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Topic: Spacetime symmetries

Related Topics

spontaneous symmetry breaking

symmetry of second derivatives

bilateral symmetry

CP symmetry

radial symmetry

P symmetry

T symmetry

CPT symmetry

mirror symmetry

rotational symmetry

gauge symmetries

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	Spacetime - Wikipedia, the free encyclopedia
		In physics, spacetime is a model that combines three-dimensional space and one-dimensional time into a single construct called the space-time continuum, in which time plays the role of the 4th dimension.
		Second, for a manifold, the property of connectedness and path-connectedness are equivalent and one requires the existence of paths (in particular, geodesics) in the spacetime to represent the motion of particles and radiation.
		In general relativity, it is assumed that spacetime is curved by the presence of matter (energy), this curvature being represented by the Riemann tensor.
	en.wikipedia.org /wiki/Spacetime (2640 words)

	Spacetime symmetries - Wikipedia, the free encyclopedia
		Spacetime symmetries refers to aspects of spacetime that can be described as exhibiting some form of symmetry.
		Spacetime symmetries are used to simplify problems and find ample application in the study of exact solutions of Einstein's field equations of general relativity.
		For example, in the Schwarzschild solution, the role of spherical symmetry is important in deriving the Schwarzschild solution and deducing the physical consequences of this symmetry (for example, the non-existence of gravitational radiation in a spherically pulsating star).
	en.wikipedia.org /wiki/Spacetime_symmetries (1143 words)

	[No title] (Site not responding. Last check: 2007-10-11)
		We examine the structure of spacetime symmetries of toroidally compactified string theory within the framework of noncommutative geometry.
		We show that the spacetime duality and discrete worldsheet symmetries of the string theory are a consequence of the existence of two independent Dirac operators, arising from the chiral structure of the conformal field theory.
		We explore some larger symmetries of the algebra in the context of a universal gauge group for string theory, and connect these symmetry groups with some algebraic structures which arise in the theory of vertex operator algebras, such as the Monster group.
	www.ma.utexas.edu /mp_arc/a/97-413 (248 words)

	Gravitation and Gauge Symmetries - Synopsis
		Spacetime symmetries In physical processes at law energies the gravitational field does not have a significant role, since the gravitational interaction is extremely weak.
		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.
		Symmetries and conservation laws The existence of gauge symmetries is related to the presence of arbitrary multipliers in the total Hamiltonian, i.e.
	mail.phy.bg.ac.yu /~mb/ggssyn.html (2849 words)

	Symmetry and Symmetry Breaking
		The extension of the concept of continuous symmetry from “global” symmetries (such as the Galilean group of spacetime transformations) to “local” symmetries is one of the important developments in the concept of symmetry in physics that took place in the twentieth century.
		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).
		Another reason for attributing symmetries to nature is the so-called geometrical interpretation of spatiotemporal symmetries, according to which the spatiotemporal symmetries of physical laws are interpreted as symmetries of spacetime itself, the “geometrical structure” of the physical world.
	plato.stanford.edu /entries/symmetry-breaking (9818 words)

	PhysOrgForum Science, Physics and Technology Discussion Forums -> Unified Geometry:Overlooked SymmetriesOf Spacetime
		Consequently, symmetries of all particles would coincide with that of the “external” spacetime and hence answers all the 3 ultimate questions in the same way photon does.
		It is suspected that the so-called internal symmetry may actually be the symmetry of solid (or even higher dimensional) angle rotation “of the external spacetime”.
		Symmetry of solid angle rotation is suspected to be those of iso-spin, strangeness, charm, etc. The interaction through solid angle rotation is believed to be weak interaction.
	forum.physorg.com /index.php?showtopic=3458 (3071 words)

