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Topic: Spontaneous symmetry breaking

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Asymmetry

Symmetry

Supersymmetry breaking

Fermion condensate

Chirality (mathematics)

Soft SUSY breaking

Supersymmetric

Relevant operator

Supersymmetry

Bilateral symmetry

Minimal Supersymmetric Standard Model

Supersymmetry breaking scale

Vacuum state

Standard Model

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	Unification of Forces
		The difference in masses is attributed to spontaneous symmetry breaking as the hot universe cooled.
		The concept of spontaneous symmetry breaking is important to the understanding of electroweak unification and further unifications.
		This is an apt analogy for the electroweak unification, since the symmetry between the Coulomb force and the weak interaction is certainly not evident at low temperatures.
	hyperphysics.phy-astr.gsu.edu /hbase/forces/unify.html (897 words)

	Symmetry and Symmetry Breaking (Stanford Encyclopedia of Philosophy)
		According to Curie, symmetry breaking has the following role: for the occurrence of a phenomenon in a medium, the original symmetry group of the medium must be lowered (broken, in today's terminology) to the symmetry group of the phenomenon (or to a subgroup of the phenomenon's symmetry group) by the action of some cause.
		Spontaneous symmetry breaking (SSB) occurs in a situation where, given a symmetry of the equations of motion, solutions exist which are not invariant under the action of this symmetry without any explicit asymmetric input (whence the attribute “spontaneous”).
		Symmetries may be used to explain (i) the form of the laws, and (ii) the occurrence (or non-occurrence) of certain events (this latter in a manner analogous to the way in which the laws explain why certain events occur and not others).
	plato.stanford.edu /entries/symmetry-breaking (9828 words)

	Universal Symmetry
		But the symmetry of the tetrahedron is not quite the same as that of a snowflake because the snowflake has a transformation which must be repeated six times to restore it to its original position and the tetrahedron does not.
		Symmetry is proving to be a powerful unifying tool in particle physics because through symmetry and symmetry breaking, particles which appear to be different in mass, charge etc. can be understood as different states of a single unified field theory.
		Gauge symmetry is a symmetry of the classical field which is preserved in the process of quantisation.
	www.weburbia.com /pg/symmetry.htm (4557 words)

	24 April 2007 - KEK: Spontaneous symmetry breaking in QCD reproduced on supercomputer
		Chiral symmetry is a symmetry distinguishing right-handed spinning quarks from their left-handed cousins.
		This symmetry is exact when the quarks can fly at the speed of light which is possible if they are massless.
		In 1961 Yoichiro Nambu and his collaborator proposed the idea of spontaneous chiral symmetry breaking, inspired by the BCS (Bardeen-Cooper-Schrieffer) mechanism of superconductivity.
	www.interactions.org /cms/?pid=1025133 (468 words)

	Spontaneous symmetry breaking
		Spontaneous symmetry breaking in physics takes place when a system that is symmetric with respect to some Lie group goes into a vacuum state that is not symmetric.
		In the Standard Model, spontaneous symmetry breaking is accomplished by using the Higgs boson and is responsible for the masses of the W and Z bosons.
		General relativity has a Lorentz gauge symmetry, but in FRW cosmological models, the mean 4-velocity field defined by averaging over the velocities of the galaxies (the galaxies act like gas particles at cosmological scales) acts as an order parameter breaking this Lorentz symmetry.
	www.mcfly.org /Spontaneous_symmetry_breaking (723 words)

	spontaneous symmetry breaking concept from the Astronomy knowledge base (Site not responding. Last check: )
		In the standard model of particle physics, the symmetry between electrons and neutrinos is spontaneously broken by the values that are randomly chosen by the Higgs fields.
		In grand unified theories, the symmetry between electrons, neutrinos, and quarks is spontaneously broken by the values chosen randomly by the Higgs fields.
		For example, the state of minimum energy for an iron magnet is that in which the atomic spins are all aligned in the same direction, giving rise to a net macroscopic magnetic field.
	www.csi.uottawa.ca:4321 /astronomy/spontaneoussymmetrybreaking.html (243 words)

