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Topic: Loop quantization

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	Loop quantum gravity - Wikipedia, the free encyclopedia
		Loop quantum gravity (LQG), also known as loop gravity and quantum geometry, is a proposed quantum theory of spacetime which attempts to reconcile the seemingly incompatible theories of quantum mechanics and general relativity.
		At the core of loop quantum gravity is a framework for nonperturbative quantization of diffeomorphism-invariant gauge theories, which one might call loop quantization.
		LQG is a quantization of a classical Lagrangian field theory which is equivalent to the usual Einstein-Cartan theory in that it leads to the same equations of motion describing general relativity with torsion.
	en.wikipedia.org /wiki/Loop_quantization (3183 words)

	Noise shaping - Wikipedia, the free encyclopedia
		Any feedback loop functions as a filter, so by creating a feedback loop for the error itself, the error can be filtered as desired.
		The effect here is that the quantization error itself (and not the valid signal) is put into a feedback loop.
		By using noise shaping we can effectively spread the quantization error around so that more of it is focused on frequencies that we can't hear as well and less of it is focused on frequencies that we can hear.
	en.wikipedia.org /wiki/Noise_shaping (1020 words)

	Company Home Page
		A phase locked loop (PLL) is a negative feedback loop in which the phase of a generated signal is forced to follow that of a reference signal.
		The existence of quantization error in the DPA output is due to the fact that the output is a “guess” at the input and is never equal to the desired value.
		Figure 7 shows a waveform of quantization phase error where the input to the modulator is equal to 0.25, the clock frequency is at 25 MHz and the integer part of the division ratio is 100.
	www.rfengineer.cc /fracn1.htm (7023 words)

	Optimizing Color Quantization for ASP.NET Images (ASP.NET Technical Articles) (Site not responding. Last check: 2007-08-18)
		To loop through the bytes in the source image will require some unsafe code, as we'll be using pointers to speed up the process.
		Looping through the image bits is fairly simple—a pointer is set to the start of the image in memory and is incremented onto the next pixel.
		In this instance we now loop over each pixel in both the source and destination bitmaps, and assign the computed palette index of the source pixel to the destination pixel.
	msdn.microsoft.com /library/en-us/dnaspp/html/colorquant.asp (3095 words)

	online copy? Background Independent Quantum Gravity: a Status Report (Site not responding. Last check: 2007-08-18)
		Loop quantum gravity is based on the canonical formulation of general relativity expressed in terms of connection variables.
		The quantization program can be presented in terms of two (technically) distinguishable steps: in the first step the constraints governing general covariant dynamics are represented as quantum operators in a Hilbert space of kinematical states.
		Loop quantum gravity is an attempt to describe a background independent quantization of general relativity (see [1] for a review).
	www.physicsforums.com /showthread.php?t=15539 (1197 words)

	Amazon.com: Loop Spaces, Characteristic Classes and Geometric Quantization (Progress in Mathematics): Books: Jean-Luc ... (Site not responding. Last check: 2007-08-18)
		The line bundle over the loop space of a smooth manifold is constructed using the sheaf of groupoids over the manifold, and is called the anomaly line bundle associated to the sheaf of groupoids.
		When the (free) loop space is generalized to the space of oriented singular knots, and the manifold is 3-dimensional, the author shows how to obtain a bundle over this space, and shows the relation to geometric quantization.
		The central extension of the loop group is considered, interestingly, in terms of action functionals, an approach which has its origins in physics.
	www.amazon.com /exec/obidos/tg/detail/-/0817636447?v=glance (1740 words)

	Spin networks, spin foams and loop quantum gravity
		Loop quantum gravity is a theory that results from the canonical quantization of general relativity.
		Loop Quantum Cosmology, Boundary Proposals, and Inflation, 2003.
		Loop Quantization of Maxwell Theory and Electric Charge Quantization, 1997.
	jdc.math.uwo.ca /spin-foams (2360 words)

	The LQG Landscape \| Musings
		If the loop quantum gravity programme is successful, it should construct a quantum theory of the gravitational field to which one can add just about any other consistent quantum field theory for other fields.
		It is an old speculation in physics that, once the gravitational field is successfully quantized, it should serve as the natural regulator of infrared and ultraviolet singularities that plague quantum field theories in a background metric.
		In loop quantum gravity, it is their assumption that the only task is to find a different description of the classical system, a field redefinition, and then it works inevitable at the quantum level.
	golem.ph.utexas.edu /~distler/blog/archives/000855.html (12814 words)

	Intuitive content of Loop Gravity--Rovelli's program - Page 22 (Site not responding. Last check: 2007-08-18)
		Quantization proceeds in the spirit of Dirac: First one defines an algebra of basic kinematical observables and represents it through operators on a suitable Hilbert space.
		While this result is particularly important for loop quantum gravity, we are rather general: The precise definition of the abstract *-algebra of the basic kinematical observables we give could be used for any theory in which the configuration variable is a connection with a compact structure group.
		Using an effective classical Hamiltonian obtained from loop quantization of vacuum Bianchi I model, exact solution is obtained which is non-singular due to a discreteness parameter.
	www.physicsforums.com /showthread.php?p=530876 (3581 words)

