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	Noether's theorem - Wikipedia, the free encyclopedia
		Noether's theorem is a central result in theoretical physics that expresses the one-to-one correspondence between continuous symmetries and conservation laws.
		Noether's Theorem is deeply tied to quantum mechanics as it identifies physical variables that are related by the Heisenberg uncertainty principle (such as position and momentum) using only the principles of classical mechanics.
		In quantum field theory, the analog to Noether's theorem, the Ward-Takahashi identities, yields further conservation laws, such as the conservation of electric charge from the invariance with respect to the gauge invariance of the electric potential and vector potential.
	en.wikipedia.org /wiki/Noether_charge (1287 words)

	Charge (physics) - Wikipedia, the free encyclopedia
		In physics, a charge may refer to one of many different quantities, such as the electric charge in electromagnetism or the color charge in quantum chromodynamics.
		Sometimes, the word "charge" is used as a synonym for "generator" in referring to the generator of the symmetry.
		Charge conjugation simply means that a given symmetry group occurs in two inequivalent (but still isomorphic) group representations.
	en.wikipedia.org /wiki/Charge_(physics) (511 words)

	Charge conservation - Wikipedia, the free encyclopedia
		In practice, charge conservation is a physical law that states that the net change in the amount of electric charge in a specific volume of space is exactly equal to the net amount of charge flowing into the volume minus the amount of charge flowing out of the volume.
		In essence, charge conservation is an accounting relationship between the amount of charge in a region and the flow of charge into and out of that same region.
		The charge conservation can also be understood as a conclusion of the Noether's theorem, a central result in theoretical physics that expresses the one-to-one correspondence between symmetries and conservation laws.
	en.wikipedia.org /wiki/Charge_conservation (442 words)

	The Cosmic Diamond
		Among the symmetries of light conserved as charge are light's non-local character (the "location" charge of gravitation), light's two-dimensional character (electric charge), light's anonymity or lack of identity (identity charge and spin, the weak force), and the quantum or whole unit nature of symmetry charges themselves (color charge, strong force).
		Charge conservation arises from Noether's theorem, which states that in a multicomponent field, such as the electromagnetic field, (or the derivative and related metric field of spacetime), where one finds a symmetry one will also find a conservation law, and vice versa.
		Gravity represents two related charges - entropy and symmetry, since both are the consequence of velocity c and the non-local character of light (causing the entropic expansion and cooling of the Universe, and the symmetric, non-local distribution of light's energy, as well as gauging the symmetry of the spacetime metric).
	www.people.cornell.edu /pages/jag8/diamond.html (2396 words)

	Science Fair Projects - Noether charge
		Noether's theorem is a central result in theoretical physics that expresses the one-to-one correspondence between the symmetries and the conservation laws.
		A Noether charge is a physical quantity conserved as an effect of a continuous symmetry of the underlying system.
		One theoretical use of the Noether charge is in calculating the entropy of stationary fl holes.
	www.all-science-fair-projects.com /science_fair_projects_encyclopedia/Noether_charge (1590 words)

	Principles of a Unified Field Theory
		Charge conservation is the necessary guarantee to energy conservation that allows symmetry-breaking and the conversion of free energy to particles and information to go forward; thus charge conservation plays a role analogous to entropy, the necessary guarantee to energy conservation which allows the conversion of free energy to work.
		Charge conservation is a common example of this theorem enforced; the symmetry of the spacetime metric as regulated by inertial forces (and conserved by gravitation) is another example.
		The function of all charges in particle-antiparticle pairs is to cause and facilitate the annihilation of the pair, returning its energy to the symmetric state of light.
	home.earthlink.net /~johngowan/trintxt.html (5524 words)

