Poincare symmetry - Factbites

Poincare symmetry - Factbites
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Topic: Poincare symmetry

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	IV INTERNATIONAL WINTER CONFERENCE ON MATHEMATICAL METHODS IN PHYSICS
		In D= 3 dimensions the residual symmetry algebra, for generic values of the constant EM background, is isomorphic to $u(1)\oplus {\cal P}_c(2)$, with ${\cal P}_c(2)$ the centrally extended 2-dimensional Poincar\'e algebra.
		Residual symmetry algebras are also computed for specific non-constant EM backgrounds and in the supersymmetric case for a constant EM background.
		In D=4 dimension the generic residual symmetry algebra is given by a seven-dimensional solvable Lie algebra which is explicitly computed.
	mesonpi.cat.cbpf.br /wc2004/listposters.htm

	00-511.ascii.tar.mime
		Hence, the spacetime symmetry group and its action upon the observables of the theory were derived from the observables and state and not posited, as is customarily done.
		The corresponding modular symmetry groups appearing in these examples also satisfy a condition of modular stability, which has been suggested as a substitute for the requirement of positivity of the energy in Minkowski space.
		Moreover, they exemplify the conjecture that the modular symmetry groups are generically larger than the isometry and conformal groups of the underlying space--times.
	www.ma.utexas.edu /mp_arc/e/00-511.ascii.tar.mime

	93-119.tex
		Rudra, "Symmetry group of the non- linear Klein- Gordon equation"; \JPA {\bf 19} (1986), 2499 P.Rudra, "Maximal symmetry group of the Hamilton- Jacobi equation: relativistic particles in flat spacetime"; \JPA {\bf 19} (1986), 2947 P.
		Champagne and P. Winternitz, "On the infinite-dimensional symmetry group of the Davey-Stewartson equations"; \JMP {\bf 29} (1988), 1 B.
		Classification of the equations"; \JMP {\bf 28}, 520 (1987) L.M. Berkovic and M.L. Nechaevsky, "On the group properties and integrability of the Fowler-Emden equations"; in M.A. Markov, V.I. Man'ko and A.E. Shabad 1985 J.
	www.ma.utexas.edu /mp_arc/e/93-119.tex (7655 words)

	E. Noether's Discovery of the Deep Connection Between Symmetries and Conservation Laws
		For theories whose symmetry group is an infinite continuous group, the main results of theorem II are that there are certain identities, or "dependencies" as she called them [1], between Lagrange functions of the theory and their derivatives.
		The symmetry group of the theory, is a gauge group.
		This applies to theories having a finite continuous symmetry group; theories that are Galilean or Poincar invariant, for example.
	www.physics.ucla.edu /~cwp/articles/noether.asg/noether.html (5320 words)

	List Of Articles
		It is shown that the algebraic structure of the $(p=2)$ parastatistical dynamical variables allows for (symmetry) transformations which mix the parabose and parafermi coordinate variables.
		We find that if the $\kappa$-deformed Poincar\'e group is adopted as the fundamental symmetry of nature, it results in deviations from predictions of the Poincar\'e symmetry at large energies, which may be experimentally observable.
		This algebra is constructed by tensor-operator algebra of differential representation of ordinary $\text{sl}(2,\Bbb{C})$.
	theory.ipm.ac.ir /papers/all.html (5320 words)

	Gravitation and Gauge Symmetries - Synopsis
		Since the concept of gauge invariance has been established as the basis for our understanding of particle physics, it is natural to elevate the idea of supersymmetry to the level of gauge symmetry, introducing thus the gravitational interaction into the world of supersymmetry.
		Having in mind the importance of these spacetime symmetries in particle physics, we give a review of those properties of Poincare and conformal symmetries that are of interest for their localization and construction of the related gravitational theories.
		If we now want to make a physical theory invariant under local Poincare transformations, it is necessary to introduce new, compensating fields, which, actually, represent the gravitational interaction.
	www.phy.bg.ac.yu /~mb/ggssyn.html (5320 words)

	[spr] Representations of groups of "gauge symmetries"
		> However, there is one significant difference here: while the Poincare > group yields a usual symmetry of relativistic systems, the diffeomorphism > group is suppoed to yield a "gauge symmetry".
		In any case, one wouldn't expect reps of the diffeo > group popping up here in the amounts reps of the Poincare group do, just > like we don't see many reps of the gauge group in usual Yang-Mills > theory, say.
		Right: this is why I don't usually think that the representation theory of the diffeomorphism group will be all that important in quantum gravity - even assuming that spacetime is fundamentally a manifold, which I personally doubt.
	olympus.het.brown.edu /pipermail/spr/Week-of-Mon-20020909/003717.html (5320 words)

