Symmetry in Particle Physics

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Symmetry in Particle Physics

• By Hossain EKhlas and Frank Ruskowski

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What is Symmetry?

• The word symmetry comes from the Greek word
  summet ron, meaning well proportioned , well
  ordered.
• A relationship of characteristic correspondence,
  equivalence, or identity among constituents of an
  entity or between different entities.
• People often equate symmetry with beauty.

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Types of Symmetry

• There are many types of symmetry and not all of
  them have to do with the shape of an object.
• Some examples of symmetries that exist are
  local, global, space-time, discrete, super,
  guage,charge, parity and time symmetries.

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Global and Local Symmetry

• Symmetries may be broadly classified as global
  and local. A global symmetry is one that holds at
  all points of spacetime, whereas a local symmetry
  is one that only holds on a certain subset of the
  whole spacetime. Local symmetries tend to play an
  important role in physics, as measurements are
  performed in a limited region of space (or
  spacetime).

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Spacetime Symmetry

• Spacetime symmetries are those continuous
  symmetries that involve transformations of space
  and time. These may be further divided into 3
  categories. Many symmetries in physics are
  described by continuous changes of the spatial
  geometry associated with a physical system ('
  spatial symmetries '), others only involve
  continuous changes in time (' temporal symmetries
  ') or continuous changes in both space and time
  (' spatio-temporal symmetries ').

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Discrete Symmetries

• A discrete symmetry is a symmetry that describes
  non-continuous changes in a system. For example,
  a square possesses discrete symmetry, as only
  rotations by integral multiples of 90 degrees
  will preserve the square's original outlook.
  Discrete symmetries often involve some type of
  'swapping', these swaps usually being called
  reflections or interchanges
• 
  

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Super Symmetry

• Extensions of symmetry to the concept of
  supersymmetry have been used to try to make
  theoretical advances in the standard model.
  Roughly speaking, supersymmetry is based on the
  idea that there is one remaining physical
  symmetry beyond those that are well-understood, a
  symmetry between bosons and fermions, so that
  each boson would have a symmetry partner fermion,
  called a superpartner, and vice versa. There are
  significant unsolved problems with the theory of
  supersymmetry, including that no known particle
  has the correct properties to be a superpartner
  of any other known particle, so that if
  superpartners exist, they apparently all must
  have greater mass than existing particle
  accelerators have been capable of generating.

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Gauge Symmetry

• What about electric charge? The answer comes from
  a simple observation about electric voltage. It
  is possible to define an electrostatic potential
  at any point in space. The voltage of a battery
  is the difference in this potential between its
  terminals. In fact there is no way to measure the
  absolute value of the electrostatic potential. It
  is only possible to measure its difference
  between two different points. In the language of
  symmetry we would say that the laws of
  electrostatics are invariant under the addition
  of a value to the potential which is the same
  everywhere.

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Charge, Parity and Time Symmetry

• Charge symmetry states that every particle is
  replaced with its antiparticle
• Parity symmetry states that the universe is
  reflected as in a mirror.
• Time Symmetry states that the direction of time
  is reversed.
• Each of these symmetries is broken, but the
  Standard Model predicts that the combination of
  the three (that is, the three transformations at
  the same time) must be a symmetry, known as CPT
  symmetry. CP violation, the violation of the
  combination of C and P symmetry, is a currently
  fruitful area of particle physics research, as
  well as being necessary for the presence of
  significant amounts of matter in the universe and
  thus the existence of life.
• 
  

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Why is this Important

• Symmetry is important in physics because there
  are all kinds of transformations which leave the
  laws of physics invariant. For example, we know
  that the laws of physics are the same everywhere.
  I.e. we can detect no difference in the results
  of any self contained experiment which depends on
  where we do it. Another way to say the same thing
  is that the laws of physics are invariant under a
  translation transformation. The infinite
  dimensional group of translation transformations
  is a symmetry of the laws of physics.
• It is difficult to overstate the importance of
  symmetry in physical laws. Some important
  theories such as Maxwells laws of
  electrodynamics and Einsteins theory of
  relativity, are deeply rooted in symmetry.

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Importance

• Symmetry and symmetry breaking help to determine
  how the universe goes from an undifferentiated
  point to the complex structure we now see.
• The Higgs mechanism is intimately connected with
  symmetry, and in particular with broken symmetry.
  Understanding how the elementary particles
  acquire mass requires some familiarity with these
  important ideas.

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The End

• Works cited
• http//www.springerlink.com/content/d1yaxjbduv7wyt
  ku/fulltext.pdf
• http//www.karlin.mff.cuni.cz/motl/Gibbs/symmetry
  .htm
• http//en.wikipedia.org/wiki/Symmetry_in_physics
• http//www.yahoo.com.html