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	Gauge boson - Wikipedia, the free encyclopedia
		Photons are gauge bosons of the electromagnetic interaction, the weak interactions are mediated by weak bosons or "vector bosons", and the carriers of the strong interaction are known as gluons.
		Gauge bosons are described mathematically, for technical reasons such as gauge invariance, by field equations for massless particles.
		Photons and gluons are massless gauge bosons, whereas the W and Z bosons of electroweak theory have mass.
	en.wikipedia.org /wiki/Gauge_boson (345 words)

	Gauge theory - Wikipedia, the free encyclopedia
		Gauge theories became even more attractive when it was realized that non-abelian gauge theories reproduced a feature called asymptotic freedom, that was believed to be an important characteristic of strong interactions—thereby motivating the search for a gauge theory of the strong force.
		Note that although gauge theory is dominated by the study of connections (primarily because it's mainly studied by high-energy physicists), the idea of a connection is not essential or central to gauge theory in general.
		One thing to note is that not all gauge transformations can be generated by infinitesimal gauge transformations in general; for example, when the base manifold is a compact manifold without boundary such that the homotopy class of mappings from that manifold to the Lie group is nontrivial.
	en.wikipedia.org /wiki/Gauge_theory (2365 words)

	Gauge theory -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-07)
		Gauge theories are a class of physical theories based on the idea that ((mathematics) an attribute of a shape or relation; exact correspondence of form on opposite sides of a dividing line or plane) symmetry (A qualitative change) transformations can be performed locally as well as globally.
		Gauge theories became even more attractive when it was realized that non-abelian gauge theories reproduced a feature called (Click link for more info and facts about asymptotic freedom) asymptotic freedom, that was believed to be an important characteristic of strong interactions—thereby motivating the search for a gauge theory of the strong force.
		Note that although gauge theory is dominated by the study of (An instrumentality that connects) connections (primarily because it's mainly studied by (Click link for more info and facts about high-energy physicists) high-energy physicists), the idea of a connection is not essential or central to gauge theory in general.
	www.absoluteastronomy.com /encyclopedia/g/ga/gauge_theory.htm (1991 words)

	Gauge theory Article, Gaugetheory Information (Site not responding. Last check: 2007-10-07)
		Gauge theories are a class of physical theories which are based on the idea that symmetry transformations can only be performed locally.Most physical theories are described by Lagrangians which are invariant under certain transformations, when the transformations are identicallyperformed at every space-time point - they have global symmetries.
		Generalizing the gauge invariance ofelectromagnetism, they attempted to construct a theory based on the action of the (non-abelian) SU(2) symmetry group on the isospin doublet of protons and neutrons, similar to the action of the U(1) group on the spinor fields of quantum electrodynamics.
		Note that although gauge theory is dominated by the study of connections (primarily because it's mainly studied by high energyphysicists), the idea of a connection is not essential or central to gauge theory in general.
	www.anoca.org /field/lagrangian/gauge_theory.html (1604 words)

	ipedia.com: Gauge theory Article (Site not responding. Last check: 2007-10-07)
		Generalizing the gauge invariance of electromagnetism, they attempted to construct a theory based on the action of the (non-abelian) SU(2) symmetry group on the isospin doublet of protons and neutrons, similar to the action of the U(1) group on the spinor fieldss of quantum electrodynamics.
		Gauge theories became even more attractive when it was realized that non-abelian gauge theories reproduced a feature called asymptotic freedom, that was believed to be an important characteristic of strong interactions - thereby motivating the search for a gauge theory of the strong force.
		In 1983, Simon Donaldson used techniques developed in gauge theory (instantons) to show that the differentiable classification of smooth 4-manifolds is very different from their classification upto homeomorphism, and exhibited exotic differentiable structures on Euclidean 4-dimensional space.
	www.ipedia.com /gauge_theory.html (1563 words)

	The Standard Model (Site not responding. Last check: 2007-10-07)
		Gauge invariance is a powerful symmetry that tames uncontrollable infinities in quantum amplitudes and encodes the rich symmetry structure of conserved charges observed in elementary particle physics.
		The massless gauge field of this theory is known as the gluon.
		The resulting theory has massive gauge bosons but still retains the nice properties of a fully gauge invariant theory where the gauge bosons would normally be massless.
	superstringtheory.com /experm/exper2a.html (760 words)

	gauge theory
		In a gauge theory there is a group of transformations of the field variables (gauge transformations) that leaves the basic physics of the quantum field unchanged.
		In short, the structure of the group of gauge transformations in a particular gauge theory entails general restrictions on the way in which the field described by that theory can interact with other fields and elementary particles.
		This gauge invariance is preserved in the modern theory of electromagnetism called quantum electrodynamics, or QED.
	www.britannica.com /nobel/micro/228_45.html (383 words)

