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Topic: Gauge transformation

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Michael Faraday

	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.
		There are reps which transform covariantly pointwise (called by physicists gauge transformations of the first kind), reps which transform as a connection form (called by physicists gauge transformations of the second kind) (note that this is an affine rep) and other more general reps, such as the B field in BF theory.
	en.wikipedia.org /wiki/Gauge_theory (2365 words)

	Gauge - Wikipedia, the free encyclopedia
		Gauge blocks, precision measuring standards (Johansson or slip gauges).
		Gauge (knitting), the number of stitches in a given length.
		Gauge transformation, a member of a group of mathematical mappings used in physics.
	en.wikipedia.org /wiki/Gauge (176 words)

	Gauge theory (Site not responding. Last check: 2007-10-08)
		Gauge theories are a class of physical theories which are based on the idea that symmetry transformation s can only be performed locally.
		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 proton s and neutron s, similar to the action of the U(1) group on the spinor field s 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 interaction s - thereby motivating the search for a gauge theory of the strong force.
	www.serebella.com /encyclopedia/article-Gauge_theory.html (2371 words)

	Encyclopedia: Gauge theory
		Identifying the "charge" e with the usual electric charge (this is the origin of the usage of the term in gauge theories), and the gauge field A(x) with the four-vector potential of electromagnetic field results in an interaction Lagrangian Electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interactions.
		In theoretical physics, a gauge anomaly is an example of an anomaly: it is an effect of quantum mechanics - usually a one-loop diagram - that invalidates the gauge symmetry of a quantum field theory i.
		In electromagnetism, the Lorenz gauge condition is the gauge fixing in which where is the four-potential, the comma denotes a partial differentiation and the repeated index indicates that the Einstein summation convention is being used.
	www.nationmaster.com /encyclopedia/Gauge-theory (6944 words)

	Gauge theory -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-08)
		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.
		Pauli calls gauge transformation of the first type to the one applied to fields as, while the compensating transformation in is said to be a gauge transformation of the second type.
	www.absoluteastronomy.com /encyclopedia/g/ga/gauge_theory.htm (1991 words)

	Gauge transformation (Site not responding. Last check: 2007-10-08)
		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.
		The importance of gauge theories for physics stems from the tremendous success of the mathematical formalism in providing aunified framework to describe the quantum field theories of electromagnetism, the weak force and the strong force.
		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 groupis nontrivial.
	www.therfcc.org /gauge-transformation-89643.html (1445 words)

	Gauge transformation (Site not responding. Last check: 2007-10-08)
		TXL Source Transformation System Rule-based structural transformation is utilized as a paradigm for rapid generation of complex programs.
		Narrow Gauge Railway Society (UK) The NGRS publish the bi-monthly Narrow Gauge News and the quarterly journal The Narrow Gauge.
		Gauge 3 Society The society exists to support the building and running of 2 1/2" (63.5mm) gauge scenic model railways of standard gauge prototypes.
	www.serebella.com /encyclopedia/article-Gauge_transformation.html (583 words)

	gauge transformation (Site not responding. Last check: 2007-10-08)
		In physics, gauge theories are based on the idea that symmetry transformations can only be performed locally.
		If we have a principal bundle whose base space is space or spacetime and structure group is a Lie group G, then, the space of smooth (although in physics, we often don't deal with smooth functions) sections of this bundle forms a group, called the group of gauge transformations.
		In the theories of the electroweak interaction and quantum chromodynamics of the Standard Model of particle physics, the Lagrangians of bosons, which mediate interactions between fermions, are invariant under gauge transformations.
	www.yourencyclopedia.net /gauge_transformation.html (448 words)

	Gauge (Site not responding. Last check: 2007-10-08)
		Gauge is commonly used in the context of railways, where 'trackgauge' (often simply 'gauge') means the distance between the inside edges of the two rails forming the track (eg standard gauge, narrowgauge) and 'loading gauge' refers to the set of height and width profiles governing the maximum dimensions of railwayvehicles.
		In mathematics and physics, a gauge transformation is a member of a group of mappings to a space or a spacetime, where this group of mappings satisfies certain properties.
		Gauge theories inphysics postulate that symmetry transformations canonly be performed locally.
	www.therfcc.org /gauge-78066.html (296 words)

	Gauge
		In mechanics, a pressure gauge is a device for indicating liquid or gas pressure, a vacuum gage indicates gas pressure less than atomospheric pressure.
		Gauge is commonly used in the context of railways, where 'track gauge' (often simply 'gauge') means the distance between the inside edges of the two rails forming the track (eg standard gauge, narrow gauge) and 'loading gauge' refers to the set of height and width profiles governing the maximum dimensions of railway vehicles.
		The gauge is determined by the number of solid spheres of a diameter equal to the inside diameter of the barrel that could be made from a pound of lead.
	www.brainyencyclopedia.com /encyclopedia/g/ga/gauge.html (346 words)

	Gauge Symmetry Breaking and Boundary Conditions for Gauge Transformation (Site not responding. Last check: 2007-10-08)
		In gauge symmetry breaking, on the other hand, the resulting set is Gglobal/Hglobal and not Ggauge/Hgauge (where the "global" and "gauge" indices indicate the groups of global and gauge transformations respectively) as "naively" expected.
		Moreover, gauge transformations leave physical states invariant (in other words, states related by a gauge transformation are considered equivalent), and the vacuums are definitely physical states (and inequivalent ones, I guess, otherwise the division to sectors would be meaningless in the physical state space).
		Therefore, the gauge transformations may be classified by their limit in the infinity into a Gglobal group.
	www.lns.cornell.edu /spr/2000-03/msg0022791.html (335 words)