	Hidden symmetries \| Cosmic Variance
		To physicists, a “symmetry” is a situation where you can rearrange things a bit (values of quantum fields, positions in space, any of the characteristics of some physical state) and get the same answer to any physical question you may want to ask.
		This idea of spontaneous symmetry breaking has a long history in physics —; it was elucidated in condensed matter physics by Philip Anderson (Nobel 1977) and others, and in particle physics by my colleague Yochiro Nambu and erstwhile colleague Jeffrey Goldstone (no Nobel yet, which is a shame).
		But other times you have gauge symmetries, which aren’t really symmetries at all — they are just situations in which it’s useful to introduce more fields than really exist, along with a symmetry between them, to make a more elegant description of the physics.
	cosmicvariance.com /2005/10/24/hidden-symmetries (2864 words)

	20th WCP: Ontological Levels and Symmetry Breaking
		The roots of symmetry principles are partly in ancient philosophical thinking, partly in ancient mathematics, when science and philosophy, arts and crafts, crafts and science had not yet been separated.
		Consequently, the precondition of the development (in its relative totality) of a qualitatively new (material) level is the breaking of a certain symmetry (property), and at the same time, the condition of the continuance (existence) of the new level is to possess (new?) conserved properties.
		The loss of the symmetry of the brain is also a typical example of the violation of a symmetry, which did not exist 'always', only since one can speak of 'brain' or 'neural system' as a quality, as an organ of living organisms (2c-d).
	www.bu.edu /wcp/Papers/Scie/ScieDarv.htm (4644 words)

	Symmetry Breaking in Software Patterns
		In general, a large symmetry of the simplified neoclassicist type rarely contributes to the life of a thing, because in any complex whole in the world, there are nearly always complex, asymmetrical forces at work--matters of location, and context, and function--which require that symmetry be broken.
		Symmetry slowly breaks as we descend the hierarchy.
		Patterns precipitate from symmetries in response to both internal and external forces that are the analogy of instability.
	users.rcn.com /jcoplien/Patterns/Symmetry/Springer/SpringerSymmetry.html (6001 words)

	Breaking Lorentz symmetry (March 2004) - Physics World - PhysicsWeb
		To a physicist such equality and fairness of physical laws is called a symmetry, and the symmetry that requires the laws of physics to be the same for all observers is known as Lorentz symmetry.
		Symmetry is one of the most important concepts in physics, and it is closely linked to the conservation of quantities such as energy, momentum and charge.
		The breaking of electroweak symmetry, for example, is responsible for the generation of mass in the Standard Model of particle physics.
	physicsweb.org /articles/world/17/3/7 (4463 words)

	[No title]
		The degeneracy is due to the breaking of the gauge symmetry.
		Symmetry breaking is only concerned with the operator \begin{equation} \hat\sigma^z\equiv\sigma^z-E_0(\sigma^z)=(E_++E_-)(\sigma^z); \end{equation} $\hat\sigma^z\in M_{2,sa}^1$ and we are interested in in the fluctuations of the operators $\hat\sigma^z$ together with its adjoint $J\hat\sigma^z$.
		The relation between spontaneous symmetry breaking and the absence of a gap in the energy spectrum in the ground state was originally put forward by Goldstone \cite{goldstone:1961}.
	www.ma.utexas.edu /mp_arc/papers/00-33 (7454 words)

	Plato's allegory of the cave and its parallel in modern cosmology
		Spontaneous symmetry breaking "is intimately related to the Higgs particle of the standard model" (which is "yet to be found").
		CPT symmetry breaking is currently the answer as to why the universe is dominated by matter.
		The phenomenon of chiral asymmetry (or "spontaneous symmetry breaking") therefore extends from the pre-geospheric world of elementary particles (standard model) through the geospheric chemical world of atomic elements (periodic table) to the bio-spheric world of biological molecules.
	www.geocities.com /theophoretos/allegoryofcave.html (6945 words)

