The unifying framework of symmetry reveals properties of a broad range of physical systems

Aug 29, 2014
Figure 1: Snowflakes are an example of the multiple geometric symmetries that arise in nature. Credit: aguirre_mar/iStock/Thinkstock

Symmetry is one of the most fundamental concepts in nature, and it can give rise to profound and wide-reaching physical effects. A one-dimensional wire, for example, has a different symmetry and very different mechanical properties to those of a two-dimensional sheet of the same material. Tomoya Hayata and Yoshimasa Hidaka from the RIKEN Nishina Center for Accelerator-Based Science have now studied the consequences of breaking symmetry for various systems found in nature, providing a powerful, general framework to describe the link between properties and symmetries.

Crystalline materials consist of a periodic arrangement of atoms with a certain , and as such can have a number of symmetries within each crystallographic unit. Deforming a crystal by bending elastically displaces atoms from their original crystallographic positions, breaking the through translational movement. Bending requires the application of a force, which scientists usually describe in terms of the strengths of the atomic bonds that need to be overcome for the atoms to move.

To stretch a crystal, on the other hand, requires application of a force that is determined by the length to which the crystal is stretched. Mathematically, the relationship between force and stretch is determined by a parameter of elasticity. Atomically, stretching causes atoms to undergo elastic vibrations known as Nambu–Goldstone modes. Such properties are very general, applying not only to crystals, but also to phenomena in magnetism and particle physics. Despite this broad relevance, however, "The relationships between broken symmetries, elastic variables, and Nambu–Goldstone modes have not been well understood," notes Hidaka.

The researchers tackled this problem by studying the relationship between broken symmetries and the parameters of elasticity describing such processes. They also established counting rules for the broken symmetries and the number of elastic variables needed to describe the properties of the system. The mathematical framework developed by Hayata and Hidaka is very general; they showed that it is applicable to a broad variety of systems, including molecules and crystals as well as subatomic particles and forces.

The study highlights the power of symmetry in nature and how symmetry can provide a unifying language across many natural systems. Future research by Hayata and Hidaka will focus specifically on Nambu–Goldstone modes, which in addition to symmetry and elastic variables, determine many system properties. "The next step is to clarify the relation between the elastic variables and Nambu–Goldstone modes," says Hidaka.

Explore further: A study of possible extended symmetries of field theoretic systems

More information: Hayata, T. & Hidaka, Y. "Broken spacetime symmetries and elastic variables." Physics Letters B 735, 195–199 (2014). DOI: 10.1016/j.physletb.2014.06.039

add to favorites email to friend print save as pdf

Related Stories

Theorem unifies superfluids and other weird materials

Jun 11, 2012

(Phys.org) -- Matter exhibits weird properties at very cold temperatures. Take superfluids, for example: discovered in 1937, they can flow without resistance forever, spookily climbing the walls of a container ...

Magic and symmetry in mathematics

Mar 12, 2014

We live in a three-dimensional world. Despite the many benefits this presents, it also makes for a complicated math problem, according to Northeastern associate professor of mathematics Ivan Loseu. The best ...

Breaking nature's superfluid symmetry

Sep 06, 2013

Superfluids are an exotic state of matter in which particles flow without experiencing viscosity. Hiroki Ikegami and colleagues from the RIKEN Low Temperature Physics Laboratory in Wako have now observed ...

Recommended for you

Tiny magnetic sensor deemed attractive

22 hours ago

Ultra-sensitive magnetic sensor technology pioneered at PML may soon be commercialized for a host of applications from detection of unexploded bombs and underground pipes to geophysical surveying and perhaps ...

Beams come knocking on the LHC's door

22 hours ago

Over the weekend, proton beams came knocking on the Large Hadron Collider's (LHC) door. Shooting from the Super Proton Synchrotron (SPS) and into the two LHC injection lines, the proton beams were stopped ...

User comments : 1

Adjust slider to filter visible comments by rank

Display comments: newest first

AmritSorli
1 / 5 (2) Sep 01, 2014
the real symmetry in the universe is between particles and quantum vacuum. Every particle has its own area of diminshed energy density of quantum vacuum which is origin of relativistic, inertial and gravitational mass

http://article.sc...3.11.pdf

http://article.sc...6.25.pdf

Please sign in to add a comment. Registration is free, and takes less than a minute. Read more

Click here to reset your password.
Sign in to get notified via email when new comments are made.