	[music-dsp] DSD to PCM conversion (Site not responding. Last check: 2007-08-18)
		The big insight of noise shaping/sigma-delta is that it is possible to shape the noise floor so that some minute, low-end fraction of the total bandwidth of the 1-bit signal forms a linear, low noise channel, and the quantization noise is moved upwards in frequency, while keeping the signal 1-bit.
		From another perspective, the accumulator is the ideal synthesis filter and the loop around it is a naive optimization process which attempts to synthesize a binary string which would drive it along the input waveform.
		The lowpass filter inside the loop is basically the optimal, linear reconstruction filter we're optimizing the bitstream for, and the loop is the optimizer.
	shoko.calarts.edu /pipermail/music-dsp/2005-June/030733.html (1145 words)

	LQG - Loop Quantum Gravity: Spin foam vacuum LQG versus false 'stringy theory'!
		The spin foam vacuum of loop quantum gravity is the only consistent mathematical formulation of Feynman's path integrals that seems to have the potential of addressing the physical process by which the vacuum operates.
		Loop theorists disagree, because they believe that we need a proper theory of quantum gravity as a prerequisite for any theory of everything.
		Nicolai and Peters (as well as Zamaklar) are string theorists, and given the extremely heated controversy of the last few years between the LQG and string theory community over who has the most promising approach to quantum gravity, one wonders how even-handed their discussion is likely to be.
	lqg.blogspot.com /2006/01/spin-foam-vacuum-lqg-versus-false.html (3741 words)

	Milano String Theory Group Home Page (Site not responding. Last check: 2007-08-18)
		Loop variables in nonperturbative quantum gravity and geometrical aspects in quantum theories
		A model for the canonical (nonperturbative) quantization of gravitational theories has been formulated in the framework of loop variables by Ashtekar, Rovelli and Smolin.
		Holonomy algebras and spin networks states in the loop quantization techniques in quantum gravity.
	www.mi.infn.it /~strings/research/loop.htm (115 words)

	3.5 “Quantum geometry”
		The loop representation is complicated by the existence of Mandelstam identities [190] among holonomies of loops, but for the case of the torus universe, a complete, explicit description of the states is again possible [26
		In the “timelike sector,” in which the traces of the two holonomies are both less than two, the loop transform is a simple Fourier transformation, and Chern-Simons and loop quantization are equivalent.
		This is a consistent procedure, but many of the resulting states in the Cauchy completion are no longer functions of loops in any clear sense; they correspond instead to “extended loops” [136], whose geometrical interpretation is not entirely clear.
	www.univie.ac.at /EMIS/journals/LRG/Articles/lrr-2005-1/articlesu13.html (1024 words)

	Oversampled A/D converter using filtered, cascaded noise shaping modulators (US4862169)
		An analog input signal is quantized into a digital equivalent value with a finite quantization error associated therewith in a first circuit portion.
		second filter means having an input coupled to the output of the integrator of the first loop, and an output, said second filter means filtering the output of the integrator of the first loop by a second transfer function to provide the input terminal signal for the second quantization loop;
		output means having an input coupled to the loop output signal of the second quantization loop for attenuating the loop output signal of the second quantization loop.
	www.delphion.com /details?pn=US04862169__ (435 words)

	LQG - Loop Quantum Gravity
		A loop is a rotational transformation in the vacuum.
		Loop Quantum Gravity suggests that gravity is mediated by a spin foam vacuum, and this is the main rival to string 'theory'.
		Loop Quantum Gravity researcher Lee Smolin has answered 'critics' (mainly string 'theorists' who believe in unobservables) on Peter Woit's blog, LQG for Skeptics, http://www.math.columbia.edu/~woit/wordpress/?p=330.
	lqg.blogspot.com (10911 words)

	[No title] (Site not responding. Last check: 2007-08-18)
		quantization: adjust the grid used to determine the position and duration parameters.
		This is a low pass filter with a 24dB/octave slope.
		pan: position of the loop in the stereo field.
	www.nicolasfournel.com /gloops.htm (226 words)

	Sony Acid Loop-Based Composition Software (Windows) - SameDayMusic.com
		Quantize disparate loops to a common groove, create (new in version 5) grooves from scratch, apply any number of the supplied grooves, and even extract grooves from existing loops and apply them to other samples.
		You can also create your own loops in the Chopper and add them to the timeline in real-time during playback via keyboard commands for live mixing.
		Adjust the timing of a track, or quantize and map multiple tracks or loops to a common groove.
	www.samedaymusic.com /product--SNYACID (3571 words)