	This is G o o g l e's cache of http://www (Site not responding. Last check: 2007-10-07)
		This is because the co-efficient of the quadratic term in the fields(the inverse of which is propagator or green's function) does not have the inverse as its determinant vanishes.
		The point is that current conservation follows from the global gauge invariance which is preserved even after one chooses a gauge.
		This means, the choice of gauge should be such as not to spoil the global gauge invariance.
	www.rbduncan.com /quantize.htm (717 words)

	Gauge transformations (Site not responding. Last check: 2007-10-07)
		This suggests, very strongly, that the Coulomb gauge is not the optimum gauge in the time dependent case.
		This is a slight disadvantage of the Lorentz gauge with respect to the Coulomb gauge.
		Incidentally, the fact that the part of the electric field which we ascribe to magnetic induction changes when we change the gauge suggests that the separation of the field into magnetically induced and charge induced components is not unique in the general time varying case (i.e.
	farside.ph.utexas.edu /teaching/em1/lectures/node40.html (714 words)

	[No title]
		] A massless spin-1 particle, such as the photon and gluons, whose existence is required by gauge invariance in a gauge theory; such particles can acquire mass through spontaneous symmetry breaking, as in the case of intermediate vector bosons.
		] The invariant of a surface specified by Gauss' theorem.
		At a point on a surface the product of the principal curvatures is an invariant of the surface, called the Gaussian curvature.
	www.accessscience.com /Dictionary/G/G5/DictG5.html (2128 words)

	Re: local gauge invariance
		This is the heuristic basis for locality: "The end result will only depend on things which are 'close' to me!" Now, as for the "gauge" part of it, it's not really anyone's fault.
		It's just that there is always an ambiguity on how one defines his/hers measurement device, and, in the end of the day, the net result should be independent of these arbitrarinesses.
		This is, to my knowledge, the heuristic reason for local gauge invariance.
	www.lns.cornell.edu /spr/2002-03/msg0040371.html (302 words)

	Pure gauge theories
		At the center of non-Abelian gauge theories are the gauge fields and gauge invariance.
		The problem is that gauge invariance is tied closely with spacetime dependence, involving derivatives.
		If one defines quantities on the lattice carelessly then one can use gauge invariance and one cannot expect that the theory would be a good approximation to continuum theories.
	www.physics.uc.edu /suranyi/conf-lectures/node16.html (269 words)

	Colloquium: "Historical Roots of Gauge Invariance"
		A number of reviews of gauge theories cover the period from about 1929 (Weyl's major paper on the subject) to the present day, with stress on the post-Yang-Mills epoch.
		The story continues with Maxwell, Lorenz, Helmholtz, Clausius, and Lorentz by which time the idea of different, equivalent gauges for the potentials in classical electromagnetism had been clarified completely.
		We then discuss the annus mirabilus, 1926, with Fock's discovery of the phase transformation of the wave function that must accompany a gauge change of the potentials.
	www.physics.berkeley.edu /calendar/data/1067468845.shtml (218 words)

	Local gauge invariance
		Local and momentum-independent interaction is invariant with respect to local gauge transformation, and hence energy densities (78) and (80) must then also be independent of the local gauge.
		Therefore, gauge transformation of the energy density can, in principle, be respected or not, depending on a choice of dynamics one makes.
		This obviously is the case for the pairing, spin, current, and spin-current p-p densities, while only specific combinations of kinetic, spin-kinetic, and tensor-kinetic densities are gauge invariant.
	info.fuw.edu.pl /~dobaczew/nppair60w/node8.html (269 words)

	Monopole Gauge Invariance
		To have invariance of (15), the transformation (16) must be accompanied by a shift in the electromagnetic gauge field [4]
		(43) of a theory which exhibits the analog of the monopole gauge invariance although it has no counterpart of the original electromagnetic gauge invariance.
		Sometimes, (20) is referred to as a ``singular gauge transformation" or ``general gauge transformation".
	www.physik.fu-berlin.de /~kleinert/kleiner_re203/node2.html (801 words)