	[No title] (Site not responding. Last check: 2007-10-11)
		The symmetry between these inequivalent string backgrounds leads to the notion of a {\it stringy} or {\it quantum} spacetime which forms the moduli space of string vacua and describes the appropriate stringy modification of classical general relativity.
		The spacetime is thus described by the operator algebra which describes the relations among the quantum fields of the conformal field theory.
		According to the T-duality symmetry (\ref{Tdualiso}) of the effective string spacetime, as subspaces of the quantum spacetime we have the isomorphism \beq \left(C^\infty(T^n)~,~L^2({\rm spin}^-(T^n))~,~ig^{\mu\nu}\gamma_\mu\partial_\nu\right) \cong\left(C^\infty(T^n)~,~L^2({\rm spin}^-(T^n)^)~,~i\tilde g^{\mu\nu}\tilde\gamma_\mu\partial_\nu\right) \label{Tdualitycomm}\eeq which is the usual statement of the T-duality $T^n\leftrightarrow(T^n)^$ of string theory compactified on an $n$-torus.
	www.ma.utexas.edu /mp_arc/html/papers/97-413 (15192 words)

	Particles
		So basically SU(N) is just the symmetry that says you have N different "flavors" of quarks that act pretty much the same way, at least with respect to the strong interactions, except for their masses.
		This U(1) symmetry associated with charge is a local symmetry because the coupling of the spin-1 photon of electromagnetism couples to its current (a local quantity, the distribution of charge).
		Some "internal" momenta of the propagators are determined by the "external" momenta of the wave functions (and similarly for spin and internal symmetry by their conservation or interaction-specified breaking).
	insti.physics.sunysb.edu /~siegel/particle.html (1163 words)

	Quantum Gravity Concept Map - Spacetime
		The "spacetime manifold" is the smooth, continuous domain of the field.
		Since the spacetime manifold in General Relativity can be arbitrarily curved, a consistent local definition of mass, energy, momentum and angular momentum is not possible.
		In either case, the quantity is then defined as a flux integral (flow through a surface) of the spacetime "curl" of the vector which generates the symmetry transformation.
	www.rwc.uc.edu /koehler/qg/st.html (735 words)

	References > H
		"Spacetime quantum mechanics and the quantum mechanics of spacetime" gq/9304006, in Julia and Zinn-Justin 95.
		"On the kinematics of the torsion of spacetime" FP 15 (1985) 451-471 [>torsion].
		"The affine symmetry of self-dual gravity" JMP 36 (1995) 6897-6906 [>sd].
	www.phy.olemiss.edu /~luca/Refs/h.html (12143 words)

	Bibliography Abstracts: Robert T Jantzen
		Spatially homogeneous perfect fluid spacetimes are studied from a point of view which emphasizes the spatial geometry and the action of that subgroup of the spatial gauge group of the three-plus-one formulation of general relativity which is compatible with the spatial homogeneity.
		Spatially homogeneous and non-exceptional self-similar spacetime metrics which are `exact power law metrics' are defined, explicitly parametrized and shown to have fixed conformal 3-geometry in the natural slicing of the spacetime by the orbits of the symmetry group and to admit a homothetic Killing vector field not tangent to that slicing.
		This is illustrated for the Kerr-Newmann spacetime, where the Simon-Mars tensor vanishes due to the simultaneous alignment of the principal null directions of the Weyl tensor, the Papapetrou field associated with the timelike Killing vector field and the electromagnetic field of the spacetime.
	www34.homepage.villanova.edu /robert.jantzen/research/bibabs.htm (9651 words)

	Supersymmetry in Mathematics (Site not responding. Last check: 2007-10-11)
		This supersymmetry would presumably unify the spacetime symmetries — e.g., the Poincaré or conformal symmetries — with the internal symmetries governing the spectrum of excitations in nuclear or particle physics.
		They showed that the maximal Lie algebra of symmetries of the scattering matrix of a four-dimensional relativistic quantum field theory is the direct product of a spacetime Lie algebra — the Poincaré or conformal Lie algebra — with the Lie algebra of a compact Lie group.
		Being a direct product, the Casimir invariants of the spacetime Lie algebra are also invariant under the internal symmetries and hence irreducible representations of the direct product are spin- and mass-degenerate.
	www.maths.ed.ac.uk /~jmf/Research/susy_2.html (290 words)

	Luboš Motl's reference frame: Types and meaning of the branes
		Moreover, we require that the brane does not destroy any rotational symmetries between the dimensions transverse to the brane, and it also preserves the translational and Lorentz symmetries involving the dimensions along the brane worldvolume which is the subspace of spacetime spanned by time as well as the spatial dimensions of the brane.
		The last condition implies that a sheet of paper is not quite a brane because the Lorentz symmetry is spontaneously broken by the sheet of paper: there is a preferred reference frame associated with the atoms of paper.
		This symmetry applies to all states of the closed string, including the oscillating ones, and it is preserved by the interactions.
	motls.blogspot.com /2005/01/types-and-meaning-of-branes.html (3820 words)