	Keykit tool: Riff (Site not responding. Last check: 2007-08-18)
		The Riff tool is useful for looping phrases (repeating them endlessly), and is often used as a target of the Bang tool.
		The Loop button is a toggle switch - if you turn it on, the phrase will be played repeatedly until you explicitly terminate it, either by turning the Loop mode off or by clicking the mouse within the phrase window.
		The "Loop Quant->" item lets you select the value by which the loop repeat time will be quantized.
	www.nosuch.com /keykit/doc/lib/wriff.html (321 words)

	Table of contents for Library of Congress control number 94041549 (Site not responding. Last check: 2007-08-18)
		Field-antifield description of the anomalous theories 22.Transfer matrix quantization of general relativity, and the problem of time 23.
		Quantization of 2+1 gravity for g=1 and g=2 29.
		Generalized canonical quantization of gauge theories with polarized second-class constraints 34.
	www.loc.gov /catdir/toc/cam027/94041549.html (298 words)

	Course #85, Phase Locked Loops for Wireless Communication Systems
		The concepts of open and closed loop gain, phase and amplitude margin and their link to the dynamical behavior are introduced.
		As the loop filter is a key element in any PLL, its dimensioning based on lock time and spurious requirements.
		A model of the digital fractional spurious compensation is used, and in a second step we perform a quantization noise simulation and extract a rule of thumb for practical usage.
	www.cei.se /085.htm (720 words)

	Luboš Motl's reference frame: A very meaningful paper on loop quantum gravity
		in which they review what assumptions and results they consider important about loop quantum gravity, and what do they consider to be the most important questions that would have to be answered before loop quantum gravity might be considered a serious candidate theory to say something about quantum gravity.
		They start with saying that the Wilson loop quantization of gauge theories has been a failure, and therefore it's not clear why it should be a success for gravity.
		They show that the physical meaning of the Wilson loops in LQG differs from gauge theories, and the scalar product is much more likely to vanish in LQG - which is associated with its non-separability - while in gauge theory the correlators of Wilson loops are nonzero and continuous functions of the shapes.
	motls.blogspot.com /2005/01/very-meaningful-paper-on-loop-quantum.html (3293 words)

	Abstracts of papers (Site not responding. Last check: 2007-08-18)
		We present an implementation of Wilson's renormalization group and a continuum limit tailored for loop quantization.
		I show, using this quantization scheme, how both non-relativistic quantum mechanics and quantum field theory can be given a "general boundary" formulation.
		It maps the partition function as well as the expectation values of generalized non-Abelian Wilson loops (spin networks) to expressions involving only finite-dimensional unitary representations, intertwiners and characters of G. In particular, all group integrations are explicitly performed.
	www.matmor.unam.mx /~robert/abstracts/papers.html (3368 words)

	3.2 Chern-Simons quantization
		For compact gauge groups, the quantization of Chern-Simons theory is well understood [278, 243, 244, 116, 34].
		This is the most poorly understood case; an explicit quantization of the algebra holonomies exists for genus one (see below) and genus two [214], but more general results do not yet exist.
		As far as I know, the relationship between this work, which is based on a Hamiltonian formalism and combinatorial quantization, and that of Witten and Hayashi [280, 155], which is based on geometric quantization, has not yet been explored.
	www.univie.ac.at /EMIS/journals/LRG/Articles/lrr-2005-1/articlesu10.html (638 words)

	Nucleosome Repositioning via Loop Formation -- Kulic and Schiessel 84 (5): 3197 -- Biophysical Journal
		The solid lines separate loops with different geometric characteristics: simple (1, 2, and 3), crossed (4, 5, and 6), and "exotic" (7, 8, 9, and 10) loop shapes.
		the elastic energy prevails strongly over entropy, whereas for large loops, the entropy starts to dominate the behavior, producing a shallow energy minimum in the crossover regime which roughly defines the predominant loop size.
		The small loops were already discussed by Schiessel et al.
	www.biophysj.org /cgi/content/full/84/5/3197 (5963 words)

	AACEnc 2.5.9.7, SF - Hydrogenaudio Forums
		Anyway, this method has completely different quantization and coding kernel and some other changes, like bit allocation / bitres control - currently it is not yet fully finished, but it is capable of delivering very good results.
		I say, 2 loop quantization module is too demanding in computational requirement..
		Then again, 2-loop quantization can be done very efficiently - for example, in current Nero - under normal bit/sample load (around 1.4) SFE is not at all faster than 2-loop quantization (sometimes 2-loop is faster, and I can't explain why..
	www.hydrogenaudio.org /forums/index.php?act=ST&f=14&t=15991 (1313 words)

	Loop Quantum Cosmology
		Quantized spacetime: photons with different energies should have slightly different speeds (modified dispersion relations; gamma & cosmic rays).
		"Loop quantum gravity and quanta of spacetime: a primer";
		Holonomies and fluxes are better for quantization: Smeared versions of the fields obtained by natural integration along curves and surfaces.
	olympus.het.brown.edu /chep/lqc.html (353 words)

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