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A Confrontation with

A Confrontation with. infinity. Gerard ’t Hooft, Nobel Lecture 1999. What does Renormalizability Mean ???. Understanding Small Distance Behavior !!. The Differential Equation. Discretized Space and Time. Continuous space and Time. -. +. Bare

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A Confrontation with

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  1. A Confrontation with infinity Gerard ’t Hooft, Nobel Lecture 1999

  2. What does RenormalizabilityMean ??? Understanding Small Distance Behavior !!

  3. The Differential Equation

  4. Discretized Space and Time Continuous space and Time

  5. - + Bare Mass Bare Charge + - Mass and Charge Renormalization Observed Charge Observed Mass

  6. - + Bare Charge Observed Charge Bare Mass Observed Mass Keeping the Observed Properties Fixed

  7. All problems with renormalizing infinities can be resolved by considering The Small Distance Limit of our theory(ies)

  8. The scale transformation when particles are quantized ... g g´

  9. Scaling and Dimensions

  10. Negative screening: Yang-Mills gauge theory

  11. Chiral theories: These are theories in which a field has a fixed length: Field strength

  12. Compare large distance with small distance: The quantum fluctuations at small distance in such a theory undermine its own structure. Its small-distance behaviour is ILL-DEFINED At small distances, strong curvature  strong interactions At large distance scales, the curvature is weak  near linearity = weak interactions

  13. Some theories have BAD short distance behaviour:

  14. Spontaneous symmetry breaking ( left - right symmetry ) At large distance scales, the situation is as described here At short distance scales, our particle theory looks like this This degree of freedom corresponds to the Higgs particle

  15. Breaking Rotational Symmetry Now THIS becomes an essential degree of freedom And THIS is the Higgs degree of Freedom

  16. If there were no HIGGS particle in our theory, then the “Mexican Hat” would be infinitely steep, or: This is exactly like the situation in a “chiral field theory”: Such a theory is ill-defined, since its small-distance structure runs out of control...

  17. How does force depend on distance ? Force Weak: Electro-magnetic: Strong EM Weak Strong: x 0

  18. L Higgs Graviton The Standard Model Generation I Generation II Generation III R R R Leptons L L L L L Quarks R R R g Gauge Bosons

  19. CERNSpS&LEP * *

  20. Linear Accelerator Fermilab linear booster

  21. A symmetric object can be slightly out of equilibrium …

  22. An asymmetric equilibrium is unnatural ...

  23. * * * * * * * * * * * * * * * Running Coupling Strengths 1 0.5

  24. * * * * * * * * * * * * * * * Super symmetric theories 1 0.5

  25. Super String Theory Are strings continuous or are they discrete at tiny distance scales ?

  26. A theory can only be successful if we understand completely how its dynamical variables behave at the tiniest possible time- and distance scales Otherwise, it is likely to explode ….

  27. With thanks to:M. Veltman (teaching)C.T. de Laat (animation)my wife and the rest of my family (support)many other physicistsand the Royal SwedishAcademy of Sciences Otherwise, it is likely to explode ….

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