	Strings
		Supergravity theories soon followed, in which the symmetries of spacetime were extended in this way, and supersymmetric models of particle physics were also considered, with their prediction of boson partners for the known fermions (so squarks as partners for quarks, etc.) and fermion partners for bosons (e.g., gluinos and photinos).
		And there are other dualities and "mirror symmetries" which relate a solution to one of the five consistent superstring theories compactified in a certain way to a solution of another one of the five compactified in a different way.
		It is conjectured, with growing confidence, that all five superstring theories and their various compactifications are related to one another and are just different realisations of a still more fundamental theory which one of its founders and leading advocates, Ed Witten, has called M-theory.
	monopole.ph.qmul.ac.uk /~jmc/EUni/Strings.html (4754 words)

	List Of Articles (Site not responding. Last check: 2007-10-11)
		In this article the interaction of branes at angles with respect to each other with non-zero internal gauge fields are calculated by construction of the boundary states in spacetime in which some of its directions are compact on tori.
		We study the noncommutativity of the spacetime, generalization of the Poincar\'e symmetry of the superstring, the changes of the metric, antisymmetric tensor and dilaton.
		In this paper we study the effects of noncommutativity on a closed superstring propagating in the spacetime that is compactified on tori.
	theory.ipm.ac.ir /papers/kamani.html (1374 words)

	[No title]
		But we're in trouble already, because curiously it is the extremely high degree of symmetry of general relativity that has made it hard to quantize gravity.
		The category Cob is the category whose objects are (n-1)-dimensional manifolds ("space") and whose morphisms are n-dimensional manifolds ("spacetime") having one (n-1)-dimensional manifold as "incoming" and another as "outgoing" boundary.
		The symmetries in topological quantum field theories generalize the symmetries of earlier theories, thus, since earlier theories only dealt with group representations, while TQFTs are category representations.
	www.math.niu.edu /~rusin/known-math/93_back/symmetry (2314 words)

	String Theory, Vol. 2 : Superstring Theory and Beyond (Cambridge by Joseph Polchinski [ISBN: 0521633044] - Find Cheap ...
		The final four chapters are concerned with four-dimensional string theories, and have two goals: to show how some of the simplest string models connect with previous ideas for unifying the Standard Model; and to collect many important and beautiful general results on world-sheet and spacetime symmetries.
		Supersymmetry is added to strings, more symmetries are presented, string theory phenomenology is described and many topics introduced in Volume I are developed in more detail.
		This is particularly noticeable in the chapter on Calabi-Yau compactification and in the discussion on mirror symmetry in the last chapter.
	www.gettextbooks.com /isbn_0521633044.html (1318 words)

	Warren Siegel's research
		The symmetry can be treated as a spontaneously broken symmetry, restored by the "high-energy limit" of distances shorter than the coordinate dependence.
		The dilaton, invariant under this symmetry, is required as the integration measure.
		In general this symmetry is spontaneously broken, but for states that are independent of d dimensions, an SO(d,d+n) subgroup is restored.
	insti.physics.sunysb.edu /~siegel/research.shtml (3715 words)

	2.2 Quasi-local energy-momentum and angular momentum of the matter fields (Site not responding. Last check: 2007-10-11)
		Thus observables are always associated with open subsets of spacetime whose closure is compact, i.e.
		Since, however, many of the basic concepts and ideas behind the various gravitational quasi-local energy-momentum and angular momentum definitions can be understood from the analogous non-gravitational quantities in Minkowski spacetime, we devote the present section to the discussion of them and their properties.
		does depend on the hypersurface, because this is not connected with the spacetime symmetries.
	www.univie.ac.at /EMIS/journals/LRG/Articles/lrr-2004-4/articlesu2.html (2171 words)