	Re: Coleman-Mandula theorem
		You probably meant to include a condition saying the symmetry group of the theory is not just a product of the Poincare group and some internal symmetry group.
		That's an okay definition of "internal symmetry", but again, the Coleman-Mandula theorem does not rule out internal symmetries; it just places limits on how they can be combined with Poincare symmetry.
		The Coleman-Mandula theorem makes it hard to find interesting ways to fit internal and spacetime symmetry groups into a bigger group, where "interesting" means "not just a product".
	www.lns.cornell.edu /spr/2002-03/msg0039950.html (5320 words)

	Abstract
		We show that any internal symmetry group must commute with the representation of the Poincare group (whose existence is assured by the CGMA) and each translation-invariant vector is also Poincare invariant.
		Buchholz, Detlev; Summers, Stephen J. We study spontaneous symmetry breaking for field algebras on Minkowski space in the presence of a condition of geometric modular action (CGMA) proposed earlier as a selection criterion for vacuum states on general space-times.
		The subspace of these vectors can be centrally decomposed into extremal invariant states and the CGMA holds in the resulting sectors.
	www.lqp.uni-goettingen.de /papers/04/05/04052500.html (5320 words)

	GCI Generated Page: Abstracts
		These rotations comprise additional exterior transformations that commute with the Poincar\'{e} group and form the group $SU(2)_{L}$, interior ones that constitute $SU(3)_{C}$, and a unique group of coupled double-sided rotations with $U(1)_{Y}$ symmetry.
		The four extra spacelike dimensions in the model form a basis for the Higgs isodoublet field, whose symmetry requires the chirality of $SU(2)$.
		The spinor mediates a physical coupling of Poincar\'{e} and isotopic symmetries within the restrictions of the Coleman-Mandula theorem.
	clifford.physik.uni-konstanz.de /cgi-BF/mysql_abs.cgi?&id=70 (186 words)

	► » On Lorentz contraction and other matters (answer to Harry)
		This Lorentz symmetry has been explained many times, first by Poincare in
		The question is what you add to the writings of Lorentz and Poincare.
		In fact the Lorentz transformations are the experimental ones,
	www.physics-talk.com /detail-6425249.html (543 words)

	superPS.tex
		It is called the $N=2$ supersymmetry algebra in four dimensions, another term that is likely to be encountered frequently.
		A symmetry that acts by outer automorphisms of super-Poincar\'e and in superspace acts only on the odd coordinates is called an R symmetry, a term one will often encounter.
		Either by reducing this to an ordinary Lagrangian or in any other way of your choosing, show that this is equivalent to the reduction to two dimensions of our four dimensional Lagrangian $\L_2$.
	www.math.ias.edu /QFT/spring/superPS.tex (543 words)

	Open Questions: Supersymmetry
		It was already known that when the Poincaré group is used as a local symmetry group, the field that results is precisely the gravitational field, and the field quantum is the graviton.
		Given the larger group of supersymmetry operations, which contains the Poincaré group, it's only natural to ask what happens when that is regarded as a local symmetry group.
		This boon from supersymmetry finally attracted substantial attention to string theory, so much so that it became known as the (first) "superstring revolution".
	www.openquestions.com /oq-ph007.htm (543 words)

	Lorentz transformation
		The Lorentz transformation is a group transformation that is used to transform the space and time coordinates (or in general any four-vector) of one inertial reference frame,, into those of another one,, with traveling at a relative speed of to along the x-axis.
		Lorentz believed the luminiferous aether hypothesis; it was Albert Einstein who developed the theory of relativity to provide a proper foundation for its application.
		The Lorentz transformations were first published in 1904, but their formalism was at the time imperfect.
	www.kiwipedia.com /en/lorentz-transforms.html (621 words)

	Field (physics) - Wikipedia, the free encyclopedia
		In relativity a similar classification holds, except that scalars, vectors and tensors are defined with respect to the Poincare symmetry of spacetime.
		Fields are often classified by their behaviour under the symmetry transformations of space, ie, under rotations and translations.
		Field theory - overview of QFT- gauge theory- quantization- renormalization- partition function - vacuum state - anomaly- spontaneous symmetry breaking - condensates
	en.wikipedia.org /wiki/Field_(physics) (621 words)

