0c2 E = m0c2m0c2 + = mrc2mrc2 = a

6
Quantum gravity G = T G

7
Free particles t0t0 t

8
Symmetries Rotations: X → Cos )X + Sin( Y R 1, R 2,R 3 [R i,R j ]= ijk R k Translations: X → X + a P 1,P 2,P 3 [P i,P j ]=0 Boosts: X → X - Vt K 1, K 2,K 3 [K i,K j ]= Galilean group

9
Relativistic particle x y t X ( )

10
Symmetries Rotations: X → Cos )X + Sin( Y R 1, R 2,R 3 [R i,R j ]= ijk R k Translations: X → X + a P 1,P 2,P 3 [P i,P j ]=0 Boosts: X → X – Vt) K 1, K 2,K 3 [K i,K j ]= ijk K k Poincare group Diffeomorphism: → f( ) +Diffeomorphism

11
Free string x y t X(,)X(,) X(,)X(,) X(,)X(,) Free particle: Free string:

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

13
Quantum String X(,)X(,) E J (light cone gauge)

14
String theory Tachyon Photon Massive particle Tachyon Graviton a † 1 |0>a † 2 |0> or a † 1 a † 1 |0> M 2 a † 2 |0> = 1 |0> M 2 |0> = -1 b † 1 |0> M 2 b † 1 |0> = 0 S 2 b † 1 |0> = 2 M 2 a † 1 |0> = 0 S 2 a † 1 |0> = 0

15
Quantum String (light cone gauge) [P i,P j ]=0 [J i,J j ]=i f ijk J k [J i,K j ]=if ijk K k [K i,K j ]=if ijk J k [J i,P j ]=if ijk P k [K i,P j ]=-iH ij [J i,H]=0 [P i,H]=0 [H,H]=0 [K i,H]=-i P i

16
Gauge symmetries Maxwell equations Gauge symmetries (Lorentz gauge) (Coulomb gauge) String equations (Light cone gauge) X 0 +X 1 = Gauge fixing

17
Anomalies Feynmans approach: t=t 0 t=t f ~ħ ? S→S’ = S Dx(t)→Dx(t)’ = Dx(t)

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

20
Fin

Similar presentations

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google