	Einstein's Equivalence Principle
		3) Noether's theorem - the conservation of symmetry - is exampled by the forces of charge conservation, inertia, and the primordial form of entropy (the intrinsic dimensional motion of light as gauged by "velocity c").
		Noether's theorem is enforced through the well-known principles of charge (and spin) conservation, inertia and gravity.
		Charges produce forces whose conservation purpose is to pay the symmetry debts they hold; payment of the temporal symmetry and entropy debt drives the gravitational conversion of bound to free energy - in stars, quasars, and in Hawking's "quantum radiance" of fl holes.
	people.cornell.edu /pages/jag8/equival.html (1999 words)

	Tetrahedron Model of Light and Conservation Law
		The ability of light to interact with electrically charged particles and to conserve its energy in the bound form of particle mass and momentum is the basis for the existence of the material realm of particulate matter, and its highest and most complex expression, life.
		Charges are held in the time dimension where they are balanced or neutralized until they can be annihilated or otherwise canceled by their corresponding real or virtual antimatter charges.
		Charge conservation and atomic matter form the base of the "information pyramid"; most information is carried in the chemical interactions, combinations, and permutations of the electron shells of atoms.
	home.earthlink.net /~johngowan/trintxtcut.html (4169 words)

	Principles of the Conservation Tetrahedron: Their Relation to Gravity
		Charge, symmetry, and entropy are also conserved physical quantities, although entropy is conserved in the unique sense that it is always increasing in either spatial or (metrically equivalent) temporal terms, or the sum of both.
		"Noether's Theorem" is a pivotal theorem in the effort to unify the 4 forces of physics, and in the branch of mathematics associated with that effort, known as "Group Theory".
		In that case we have two (real) particles bearing charges, charges whose original purpose was to restore the symmetry of the pair by causing their annihilation - wherefore we see directly that the charges (and spin) of matter do indeed arise as the symmetry debts of light.
	home.earthlink.net /~johngowan/trinity.html (6187 words)

	[No title] (Site not responding. Last check: 2007-10-31)
		E equals the negative gradient of V. 16.6 Conservation of Charge.
		Noether's Principle says that for every conserved quantity there is a symmetry.
		Conservation of Charge arises from the fact that there is no observable effect that depends on an absolute value of electric potential - the zero to which all measurements are referenced, or gauged, is arbitrary.
	www.hamline.edu /~arundqui/phys1240/summary/data/smartin/314-summary (101 words)

	Download Info of - Harpo (group) (Site not responding. Last check: 2007-10-31)
		Noether's theorem is a central result in theoretical physics physics that expresses the one-to-one correspondence between symmetry and conservation law s.
		Informally, Noether's theorem can be stated as (technical fine points aside): :To every differentiable symmetry generated by local actions, there corresponds a conserved current.
		One theoretical use of the Noether charge is in calculating the entropy of stationary fl hole s.
	harpo.group.en.cwap.org (2004 words)

	Lorentz-invariant electric charge? Text - Physics Forums Library
		Noether charge is Lorentz tensor of rank (n-1), where n is the rank of Noether current.
		Just as long as you describe what "electric charge" means in classical field theory (built with fields transforming under proper Lorentz transformations of their arguments after finite dimensional reps. of the universal covering group of the proper Lorentz group), the answer is trivial.
		It is conserved, iff the Noether charge is conserved.
	www.physicsforums.com /archive/index.php/t-114620.html (7108 words)

	Conclusion
		In the course of proving Noether's Theorem and using it for some of its many applications ranging from electromagnetism to field theory we have discovered that Noether's Theorem is a broad and general theorem.
		Noether's Theorem gives us the ability to derive Maxwell's Equations, many useful results in field theory, and even principles from General Relativity.
		Therefore, one must conclude that Noether's Theorem is one of the most valuable results in mathematical physics.
	www.physics.ohio-state.edu /~cairnsj/NoethersTheorem/node14.html (231 words)

	Symmetry, Conservation and Noether's Theorem [Zach Wolfson]
		These quantities might be energy, linear or angular momentum, charge, or other, sometimes less usual, observables, and knowing that such a quantity is conserved can give a wealth of knowledge about the system under consideration.
		A main result of theoretical physics that makes considerable headway in solving this problem is Noether's Theorem, which states that if a system has a particular symmetry, there is a quantity associated with that symmetry that is conserved.
		In both classical and quantum physics, Noether's Theorem proves to be very powerful because the symmetries of a system are relatively easy to find given the system's Lagrangian.
	www.swarthmore.edu /NatSci/math_stat/webspot/Wolfson,Zach/Noether/index.html (220 words)

