Sunday, July 11, 2010

A Way From Perfection- Symmetry

Noether's Theorem

"For every continuous symmetry of the law of physics, there must exist a conservation law.

For every conservation law, there must exist a continuous symmetry"

Conservation laws and symmetry

The symmetry properties of a physical system are intimately related to the conservation laws characterizing that system. Noether's theorem gives a precise description of this relation. The theorem states that each continuous symmetry of a physical system implies that some physical property of that system is conserved. Conversely, each conserved quantity has a corresponding symmetry. For example, the isometry of space gives rise to conservation of (linear) momentum, and isometry of time gives rise to conservation of energy.
The following table summarizes some fundamental symmetries and the associated conserved quantity.

Class Invariance Conserved quantity
Proper orthochronous
Lorentz symmetry
translation in time
  (homogeneity)
energy

translation in space
  (homogeneity)
linear momentum

rotation in space
  (isotropy)
angular momentum
Discrete symmetry P, coordinate inversion spatial parity

C, charge conjugation charge parity

T, time reversal time parity

CPT product of parities
Internal symmetry (independent of
spacetime coordinates)
U(1) gauge transformation electric charge

U(1) gauge transformation lepton generation number

U(1) gauge transformation hypercharge

U(1)Y gauge transformation weak hypercharge

U(2) [U(1)xSU(2)] electroweak force

SU(2) gauge transformation isospin

SU(2)L gauge transformation weak isospin

PxSU(2) G-parity

SU(3) "winding number" baryon number

SU(3) gauge transformation quark color

SU(3) (approximate) quark flavor

S((U2)xU(3))
[ U(1)xSU(2)xSU(3)]
Standard Model

 

Conservation law

From Wikipedia, the free encyclopedia

In physics, a conservation law states that a particular measurable property of an isolated physical system does not change as the system evolves.

One particularly important physical result concerning conservation laws is Noether's Theorem, which states that there is a one-to-one correspondence between conservation laws and differentiable symmetries of physical systems. For example, the conservation of energy follows from the time-invariance of physical systems, and the fact that physical systems behave the same regardless of how they are oriented in space gives rise to the conservation of angular momentum.

A partial listing of conservation laws that are said to be exact laws, or more precisely have never been shown to be violated:
There are also approximate conservation laws. These are approximately true in particular situations, such as low speeds, short time scales, or certain interactions.

See also

References

  • Victor J. Stenger, 2000. Timeless Reality: Symmetry, Simplicity, and Multiple Universes. Buffalo NY: Prometheus Books. Chpt. 12 is a gentle introduction to symmetry, invariance, and conservation laws.

External links

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