Symmetry in Particle PhysicsSymmetry in Particle Physics

By: Hossain EKhlas and Frank RuskowskiBy: Hossain EKhlas and Frank Ruskowski

What is Symmetry?What is Symmetry?

The word symmetry comes from the Greek word The word symmetry comes from the Greek word summet ronsummet ron, meaning well , meaning well proportioned , well ordered.proportioned , well ordered.

A relationship of characteristic correspondence, equivalence, or identity A relationship of characteristic correspondence, equivalence, or identity among constituents of an entity or between different entities. among constituents of an entity or between different entities.

People often equate symmetry with beautyPeople often equate symmetry with beauty..

Types of SymmetryTypes of Symmetry

There are many types of symmetry and not all of them have to do with the There are many types of symmetry and not all of them have to do with the shape of an object.shape of an object.

Some examples of symmetries that exist are: local, global, space-time, Some examples of symmetries that exist are: local, global, space-time, discrete, super, guage,charge, parity and time symmetries. discrete, super, guage,charge, parity and time symmetries.

Global and Local SymmetryGlobal and Local Symmetry Symmetries may be broadly classified as global and local. A Symmetries may be broadly classified as global and local. A global global

symmetrysymmetry is one that holds at all points of spacetime, whereas a is one that holds at all points of spacetime, whereas a local local symmetrysymmetry is one that only holds on a certain subset of the whole spacetime. is one that only holds on a certain subset of the whole spacetime. Local symmetries tend to play an important role in physics, as Local symmetries tend to play an important role in physics, as measurements are performed in a limited region of space (or spacetime).measurements are performed in a limited region of space (or spacetime).

Spacetime SymmetrySpacetime Symmetry Spacetime symmetriesSpacetime symmetries are those continuous symmetries that involve are those continuous symmetries that involve

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

Discrete Symmetries Discrete Symmetries A A discrete symmetrydiscrete symmetry is a symmetry that describes non-continuous is a symmetry that describes non-continuous

changes in a system. For example, a square possesses discrete symmetry, changes in a system. For example, a square possesses discrete symmetry, as only rotations by integral multiples of 90 degrees will preserve the as only rotations by integral multiples of 90 degrees will preserve the square's original outlook. Discrete symmetries often involve some type of square's original outlook. Discrete symmetries often involve some type of 'swapping', these swaps usually being called 'swapping', these swaps usually being called reflectionsreflections or or interchangesinterchanges

Super Symmetry Super Symmetry Extensions of symmetry to the concept of supersymmetry have been used Extensions of symmetry to the concept of supersymmetry have been used

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

Gauge SymmetryGauge Symmetry What about electric charge? The answer comes from a simple observation What about electric charge? The answer comes from a simple observation

about electric voltage. It is possible to define an electrostatic potential at any 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 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 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 of the electrostatic potential. It is only possible to measure its difference between two different points. In the language of symmetry we would say 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 that the laws of electrostatics are invariant under the addition of a value to the potential which is the same everywhere. the potential which is the same everywhere.

Charge, Parity and Time SymmetryCharge, Parity and Time Symmetry

Charge symmetry states that every particle is replaced with its antiparticle Charge symmetry states that every particle is replaced with its antiparticle Parity symmetry states that the universe is reflected as in a mirror.Parity symmetry states that the universe is reflected as in a mirror. Time Symmetry states that the direction of time is reversed.Time Symmetry states that the direction of time is reversed. Each of these symmetries is broken, but the Standard Model predicts that the 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 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 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 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 as being necessary for the presence of significant amounts of matter in the universe and thus the existence of life.and thus the existence of life.

Why is this ImportantWhy is this Important Symmetry is important in physics because there are all kinds of Symmetry is important in physics because there are all kinds of

transformations which leave the laws of physics invariant. For example, we 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 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 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 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 physics are invariant under a translation transformation. The infinite dimensional group of translation transformations is a symmetry of the laws dimensional group of translation transformations is a symmetry of the laws of physics.of physics.

It is difficult to overstate the importance of symmetry in physical laws. Some It is difficult to overstate the importance of symmetry in physical laws. Some important theories such as Maxwell’s laws of electrodynamics and Einstein’s important theories such as Maxwell’s laws of electrodynamics and Einstein’s theory of relativity, are deeply rooted in symmetry.theory of relativity, are deeply rooted in symmetry.

ImportanceImportance Symmetry and symmetry breaking help to determine how the universe goes Symmetry and symmetry breaking help to determine how the universe goes

from an undifferentiated point to the complex structure we now see.from an undifferentiated point to the complex structure we now see.

The Higgs mechanism is intimately connected with symmetry, and in The Higgs mechanism is intimately connected with symmetry, and in particular with broken symmetry. Understanding how the elementary particular with broken symmetry. Understanding how the elementary particles acquire mass requires some familiarity with these important ideas.particles acquire mass requires some familiarity with these important ideas.

The EndThe End

Works citedWorks cited

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http://www.karlin.mff.cuni.cz/~motl/Gibbs/symmetry.htmhttp://www.karlin.mff.cuni.cz/~motl/Gibbs/symmetry.htm

http://en.wikipedia.org/wiki/Symmetry_in_physicshttp://en.wikipedia.org/wiki/Symmetry_in_physics

http://www.yahoo.com.htmlhttp://www.yahoo.com.html