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Topic: Quantization (physics)

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	Quantization (physics) - Wikipedia, the free encyclopedia
		In physics, quantization is a procedure for constructing a quantum field theory starting from a classical field theory.
		One also speaks of field quantization, as in the "quantization of the electromagnetic field", where one refers to photons as field "quanta" (for instance as light quanta).
		Canonical quantization of a field theory is analogous to the construction of quantum mechanics from classical mechanics.
	en.wikipedia.org /wiki/Quantization_(physics) (673 words)

	Quantum mechanics - free-definition
		It also explains the behavior of many physical systems that contradict classical mechanics, such as the existence of stable atoms and the fact that the total radiation emitted by a fl body is finite.
		Examples of quantized observables include angular momentum, the total energy of a bound system, and the energy contained in an electromagnetic wave of a given frequency.
		The weak nuclear force and the electromagnetic force were unified, in their quantized forms, into a single quantum field theory known as electroweak theory.
	www.netlexikon.akademie.de /Quantum-mechanics.html (3315 words)

	Physics Today December 2003 - Stern and Gerlach: How a Bad Cigar Helped Reorient Atomic Physics
		A new center for experimental physics at the University of Frankfurt was recently named in honor of Stern and Gerlach (see figure 1).
		They were disappointed that invoking space quantization failed to elucidate the vexing problem of the "anomalous" Zeeman effect, the complex splitting patterns of spectral lines in a magnetic field.
		This direct demonstration of spatial quantization was immediately accepted as among the most compelling evidence for quantum theory (see the box at right).
	www.physicstoday.org /vol-56/iss-12/p53.html (4248 words)

	A CONCEPT OF QUANTUM GRAVITY
		While loop quantum gravity is still an approach that is a quantization procedure with a goal of constructing a projective Hilbert space of states, its two main features are that it does avoid the assumption of a "background metric", and concommitantly that field on which attention is focused is an affine connection.
		It says that real measureable physical objects are those that transform as tensors under the infinite dimensional pseudogroup of general coordinate transformations (the Bondi-Metzner-Sachs group) of the manifold and that the laws of physics should be form invariant (expressed tensorially) under that pseudogroup.
		In classical physics the readability or observation of the values of (q, p) is assumed selfevident; in quantum physics the connection observations and formalism is through expectation values of observables that are represented by operators.
	graham.main.nc.us /~bhammel/FCCR/qg.html (9755 words)

	Quantized Angular Momentum
		It is a characteristic of angular momenta in quantum mechanics that the magnitude of the angular momentum in terms of the orbital quantum number is of the form
		The relationship between the magnitude of the angular momentum and its projection along any direction is space is often visualized in terms of a vector model.
		This quantum number is used to characterize the splitting of atomic energy levels, such as the spin-orbit splitting which leads to the sodium doublet.
	hyperphysics.phy-astr.gsu.edu /hbase/quantum/qangm.html (343 words)

	Jem's Page: Thesis
		Unfortunately most solutions to physical gauge theories are perturbative, so in cases where asymptotic freedom is present, they only work for short distances(footnote).
		The physical formalism clearly enunciates the constraints and gauge invariance in pure Yang-Mills theory and identifies the physical degrees of freedom, aspects of the theory which are difficult to identify in Rajeev's paper.
		The quantization given in this paper is almost a closed case, although further work in this field, for instance coupling to point particles, such as in the article (cite), is possible.
	moray.ucc.gu.uwa.edu.au /~jem/thesis.html (1175 words)

	Wave nature of electron
		One of the implications of these quantized energy states is that only certain photon energies are allowed when electrons jump down from higher levels to lower levels, producing the hydrogen spectrum.
		This quantization of angular momentum is a crucial result and can be used in determining the Bohr orbit radii and Bohr energies.
		In t he Bohr theory, this classical result was combined with the quantization of angular momentum to get an expression for quantized energy levels.
	hyperphysics.phy-astr.gsu.edu /hbase/bohr.html (369 words)