	2-Holonomy LEGO \| The String Coffee Table
		Gauge invariance of the global holonomy is a consequence of cancelling of adjacent ‘onion slices’:
		Note how it is sufficient for proving global gauge invariance to prove that every piece of holonomy transforms under gauge transformations only by being conjugated at its ‘boundary’; while the ‘internal’ conjugations mutually cancel.
		A gauge transformation on a piece of local 2-holonomy (which is a 2-morphism in a 2-group) is a ‘2-conjugation’:
	golem.ph.utexas.edu /string/archives/000503.html (1135 words)

	Gauge transformations (Site not responding. Last check: 2007-10-08)
		This is clearly a generalization of the gauge transformation which we found earlier for static fields:
		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.
	farside.ph.utexas.edu /teaching/em1/lectures/node40.html (714 words)

	Re: Category Theory and Physics \| The String Coffee Table
		A state of gauge theory is a principal fiber bundle with connection.
		That’s because these transition laws are formally nothing but gauge transformations (the transition from one patch to another is locally just a gauge transformation in the obvious sense), and gauge transformations need to be understood in any case.
		If the background gauge fields are Abelian, their contributions to the action will be their holonomies, but if they are non-Abelian, you get something else – basically you have to saturate the group indices so that you have a number for the action.
	golem.ph.utexas.edu /string/archives/000479.html (3853 words)

	[No title] (Site not responding. Last check: 2007-10-08)
		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...
		Zumino: Gauge Transformation of Propagators in Quantum Electrodynamics, Lectures on Field Theory and the Many-body Problem (Academic Press, London, 1961) p.27.
	www.physics.rutgers.edu /~zrwan/QED-historical/QED_Ref3.3.html (143 words)

	Gauge Transformation (Site not responding. Last check: 2007-10-08)
		Transformations of the polarizability from point to point induce phase shifts in the propagator analogous to impedance transformations along a wave transmission line.
		Lorentz transformations of the components of the Moments tensor can then be seen immediately as transformations in the values of inductance and capacitance.
		Gauge transformations affect the phase of the wave function.
	www.tjd-online.com /New/gauge.htm (413 words)

	Dialogue with Tom Van Flandern (Site not responding. Last check: 2007-10-08)
		I use gauge transformation of the second kind, a local gauge transformation within special and general relativity which conserves the action, and is the basis for all modern gauge field theory.
		This means that the e/m and gravitational fields would not be gauge invariant, and the foundation of gauge theory for the past sixty years collapses.
		It could be looked for in resgions of zero gravitational gauge field but non-zero gravitational potential field generated by the local or second gauge transformation.
	www.aias.us /Comments/dialog/cmnt02.html (430 words)

	Topics: Gauge Transformations
		Gauge transformation: A map between fields (or solutions of the dynamical equations) in a field theory under which the values of all physical observables are invariant; i.e., it applies to a field but is defined by a property of the theory.
		On Lie-valued 1-forms: Local gauge transformations ("of the second kind") are fiber-preserving diffeomorphisms in the pfb of a gt, which can be written as G-valued functions g(x) on M.
		Dirac's approach: Gauge transformations are applied to fields at a given t, aot spaceetime fields; The dynamics is modified by substituting the extended Hamiltonian (including all first-class constraints) for the total Hamiltonian (including only the primary first-class constraints).
	www.phy.olemiss.edu /~luca/Topics/g/gauge.html (273 words)

	Lattice evidence for center vortices
		Vortices are not defined as topological objects that are results of the singularities of the gauge fixing procedure.
		To see that consider that the gauge transformation can be transformed in two steps.
		Consequently, the plaquette that is intesected by the singularity of the gauge transformation is frustrated.
	www.physics.uc.edu /suranyi/conf-lectures/node24.html (745 words)

	Monopole Gauge Invariance
		To have invariance of (15), the transformation (16) must be accompanied by a shift in the electromagnetic gauge field [4]
		It must be emphasized that this transformation has no relation with the original gauge transformation (3).
		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)

	Gauge Theory(I) (Site not responding. Last check: 2007-10-08)
		The interaction between two particles is determined by the gauge field which is introduced to make the Lagrangian invariable under the local gauge transformation.
		The gauge transformation is defined as the automorphism of Lie group on operator field fundamentally, but since that transformation is difficult to calculate, we use Lie ring (algebra) as the operator on Hilbert space instead of Lie group.
		However since the expression of gauge transformation with Lie group is too difficult to calculate as I've mentioned above, we have to use perturbative method to distinguish between them.
	www.geocities.com /tontokohirorin/gauge3.htm (293 words)

	Gauge Invariance
		Gauge invariance of Maxwell's equations in the quantum form of the theory is directly related to an invariance under a local phase transformation of the quantum fields.
		In a global invariance the same transformation is carried out at all space-time points: it has an ``everywhere simultaneously'' character.
		The ultimate reason for this is that the global form of charge conservation would necessitate the instantaneous propagation of signals and this conflicts with special relativity.
	www.phys.ualberta.ca /~gingrich/phys512/latex2html/node30.html (440 words)

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