	Brazilian Journal of Physics - New developments in the quantization of supersymmetric solitons (kinks, vortices and ... (Site not responding. Last check: 2007-10-31)
		The susy generators are the Noether charges for rigid susy, and as any Noether charge they are the space integrals over the time components of the Noether currents.
		There are also nonvanishing corrections to the central charge, due to the central charge anomaly (which sits in the same multiplet as the conformal susy anomaly and the trace anomaly).
		The nontrivial anomalous quantum correction to the central charge operator is thus seen to be entirely the remnant of the spontaneous parity violation in the higher-dimensional theory in which a susy kink can be embedded by preserving minimal susy.
	www.scielo.br /scielo.php?pid=S0103-97332004000700002&script=sci_arttext&tlng=en (7807 words)

	[No title] (Site not responding. Last check: 2007-10-31)
		Following their prescriptions, the effects of coupling (charged) Higgs and fermionic matter fields to the $GL(2,C)$ formulation of electromagnetism and gravity by Robinson, \cite{DC1} are presented in Chapter 4.
		The notion of a spinor density is employed to describe the charged complex (Higgs) scalar field and the theory as developed previously by Plebanski, \cite{Pleb2} is summarised in the appendix.
		Further illustration of the symplectic techniques and the formulation of chiral Lagrangians is provided in the presentation of a chiral Lagrangian for spin $\thalf$ fields propogating on a (fixed) curved backgroung spacetime.
	www.ma.utexas.edu /mp_arc/html/papers/03-416 (3333 words)

	Pasti - Re: Noether theorem vs. Runge_Lenz (cont'd)
		We are not missing anything.CPT is a discrete symmetry,and cannot be described via Noether theoremBut the fact that you cannot associate a Noether current with this symmetry, and correspondingly a Noether charge does not mean that lagrangeans cannot have these symmetries.They do have them.
		Noether theorem was developed for continuous symmetries, and in the present frame works only for that(whether gauge symmetries or diffeos).
		Maybe the Lagrangean formalism and the Hamiltonian formalism are equivalent, but the hamiltonian and the lagrangean are not equivalent.They are related through a Legendre transform,and for a lagrangean that admits time translations as symmetry, the canonical energy (hamiltonian) is the corresponding conserved Noether charge.
	www.scienceagogo.com /message_board4/messages/1308.shtml (676 words)

	[No title]
		In one paper, I examined topological extensions of Noether charge algebras carried by Dp-branes which are propagating in topologically non-trivial spacetimes.
		It was shown that these charges could be interpreted as corresponding to non-trivial topological configurations of the gauge field on the brane; in particular, the central charge carried by a D2-brane was shown to correspond to a magnetic monopole on the brane; see paper [Noether].
		In another paper, I could show how the isometry group of a lower-dimensional spacetime which was obtained through orbifoldization from a simply connected higher-dimensional spacetime possibly exhibited a natural semigroup extension, provided that the quotient procedure was performed with respect to a light-like lattice; see paper [Semigroup].
	www.weizmann.ac.il /chemphys/hanno (674 words)

	Black Hole Entropy and the Hamiltonian Formulation of Diffeomorphism Invariant Theories - Brown (ResearchIndex)
		Abstract: Path integral methods are used to derive a general expression for the entropy of a fl hole in a diffeomorphism invariant theory.
		The result, which depends on the variational derivative of the Lagrangian with respect to the Riemann tensor, agrees with the result obtained from Noether charge methods by Iyer and Wald.
		The method used here is based on the direct expression of the density of states as a path integral (the microcanonical functional integral).
	citeseer.ist.psu.edu /brown95black.html (350 words)