	BUCHHOLZ SPECIAL HISTORY LECTURE (Site not responding. Last check: 2007-10-11)
		A first breakthrough was made by Wigner, who proposed to describe particles as irreducible quantum systems whose states transform covariantly under the action of the spacetime symmetries.
		On the mathematical side, this triggered the theory of induced representations of non-compact groups, and it led to an understanding of the properties of mass and spin.
		Further progress was made when it was realized that the spacetime localization properties of observational procedures and their causal structure have to be taken into account in the mathematical formalism.
	www.math.ufl.edu /dept_news_events/special/buchholz (390 words)

	NEW STRUCTURE MODELS OF HADRONS, NUCLEI AND MOLECULES PERMITTED BY HADRONIC MECHANICS, THEIR EXPERIMENTAL VERIFICATIONS ...
		Once the fundamental spacetime symmetries of quantum mechanics are seen as being approximately valid in nuclear physics, so must be quantum mechanics itself.
		These systems are "closed" in the sense of being isolated from the rest of the universe, thus verifying conventional total conservation laws and are given by aggregates of constituents at small mutual distances, as occurring for Jupiter at the classical level or for nuclei at the particle level.
		For the case of the more general closed non-Hamiltonian systems (such as Jupiter, a hadron, a nucleus or a star considered as isolated from the rest of the universe), we have the conservation of the total angular momentum, while the angular momentum of the constituents are generally nonconserved.
	www.neutronstructure.org /part6.htm (8374 words)

	Centre for Time : Events : Time-Symmetry in Quantum Mechanics
		For RBW, dynamical laws are neither ontologically nor explanatorily fundamental; rather, the fundamental spacetime symmetries interpreted as irreducibly relational structures, plus initial and boundary conditions, give rise to the Schrˆdinger equation and the QM probabilities.
		Thus, the determination of events is made not dynamically, but rather non-dynamically, by imposing a global determination relation (which is both non-local and non-separable) on a spacetime structure whose symmetries, and the geometry they support, are irreducibly relational.
		Quantum non-locality and non-separability are not mysterious according to RBW since they are straightforward consequences of the geometry of spacetime as given by the restricted PoincarÈ group.
	www.usyd.edu.au /time/conferences/5002mq-old.htm (2650 words)

	MPI MIS Leipzig - Preprint Nr. 23/2001
		Gauge theories of conformal spacetime symmetries are presented which merge features of Yang-Mills theory and general relativity in a new way.
		The models are local but nonpolynomial in the gauge fields, with a nonpolynomial structure that can be elegantly written in terms of a metric (or vielbein) composed of the gauge fields.
		General relativity itself emerges from the construction as a gauge theory of spacetime translations.
	www.mis.mpg.de /preprints/2001/prepr2301-abstr.html (102 words)

	Vortex Symmetries
		The External Symmetries of a Compton Radius Vortex are those of Position in SpaceTime, Mass=Area, Spin=Angular Momentum, Electric Charge, and Color Charge.
		The External Symmetries of a Classical Radius Black Hole are those of Position in SpaceTime, Mass=Area, Spin=Angular Momentum, Electric Charge, and Color Charge.
		My remarks are that these symmetries are consistent with the HyperDiamond Lattice structure of the D4-D5-E6 physics model, and that Saul-Paul's work with S4 was a key that led me to construct the D4-D5-E6 physics model.
	www.valdostamuseum.org /hamsmith/worm4holes.html (2807 words)

	[No title]
		The curved spacetime paradigm contrasted with the nonlinear field theory paradigm.
		Instability of Cauchy horizon E. Misner Spacetimes and its Causal Structures 1.
		The Dynamics of Spacetime Geometry A. 3+1 split of spacetime and of Einstein's equations 1.
	www.pma.caltech.edu /Courses/ph236/public_html/outline98.txt (1127 words)

	Quantum Gravity Concept Map - Symmetries
		When a set of transformations is closed (any transformation can be expressed as the product of other transformations in the set), the set is called a "symmetry group".
		Note that the fields associated with the nonabelian symmetries can be divided into "electric" (curl-free) and "magnetic" (divergence-free) fields just as in the the abelian case (electromagnetism).
		The author is interested in any comments you may have about either the content or the effectiveness of the hypertext concept map in the organization of that content.
	www.rwc.uc.edu /koehler/qg/sym.html (593 words)

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