	Spontaneous Symmetry Breaking in Women's Genes -- Physics News Update 813
		A spontaneous aggregation of proteins randomly determines which of the two X chromosomes in a woman's cell will remain active, and which one will stay silenced, according to a new physical model.
		Recently it has been proposed that an X remains active when certain proteins aggregate at a specific spot on the chromosome, shutting down its "suicide gene" XIST.
		But it remained unclear why proteins floating in the nucleus would aggregate around one of the chromosome, but not around the other -- an example of what physicists call spontaneous symmetry breaking.
	www.aip.org /pnu/2007/split/813-1.html (423 words)

	HYLE 3 (1997): Symmetry and Complexity-Fundamental Concepts of Research in Chemistry
		Pasteur recognized that the relationship between symmetry of reflection and optical activity is not a function of the crystal structure of a substance.
		The next symmetry element is inversion in which a molecule remains unchanged during a reflection of all atomic coordinates (x, y, z) at the point of inversion to (-x, -y, -z).
		Spontaneous symmetry breaking in quantum chemistry can be introduced by superselection rules forbidding the symmetric achiral superposition states which can be realized by a special physico-chemical environment (e.g.
	www.hyle.org /journal/issues/3/mainzer.htm (7464 words)

	Dolan-Jackiw paper
		Spontaneous symmetry breaking at finite temperature is studied.
		He then began to develop a complete analysis of spontaneous symmetry violation andjor persistence at finite temperature, with special emphasis on gauge theories with local symmetries.
		The restoration of a spontaneously broken symmetry above a critical temperature is a phenomenon whose aspects in field theory have been exhibited in this investigation.
	www.physics.ucla.edu /~cwp/articles/Dolan-Jackiw/conclusion.html (596 words)

	Re: Spontaneous supersymmetry breaking
		However, the physical phenomenon of spontaneous symmetry breaking (SSB), that the proponents of supersymmetry are trying to leverage, is well known as well as widely observed and studied.
		The symmetry breaking corresponds to the fact that once the sphere becomes magnetized, we can identify two special points on its surface: the North and South poles.
		If the interaction between two nearby particles energetically favors both of them to be of the same statistics (bosonic or fermionic), then at low enough temperature one would generically expect a symmetry-broken phase, where each particle is either a fermion or a boson.
	www.lns.cornell.edu /spr/2006-08/msg0075086.html (848 words)

	Definition of Spontaneous symmetry breaking
		In physics, one way of seeing spontaneous symmetry breaking is through the use of Lagrangians.
		Above the Curie temperature, the order parameter is zero, which is spatially invariant and there is no symmetry breaking.
		The residual rotational symmetries which leaves the orientation of this vector invariant remain unbroken but the other rotations get spontaneously broken.
	www.wordiq.com /definition/Spontaneous_symmetry_breaking (818 words)

	Spatial symmetry breaking
		In this case, because the particular symmetry which is broken is a spatial symmetry, we refer to the process by which the symmetry breaking solution suddenly appears, as the control parameter
		Spontaneous symmetry breaking, which is the fundamental non-linear process illustrated in the above discussion, plays an important role in many areas of physics.
		Symmetry breaking also plays a pivotal role in the so-called ``inflation'' theory of the expansion of the early universe.
	farside.ph.utexas.edu /teaching/329/lectures/node52.html (589 words)

	Nonlocal Models of Goldstone Bosons ...
		The aim of this thesis is to study spontaneous chiral symmetry breaking in asymptotically free gauge theories, in particular, we focus on quantum chromodynamics (QCD) and technicolour theories.
		The symmetry that is apparent in the spectrum is the diagonal subgroup SU(3)_V (the subscript indicates a vector symmetry, since the left and right-handed quarks are rotated by the same amount) or, as it is more commonly known SU(3)_flavour.
		Spontaneous symmetry breaking refers to the situation where the ground state (or vacuum) does not enjoy the symmetry of the Lagrangian.
	particle.physics.ucdavis.edu /terning/archive/Thesis.html (4902 words)