	Quanta & Consciousness: Symmetry
		Symmetry plays a great role in ordering the atomic and molecular spectra, for the understanding of which the principles of quantum mechanics provide the key.
		The starting-point here is the geometrization of gravity: making Poincaré symmetry local removes the flatness of space-time and requires the introduction of some geometrical structures of space-time, such as metric, affine connection, and curvature, which are correlated with gravity.
		There are internal symmetry spaces: phase space, for electromagnetism, which looks like a circle...
	mindbody.blogspot.com /2005/02/symmetry.html (621 words)

	STR: The Symmetry of the Lorentz Distortions
		The symmetry of Lorentz distortions is, therefore, a symmetry betwen real distortions in reference frames in absolute motion and apparent distortions in the reference frame at absolute rest, and it is a thoroughgoing symmetry, which holds for all the basic ways of measuring the other frame's clocks and measuring rods.
		The apparent symmetry of the distortions is a result of the actual Lorentz distortions suffered by the moving frame, together with the mis-synchronization of moving clocks, as we can see by considering how the measurements of the others’ clocks and rods are made.
		Since transformation equations must work both ways between any two inertial reference frames, this symmetry is entailed by Einstein's argument for the Lorentz transformation equations in his special theory of relativity.
	www.twow.net /ObjText/OtkCaLbStrD.htm (4752 words)

	Invariance properties of the Dirac equation with external electro-magnetic field
		The Poincar\'e group, which is the maximal symmetry group for field free case, is constrained by the presence of the external field.
		Introducing infinitesimal transformation of $x$ and $\psi$, we apply Lie's extended group method to obtain the class of external field which admit of the invariance of the equation.
	www.ias.ac.in /pramana/v60/p11/abs.htm (132 words)

	Quantum Overview/2
		Gravitation can likewise be conceived as a symmetry of the Lorenz transformations of relativity, usually referred to as Poincare invariance.
		When the larger symmetry between the weak and electromagnetic forces is broken, by some of the particles gaining a non-zero rest mass, the two forces gain their distinctive character.
		Because the broken-symmetry state has lower energy the universe is no longer in the symmetrical state.
	www.dhushara.com /book/quantcos/quant1/quantsb.htm (132 words)

	199510011.tex.html
		In the case of crystallographic groups, the successful classification of relevant symmetry groups in the nineteenth century made possible many predictions of what may actually be observed in nature.
		The first chapter provides a gentle introduction to groups (both finite and compact) and group actions, with excursions into the role of groups in crystallography, the classification of finite subgroups of $O(3)$, and the interplay of the icosahedral group and Euler's formula with fullerenes (``buckyballs'').
		Group theory provides a precise language with which to describe the possible symmetries of a physical system.
	www.ams.org /bull/pre-1996-data/199510/199510011.tex.html (1309 words)

	symmetries
		Poincaré realized that the symmetry group of Maxwell's equations was (at least) the Poincaré group.
		The group consisting of the Poincaré group and dilations is sometimes called the "Weyl group".
		The representation theory of the Poincar´ group dominates relativistic physics, while the representation theory of the Galilei group dominates nonrelativistic physics.
	math.ucr.edu /home/baez/symmetries.html (2452 words)

	standardmodel5.html
		Also, if supersymmetry were an unbroken symmetry, which it obviously is not, these contributions to the vacuum energy from the equal number of bosons and fermions would exactly cancel out at all energy scales, and we would have no vacuum or zero point energy.
		This is a weakening of the assumptions of the Coleman-Mandula theorem which says that the only allowed symmetries of the S-matrix are Poincare invariance, internal global symmetries related to conserved quantum numbers, and the C, P, and T symmetries.
		Then the action has a symmetry resulting of the original gauge invariance, which is lost when gauge fixing, called BRST symmetry, named after Becchi, Rouet, Stora, and Tyupin.
	www.geocities.com /jefferywinkler/standardmodel5.html (2452 words)

