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Thursday, December 22, 2011

Symmetries and conservation Laws: Part 1

  • Every conservation principle corresponds to symmetry in nature
  • A symmetry of a particular kind exists when a certain operation leaves something unchanged.
  • There is an intimate connection between symmetry and so called conserved quantities.
  • Well known conserved quantity is energy and corresponding symmetry in this case is time translation.
Momentum Conservation
  • Holds for all type of interactions
  • Related to the invariance of physical laws under translation in space.
  • Thus laws of interaction do not depend on the place of measurement so the space is homogeneous.
  • This transnational uniformity of space leads to the conservation of linear momentum.
  • Particle at rest have no momentum. If it  decays into two less massive particles , momentum conservation requires that the two particles travel away in exactly opposite directions.
Conservation of Energy
  • Holds for all type of interactions.
  • related to the invariance of physical laws under translations along the time axis i.e., homogeneity of time.
  • laws of interaction do not depend on the time of measurement
Angular momentum conservation
  • In addition to transnational symmetry , space also has a rotational symmetry.
  • This symmetry of space gives rise to another conserved quantity , angular momentum.
  • This law is also of general validity for all types of interactions.
  • It is related to the invariance of the physical laws under rotation (isotropy of space).
  • The orbital and spin angular momentum may be separately conserved.
Parity Conservation
  • Holds for strong, nuclear and electromagnetic interactions but is violated in case of week interactions.
  • related to the invariance of the physical laws under inversion of space co-ordinates. x,y,z are replaced by -x.-y,-z.
  • is equivalent to combined reflection and rotation.
  • physical laws do not depend on the right handedness of co-ordinate system.
  • Parity operation symmetry represents discrete symmetry (reflection and rotation through 180 degree)
  • Every particle with non zero mass has an intrinsic parity  π which can either be +1(even) or -1 (odd). Thus total parity of a system of n particles is the product of their intrinsic parities and the orbital parity (-1)l.
  • Thus, πtot1π2π3.......πn(-1)l
  • Intrinsic parity of pions is odd.
Conservation of charge

  • Conservation of electric charge is related to gauge transformations which are shifts in the zeros of the scalar and vector electromagnetic potentials V and A
  • Gauge transformations leave E and B unaffected since the latter are obtained by differentiating potentials , and this invariance leads to charge conservation.
  • Charge and baryon number are conserved in all interactions.

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