	THEORETICAL PHYSICS: ON THE AETHER AND BROKEN SYMMETRY
		The symmetry in question is called chiral symmetry, and it involves the behavior of quarks, the principal constituents of the protons and neutrons in atomic nuclei (among other things).
		symmetry and symmetry breaking: If a theory or process does not change when certain operations are performed on it, the theory or process is said to possess a symmetry with respect to those operations.
		Spontaneous symmetry breaking refers to a situation in which the solution of a set of physical equations fails to exhibit a symmetry possessed by the equations themselves.
	scienceweek.com /2005/sw050708-6.htm (2750 words)

	Unification and distance scales
		The success of spontaneous symmetry breaking in explaining electroweak physics led physicis to wonder whether the three particle theories of the SU(3)xSU(2)xU(1) model could be the spontaneously broken version of a higher unified theory at some higher energy scale, a single theory with only one gauge group and one coupling constant.
		However, these are supersymmetric theories in ten spacetime dimensions, so the symmetry breaking scheme also has to be involved with breaking the supersymmetry (because fermions and bosons don't come in pairs in the real world) and dealing with the extra six space dimensions in some manner.
		The spontaneous symmetry breaking mechanism would presumably be scalar field potentials of the form shown above, where a subset of the scalar fields with normal modes like the radial mode become massive, and the remaining massless scalar fields become longitudinal modes of massive gauge bosons to break the gauge symmetry down to the next level.
	superstringtheory.com /experm/exper3a2.html (1002 words)

	God Particle Discovered
		Spontaneous symmetry breaking occurs when a system or object naturally looses its rotational invariance.
		It is a deep result of quantum field theory that when this happens that the W and Z, which are messengers of the symmetries broken by the Higgs, acquire masses.
		In other words, without spontaneous symmetry breaking the W and Z would be massless.
	www.jupiterscientific.org /sciinfo/higgs.html (1443 words)

	IEP's preprints
		In the nonlinear chiral SU(3)´SU(3) dynamics with modified multiplet symmetry breaking the anomalous magnetic moments of baryons are taken into account and the differential cross-sections of the reaction of photoproduction of K mesons on the nucleons at the threshold and near it are calculated.
		The breaking of isotopic invariance is introducod in the non-linear chiral SU(3)´SU(3) dynamics with the help of Cabibbo rotation in the unitarity spac of Lagrangian broken to the SU(2) symmetry by the modified multiplet way.
		The relativistic invariance of this subsystem of Maxwell equations is proved, the three additional symmetries are found — three representations of conformal algebra C(1,3) and three respective representations of 32-dimensional algebra, wich is isomorphic to the algebra C(1,3)Å C(1,3)Å{e}, where e is the duality operator.
	www.iep.uzhgorod.ua /preprints.html (2850 words)

	Not Even Wrong » Uncategorized
		One is well-known, and many people have also tried this, it’s the idea of bringing together the internal gauge symmetry and the symmetry of local frame rotations.
		In the SM, the electroweak symmetry breaking (EWSB) is produced by the vacuum expectation value of the hypothesized Higgs field.
		But this breaking is simply put in by hand, via an ad hoc choice of a negative coefficient for the quadratic Higgs term.
	www.math.columbia.edu /~woit/wordpress/?cat=1 (5661 words)

	Breaking Supersymmetry
		Supersymmetry seems to be a necessary ingredient of a quantum theory of gravity and is an important part of most of the theories beyond the Standard Model.
		An attractive possibility for spontaneous supersymmetry breaking is to exploit non-perturbative mechanisms in supersymmetric gauge theories.
		Confinement and spontaneous chiral symmetry breaking has been investigated in the range of light gauginos including the massless limit.
	www.desy.de /desy-th/breaking_supersymmetry.html (180 words)

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