	Rational Quantum Physics
		Schrödinger himself was of the opinion that the wave model for quantum processes in physical systems, for which the wave equation is an expression, is only a mathematical emergency solution, lacking a better understandable quantum physical theory.
		Finding that the physical space quantum, called elementary length, in our daily practical units (eg meter), is an extremely small number, we can not daily observe the consequences of quantization of space and time.
		Furthermore, the quantization of space and time require that the relativistic Lorentz transformations are quantized, too, being thus transformation equations between space and time quantum numbers.
	louis.rostra.dk /quant_03.html (2429 words)

	Re: VRD: first ,second and nth quantisation
		It is sometimes helpful to think of first quantization as the quantization of angular momentum in integer multiples of the fundamental unit h-bar.
		For electrons, protons or any other charged particles, quantization of particle number is essentially the same as quantization of the electric charge.
		Quantization of particle numbers is not merely a result of charge conservation.
	www.madsci.org /posts/archives/may2000/959709127.Ph.r.html (330 words)

	Home Page of Physics 483 (Site not responding. Last check: 2007-10-22)
		In many areas of Physics, such as High Energy Physics, Gravitation, and in Statistical and Condensed Matter Physics, the understanding of the essential physical phenomena requires the consideration of the collective effects of a large number of degrees of freedom.
		Physics 483 is the first half of a two-semester sequence of courses in Quantum Field Theory.
		Quantization of the Dirac Theory: ground state, spectrum, quantum numbers of excitations, causality and spin-statistics theorem.
	w3.physics.uiuc.edu /~efradkin/phys582/physics483.html (825 words)

	Physics Graduate Course Descriptions (Site not responding. Last check: 2007-10-22)
		Prerequisites: PHYS 304, 406, and 508, or consent of instructor.
		Fundamentals of Health Physics will be presented with an emphasis on problem-solving and computer modeling.
		Continuation of the basic Health Physics sequence, including: neutron production and interaction with matter; methods of radiation detection; radiation dosimetry; chemical and biological effects of radiation; radiation protection standards; shielding; dosimetric models; accelerator, reactor and medical health physics.
	www.iit.edu /~bcps/database/search.cgi/Physics/Physics:/frontend/grad/grad_course_listing (939 words)

	School of Physics: People : Professors : David Finkelstein
		Heisenberg's quantization moved theories from the peaks to adjacent ridges, leaving them still singular and unstable but less so.
		General quantization moves theories to the valley, leaving singularity behind; specifically to full matrix algebras.
		The progressive relativization of physics through classical mechanics, special and general relativity and fl holes, quantum mechanics, quantum gauge field theory, and beyond.
	www.physics.gatech.edu /people/faculty/dfinkelstein.html (1977 words)

	Abstracts of Papers and Talks (Site not responding. Last check: 2007-10-22)
		Student answers and interviews were used to build questions for a questionnaire to examine the initial knowledge state of students on concepts of quantization and photons, which was given to a small sample of typical physics students.
		The Physics Education Research Group is conducting an ongoing study to determine if these or other difficulties are seen in introductory physics classes at OSU and to develop methods for addressing them.
		In the Physics Education Research Group at OSU, we are investigating students' conceptually understanding of internal energy and how this understanding affects their performance in problem solving.
	www.physics.ohio-state.edu /~physedu/projects/details/abstract.htm (2837 words)

	THEORETICAL PHYSICS: EINSTEIN AND QUANTIZING CHAOS (Site not responding. Last check: 2007-10-22)
		Epstein's name has not survived in the context of the Sommerfeld rule, and the quantization condition discussed by Einstein is now referred to as either Bohr-Sommerfeld or WKB (Wentzel-Kramers-Brillouin) quantization.
		With his introduction of the photon concept in 1905, his clear identification of wave-particle duality in 1909, his founding of the quantum theory of radiation in 1917, and his treatment of the Bose gas and its condensation in 1925, Einstein laid much of the foundation of the theory.
		The same resonance occurs in a simplified model of the two main classical vibrational modes of the carbon dioxide molecule, and the first mathematical analysis of the swing-spring was inspired by this model.
	scienceweek.com /2005/sw050902-6.htm (1547 words)