	Citebase - Black Hole Entropy is Noether Charge (Site not responding. Last check: 2007-10-31)
		Assuming only that the theory admits stationary fl hole solutions with a bifurcate Killing horizon, and that the canonical mass and angular momentum of solutions are well defined at infinity, we show that the first law of fl hole mechanics always holds for perturbations to nearby stationary fl hole solutions.
		Furthermore, we show that this fl hole entropy always is given by a local geometrical expression on the horizon of the fl hole.
		Our results show that the validity of the ``second law" of fl hole mechanics in dynamical evolution from an initially stationary fl hole to a final stationary state is equivalent to the positivity of a total Noether flux, and thus may be intimately related to the positive energy properties of the theory.
	citebase.eprints.org /cgi-bin/citations?id=oai:arXiv.org:gr-qc/9307038 (327 words)

	Quantum Field Theory
		is the charge density, and c is the velocity of light.
		Thus, when the bare charge is replaced by renormalized electric charge in Eq.(39d), most of the divergent terms disappear from the formulation.
		Conversely, at larger distances, the color charge increases, so that the quarks tends to bind more tightly together giving rise to quark confinement, which is the flip side of asymptotic freedom.
	universe-review.ca /R15-12-QFT.htm (12634 words)

	Lorentz-invariant electric charge?
		Well, I suppose that answer is that the four-current appears in the Lagrangian the way it does, and also that the 0th component of the four-current is this thing we call charge.
		I think that the best answer to my knowledge, is: because spacetime is a 4-dimensional geometrical entity with certain properties ; and as such, all "things" that are defined on it, and are supposed to have a physical existance, must conform to its geometry - which is Lorentz-invariance in the case of flat Minkowski space.
		Well, I suppose that answer is that the four-current appears in the Lagrangian the way it does, and also that the 0th component of the four-current is this thing we call charge density.
	www.physicsforums.com /showthread.php?t=114620&page=3 (1702 words)

	[No title] (Site not responding. Last check: 2007-10-31)
		When it comes to quantum field theory, the invariance with respect to general gauge transformations also gives the law of conservation of quantities such as electric charge, though there are some subtleties here; the conservation law here is based on the
		conserved quantity called the Noether charge (provided, of course, if M is noncompact, the currents fall off sufficiently fast at infinity).
		This means we can extend Noether's theorem to larger Lie algebras.
	www.brujula.net /english/wiki/Noether's_theorem.html (1242 words)

	[No title] (Site not responding. Last check: 2007-10-31)
		Specifically, approaches (i) and (ii) appear to be restricted to a class of theories satisfying certain properties listed in section 2; approach (iii) appears to require the Lagrangian density to be linear in the curvature; and approach (iv) requires the existence of suitable instanton solutions.
		However, we show that within their domains of applicability, all of these approaches yield results in agreement with the Noether charge approach.
		In an appendix, we show that in an arbitrary diffeomorphism invariant theory of gravity, the ``volume term" in the ``off-shell" Hamiltonian associated with a time evolution vector field $t^a$ always can be expressed as the spatial integral of $t^a {\cal C}_a$, where ${\cal C}_a = 0$ are the constraints associated with the diffeomorphism invariance.
	celestial.eprints.org /oai/arXiv.org?verb=GetRecord&identifier=oai:arXiv.org:gr-qc/9503052&metadataPrefix=oai_dc (201 words)

	Usenet Archive (Site not responding. Last check: 2007-10-31)
		Noether in 1915 showed (loosely) that to every symmetry in a systems lagrangeian there corresponds a conserved quantity and the conserved quantity (technically called the conserved Noether charge) associated with symmetry in time was found to be what is called energy.
		See http://www.mathpages.com/home/kmath564/kmath564.htm > > > Noether > > sorted all this out 90 years ago - energy conservation is simply an > > expression of underlying symetries in the lagrangain.
		In modern times energy is defined at the conserved Noether charge associated with time symetry of the lagrangeian.
	www.allusenet.org /File.asp?service=29685 (7163 words)

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