The Ideas of Unified Theories of Physics Tareq Ahmed Mokhiemer PHYS441 Student
Why do we need a single unified theory What’s missing in the standard model? Prescriptions of a unified theory Gauge theories Electroweak theory Grand unified theory Klein Kaluza theory Conclusion
Why Do we need a single theory? “Everyone’s goal is a theory of everything, an economic, simple theory that works at all energies, at all scales, for all time.”
Why Do we need a single theory? Because there is only One God All the laws should be part of a single pattern. A single theory is more beautiful than many theories The the early phases of the universe, only one force is thought to have been effective.
What’s missing in the standard model? “Deep inside the Standard Model, physicists think, something is wrong. There must be a larger, more elegant theory, a theory of everything.”
Why four forces? Charge is quantized while mass is not! Why is the electron’s charge equal to the proton’s charge? What about gravity? Electroweak is not unified with the strong force !! Why so many constants ? Where is the Higg’s Boson? What’s missing in the standard model?
Prescriptions for a unified theory A gauge theory that represents a great and natural symmetry of the universe. Breaks down under spontaneous symmetry breaking into different sub- symmetries. Unification means that at a GUT scale, where masses can be ignored, all fundamental particles appear in the same multiplet.
What’s meant by a gauge theory? A theory described by a Lagrangian having local symmetry properties (Invariant under local transformations) Associated with each gauge symmetry is a conserved quantity and a gauge field [The symmetry is an internal symmetry in most gauge theories] Example: Electromagnetism
trouble: Schroedinger equation [physics] depends on local phase
covariant derivative Maxwell’s electromagnetic field appears due to the gauge invariance principle the x-component of the “gauge field” A
Three distinct gauge theories Electroweak gauge theory Color gauge theory General relativity gauge theory ?
General Relativity as a Gauge Theory Require the laws of physics to be invariant under local Poincare transformations (shifting each space- time point by an arbitrary amount) Introduce the gravitational field to “ straighten out ” distortions
Why incorporating gravity in SM is difficult? Gravity is associated with a dynamical symmetry group ( symmetry of the spacetime), other gauge theories are built on internal symmetries. Gravity is very weak compared to the three other forces No acceptable quantum theory of gravtiy
Electroweak theory SU(3) * U(1) symmetry group that breaks down at energies lower than (80 GeV) to electromagnetic and weak forces. Symmetry breaking is provided through the (persumed) Higgs field
Spontaneous Symmetry Breaking The laws of physics are symmetric but the state of the system is not. [ Symmetry is hidden, not broken.] Classical Example: Equations of motion are not symmetric in horizontal and vertical directions by the background gravitational filed
Consequences of SSB Iso-spin symmetry breaking in the masses between members of the same iso-spin multiplet. In Electroweak theory: Mw,Mz >>0 Massive gauge quanta are possible when gauge symmetry is broken!
Superconducting analogy The alignment of the phases creates an ordered rigid structures giving rise to rejection of the electro- magnetic field (Meissner effect). The photons become massive What mechanism causes the phase alignment in the SU(2)xU(1) internal space???
Higgs Field and symmetry breaking Space is supposed to be filled by a hypothetical background field permuting all the space. Particles acquire momentum (mass) by interacting with this field. [The distortion - the clustering of the field around the particle - generates the particle's mass.] Particles that interact strongly with the Higgs field are heavy, while those that interact weakly are light.
Grand Unified theory (GUT) An intermediate step towards a single unified theory Combines Electroweak with strong force Six leptons related to six quarks Its Lagrangian should be symmetric under a symmetry group that contains SU(2) * U(1), SU(3) as subgroups A possible candidate: SU(5)
SU(5) – Georgi-Glashow Theorem Incorporates the known fermions into multiplets (leptons and quarks). Quark and leptons can transform to each other through X,Y bosons. Baryon number not conserved (e.g proton decay)
Proton Decay ugug ubub drdr e+e+ drdr anti-d anti-r P X anti-r
Kaluza-Klein theory Added one extra spatial dimension to our conventional space-time. Introduced 5-D metric tensor, which can be decomposed into two parts
Conclusion Physicists are trying to find a single theory that explains the whole universe. My belief is that there will always be some gaps. The part of the universe that we can percieve is very small compared to the part we can not. Cosmological observations (e.g, dark matter, dark energy, … ) indicate that we are still crawling under the mountain of a single unified theory