	Class minutes---week 13
		But this disagrees with Dirac's quantization condition: we are leaving out the quantum charge, whose wave function also changes under the gauge transformation, by the phase factor exp(i(e/hbar c) alpha).
		Also, only if div B fails to vanish somewhere inside the sphere is it possible that there is no global vector potential for which B = curl A. As already mentioned, div B might not vanish if there is a singularity at the monopole, but this is not a physical model.
		Then the magnetic field is only part of a nonabelian gauge field that satisfies some generalization of Maxwell's equation.
	www.glue.umd.edu /~tajac/622c/622minutes13.html (1706 words)

	O'Raifeartaigh, L.: The Dawning of Gauge Theory.
		During the course of this century, gauge invariance has slowly emerged from being an incidental symmetry of electromagnetism to being a fundamental geometrical principle underlying the four known fundamental physical interactions.
		In the first stage (1916-1956) the geometrical significance of gauge-invariance gradually came to be appreciated and the original abelian gauge-invariance of electromagnetism was generalized to non-abelian gauge invariance.
		In the second stage (1960-1975) it was found that, contrary to first appearances, the non-abelian gauge-theories provided exactly the framework that was needed to describe the nuclear interactions (both weak and strong) and thus provided a universal framework for describing all known fundamental interactions.
	pup.princeton.edu /titles/5989.html (312 words)

	Demand for gauge invariance
		Is the gauge field a higher rank tensor in GR compared to EM because the field equations are also higher?
		The strong and weak field theories, modeled after EM, I suspect are also invariant under gauge transformation.
		We can thus conclude that at our current level of understanding which is deep, all known forces have fields that are invariant under gauge transformation.
	www.lns.cornell.edu /spr/2004-02/msg0058657.html (280 words)

	[No title] (Site not responding. Last check: 2007-10-07)
		Also of great importance is the method (shown in Section 4.A) for constructing the appropriate gauges needed in the RWM method to check that extinctions are not accidental results of the initial choice of gauge.
		This paper shows how the phase functions, requirement of gauge invariance, and other aspects of the Rokhsar-Wright-Mermin formulation are equivalent to the elements of a cohomology theory.
		Along with a review of the Type-I invariant being the condition for missing Bragg peaks and the Type-II invariant being the condition for necessary degeneracy, a third type of invariant is derived and discussed.
	ewald.cas.usf.edu /quasibiblio.txt (4282 words)

	[No title] (Site not responding. Last check: 2007-10-07)
		We present papers which deal with problems on gauge invariance of the S-matrix and related problems.
		The Landau-Khalatnikov gauge and the Fried-Yennie gauge are introduced in...
		The fact that Z_1=Z_2 is gauge dependent was shown by Johnson and Zumino in...
	www.physics.rutgers.edu /~zrwan/QED-historical/QED_Ref3.3.html (143 words)

	Predrag Cvitanovic´ - quantum field theory publications
		For me the conceptually most striking lesson of these long QED calculations were the amazing cancellations induced by gauge invariance.
		In the case of QED vertex corrections, the smallest gauge invariant set contributing to (m+m'+k)th order consists of m photon "strands" attached to the incoming electron, m' photon "strands" attached to the outgoing electron, and k photon "strands" crossing the external photon vertex.
		Mass-shell amplitudes for both QED and QCD are defined via dimensional regularization, and shown to to be gauge invariant trough a cancellation between UL and IR singularities.
	www.nbi.dk /~predrag/papers/preprQFT.html (655 words)

	Independent Nature of New Gauge Invariance (Site not responding. Last check: 2007-10-07)
		We now turn to demonstrating that the new monopole gauge invariance is completely independent of the original electromagnetic gauge invariance.
		The same thing will be seen to be true for the dual magnetoelectric and charge gauge invariances.
		The demonstration is given by presenting two counterexamples of systems which do not possess an original gauge invariance at all while possesing the new gauge invariances.
	www.physik.fu-berlin.de /~kleinert/kleiner_re203/node5.html (75 words)

	»»Theoretical Reviews««
		The concept of gauge invariance is now ubiquitous in elementary particle physics, and has become very important in pure mathematics also.
		It was written shortly after the awarding of the Nobel prizes to Sheldon Glashow, Steven Weinberg, and Abdus Salam for their work on the electroweak interaction (their Nobel lectures are reprinted in the back of the book), but before the discovery of the W and Z bosons in 1982.
		Attempts to solve chapter ending problems invariably lead to frustration, as the questions are vague, and the suggested results are impossible to obtain without consulting other, more detailed texts like Dejenqueres and Spanjaard.
	www.financial-book-review.com /Theoretical/Theoretical_50.html (1420 words)

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