	Pure and Applied Geometry - Polyhedral Models of Klein's Quartic
		The motivation for such 3-dimensional models is to find realizations as close as possible to the Platonic solids, hence built up of planar (and convex) polygons and with maximal possible symmetry.
		Altogether this polyhedral model is the simplest one to understand the structure of Klein's group PSL (2,7).
		The planar one is the general and unsurpassable Poincar\'{e} model (cf.
	www.math.uni-siegen.de /wills/klein (2452 words)

	2.2 The emergence of the current picture
		The emergence of this group came as a surprise because one would have expected the Poincaré group as the asymptotic symmetry group, but one obtained a strictly larger group.
		However, the structure of the BMS group is quite similar to the Poincaré group.
		By application of Stokes’ theorem, the three-dimensional integral can be converted to a surface integral over the boundary, the sphere at infinity, of certain components of the so-called “superpotentials” for the energy-momentum pseudo-tensor.
	www.math.ethz.ch /EMIS/journals/LRG/Articles/lrr-2004-1/articlesu2.html (2452 words)

	Mathematics - Open Encyclopedia
		Group theory investigates the concept of symmetry abstractly and provides a link between the studies of space and structure.
		The modern fields of differential geometry and algebraic geometry generalize geometry in different directions: differential geometry emphasizes the concepts of functions, fiber bundles, derivatives, smoothness, and direction, while in algebraic geometry geometrical objects are described as solution sets of polynomial equations.
		Pythagorean Theorem – Fermat's last theorem – Goldbach's conjecture – Twin Prime Conjecture – Gödel's incompleteness theorems – Poincaré conjecture – Cantor's diagonal argument – Four color theorem – Zorn's lemma – Euler's identity – Scholz Conjecture – Church-Turing thesis
	open-encyclopedia.com /Mathematics (2452 words)

	Energy Citations Database (ECD) - Energy and Energy-Related Bibliographic Citations
		66 PHYSICS ; POINCARE GROUPS; ALGEBRA; ANGULAR MOMENTUM; LIE GROUPS; MASS; SPIN; SYMMETRY GROUPS
	www.osti.gov /energycitations/product.biblio.jsp?osti_id=279738 (202 words)

	9601003.rdf
		For all odd dimensions, the local symmetry group is a non trivial supersymmetric extension of the Poincar\'e group.
		In $2+1$ dimensions the gauge group reduces to super-Poincar\'e, while for $D=5$ it is super-Poincar\'e with a central charge.
	www.cs.odu.edu /~dlibug/ups/rdf/xxx/gr-qc/9601003.rdf (144 words)

	Classical particles with internal structure: general formalism and application to first-order internal spaces.ePrints@IISc - Open Access Archive of IISc Research Publications
		The theories involving group theory primarily consider the Poincar´e group as the underlying symmetry group and the internal space admits a transitive action of the Lorentz subgroup.
		Using the Kostant-Kirillov-Souriau theorem, it is further shown that there exist three possible first-order spaces; two are related respectively to the so-called generic and exceptional orbits in G, the orbits corresponding to two possible two-dimensional subgroups H; and the third is related to a two-fold covering of the exceptional orbit.
		Classical relativistic particles with internal structure have been the subject of extensive studies.
	eprints.iisc.ernet.in /archive/00000975 (235 words)

	Fields of Mathematics
		It is the harmony of the diverse parts, their symmetry, their happy balance; in a word it is all that introduces order, all that gives unity, that permits us to see clearly and to comprehend at once both the ensemble and the details.
		Jules Henri Poincaré, (1854-1912) [Whether or not he actually said this is a matter of debate amongst historians of mathematics.] The Mathematical Intelligencer, vol 13, no. 1, Winter 1991.
		A good first guess might be 4000 miles - and that would be quite correct as measured on a small map by leaving out the Baltic Sea and making judicious short cuts over most fiords and river mouths.
	www.chemistrycoach.com /fields_of_mathematics.htm (11624 words)

	2.2 The emergence of the current picture
		The emergence of this group came as a surprise because one would have expected the Poincaré group as the asymptotic symmetry group, but one obtained a strictly larger group.
		However, the structure of the BMS group is quite similar to the Poincaré group.
		The support for this suggestion was overwhelming from an aesthetical point of view, but a rigorous support for this claim was provided essentially only from the examination of the formal expansion type solutions of Bondi-Sachs and Newman-Unti and the analysis of explicit stationary solutions of the field equations.
	www.math.ethz.ch /EMIS/journals/LRG/Articles/lrr-2004-1/articlesu2.html (11624 words)

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