Symmetry (physics)

Under a symmetry (from the ancient Greek. Σύν syn "together", μέτρον métron " measure " ) is understood in physics, the properties of a system, after a certain change ( transformation, particularly coordinate transformations ) to remain unchanged ( to be invariant ). If a transform does not change the state of a physical system, these transformations symmetry or symmetry transformations are called operations. A distinction is made discrete symmetries ( eg mirror symmetry), which have only a finite number of symmetry operations, as well as continuous symmetry ( rotational symmetry, for example ) that have an infinite number of symmetry operations.

The mathematical description of symmetries made ​​by the group theory.

Classification

Symmetries play an important role in modern physics research. If a symmetry observed in an experiment, so must the corresponding theory, which is represented by a Lagrangian or an " action functional ", be invariant under a corresponding symmetry operation. In the frequently used in particle physics gauge theories, ie theories that are invariant under a gauge transformation, this symmetry sets largely determined the nature and relative strength of the couplings between the particles.

• Knowledge about symmetries often proved to be the starting point for completely new theories. Thus, the invariance of Maxwell's equations was under Lorentz transformations a starting point for Albert Einstein to develop special relativity, and some patterns in the spectrum of elementary particles led to the development of the quark model for atomic nuclei (eg for the proton ).

• Symmetries are closely linked to conservation laws:

The so-called Noether 's theorem says for example that every continuous symmetry of a conserved quantity can be assigned. Thus, for example, follows from the Zeittranslationsinvarianz the energy conservation of the system; in the Hamiltonian mechanics converse is also true. Thus, the associated balance Zeittranslationsinvarianz is considered for a system with energy conservation.

• Important are not only the symmetries themselves, but also symmetry breaking:

Thus, in the theory of electroweak interactions, the gauge symmetry is broken by the Higgs mechanism, for which the only not been proven particles of the Standard Model of elementary particle physics, the Higgs boson, is needed. Also symmetry breaking processes may be associated with phase transitions, similar to the ferromagnetic phase transition.

Survey

The following table provides an overview of important symmetries and their conserved quantities. They are divided into continuous and discrete symmetries.

Transformations

Transformations or symmetry operations themselves can be continuous or discrete, such as the symmetries. An example of a continuous transformation, the rotation of a circle about an arbitrary angle. Examples of the discrete transform is the reflection of a two-sided symmetrical figure, the rotation of a regular polygon or the displacements to integral multiples of the lattice spacing. Determine the feasible transformations to which type of symmetry is. While discrete symmetries by symmetry groups (such as point groups and space groups ) are described, used to describe continuous symmetries Lie groups.

Transformations which do not depend on the place called global transformations. Can the transformation parameters (apart from continuity conditions ) at any place be chosen freely, it is called local transformations or gauge transformations. Physical theories whose action is invariant under gauge transformations are called gauge theories. All fundamental interactions, gravity, electromagnetic, weak and strong interactions are described by gauge theories, according to current knowledge.

Symmetry breaking

Thermodynamics is not time-invariant, since "reverse heat flow " ( from cold to hot) do not exist and the increase of entropy characterizes the direction of time:

The weak interaction is not invariant under space reflection analog, as was shown in 1956 in the Wu experiment. The behavior of K- mesons and B- mesons is not invariant under simultaneous reflection and charge exchange. Without this CP violation in the Big Bang equal amounts of matter would be created as antimatter and now still exist to the same extent. Only through the CP- symmetry breaking ie, the baryon asymmetry, which is today's preponderance of matter are explained.

In the transition from classical to quantum theories additional symmetry breaking can take place. Examples are the Higgs mechanism as a dynamic symmetry breaking and the chiral anomaly.

An example from chemistry are mirror image, which not only look the same (except for the reflection ) but also same energy levels and transition states. From a prochiral molecule they occur with equal probability and reaction kinetics. By autocatalytic reaction mechanisms, ie at the latest with the origin of life, but the mirror image symmetry see chirality (chemistry) is spontaneously broken, # biochemistry.

Symmetric potential

An important example of a symmetry is a spherically symmetrical or rotationally symmetrical potential as the electric potential of a point charge (for example, an electron) or the gravitational potential of a compound ( such as a star). The potential is only on the distance to the charge or the mass -dependent, but not from the angle to a selected axis. So it does not matter which reference system is chosen to describe as long as charge or mass located at the origin. As a result, the symmetry is valid for a particle in a spherically symmetric potential, the conservation of angular momentum. Because of the lack of translational symmetry of the momentum of the particle is not a conserved quantity in this example.

Postgraduate

• Louis Michel: Symmetry defects and broken symmetry. Configurations Hidden Symmetry. In: Reviews of Modern Physics. 52, 1980, pp. 617-651, doi: 10.1103/RevModPhys.52.617.
• Werner Hahn: Symmetry as a development principle in nature and art. With a foreword by Rupert Riedl. Königstein i Ts ( Langewiesche Verlag ) 1989
• Mouchet, A. " Reflections on the four facets of symmetry: how physics exemplifies rational thinking". European Physical Journal H 38 (2013 ) 661
• Symmetry and Symmetry Breaking. Listing In: Edward N. Zalta (ed.) Stanford Encyclopedia of PhilosophyVorlage SEP / Maintenance / Parameter 1 and Parameter 2 not yet Parameter 3

References and Notes

• Symmetry (Physics)