	[No title] (Site not responding. Last check: 2007-10-22)
		October 2003-December 2003: Adjunct Professor at the Department of Physics and Astronomy, University of Mississippi, USA, and Visiting Professor at the Department of Theoretical Physics, University of Torino, Italy.
		Physics with friendly fl holes of known mass at a muon collider, invited colloquium at the University of Mississippi, Oxford MS, April 27th, 2004.
		Quantization of Constrained Systems: Application to Quantum String Cosmology, contributed talk at the XII Italian Conference on General Relativity and Gravitational Physics, Rome, Istituto Superiore di Sanita`, September 27th, 1996.
	www.phy.olemiss.edu /~cavaglia/personal/cv.txt (4200 words)

	Ovid Jacob's Research
		My work so far has been mostly in particle physics, but have worked in string theory as well as in statistical physics (spin-glasses) and in computer networks.
		It turns out that the question of quantization can be posed as a initial value problem, which is what I am doing, or it can be looked at as a mixed initial value boundary problem, as does Heinzl and Werner (Regensburg preprint 93-3).
		I have been able to formulate heavy quark effective theory in this Penrose quantization and have computed the renormalization constants for both the full QCD theory and for the effective theory.I hope to be able to develop an effective theory for B-mesons in null-surface quantization.
	www.mishkan.com /research.html (971 words)

	[No title] (Site not responding. Last check: 2007-10-22)
		Cavity and external quasi-mode functions associated with the quasi-mode theory of macroscopic canonical quantization are then obtained via an idealised choice of output mirror parameters.
		The coupling constants describing photon exchange processes between the single cavity quasi-mode associated with each Fabry-Perot resonance and various external quasi-modes are calculated, and their slow dependence on the external quasi-mode frequency shows that the conditions for irreversible Markovian damping of the cavity quasi-mode are satisfied.
		The research project is a collaboration between the Lasers and Optics Group in the Department of Physics and Mathematical Physics at The University of Adelaide and DSTO.
	www.physics.uq.edu.au /people/billm/qonewsletter/011199.txt (2836 words)

	HISTORY OF PHYSICS: EINSTEIN AND RADIATION (Site not responding. Last check: 2007-10-22)
		His 1905 paper on quantization of the radiation field (often referred to, inaccurately, as the photoelectric-effect paper) was built on simple statistical arguments, and in subsequent years he returned repeatedly to questions centered on statistics and thermal fluctuations.
		The oscillators for which Planck proposed energy quantization were fictitious, and his theory for flbody radiation lacked obvious physical consequences.
		In physics, an ideal radiator or absorber absorbs and thus emits radiation of all frequencies equally and fully.
	scienceweek.com /2005/sw050325-5.htm (2416 words)

	Physics 365 (Site not responding. Last check: 2007-10-22)
		One-body and two-body operators in first and second quantization: total linear and angular momentum, kinetic energy, particle density.
		Hamiltonian in first and second quantization, ground state energy per particle in first-order perturbation theory.
		Historical interlude: Hartree method in atomic physics (1928), generalization to Hartree-Fock method (1932), one-body mean field (HF potential).
	www.physics.vanderbilt.edu /volker/p365/course_content.html (366 words)

	Quantization errors - GameDev.Net Discussion Forums (Site not responding. Last check: 2007-10-22)
		Quantization means, basically, taking a number and rounding it to fit some step size.
		Quantization is kind of a key factor in the sampling theory that is used in digital images and video (think textures and texture sampling), digital audio (think wave and mp3 files that are quantized to a certain bit rate), and other things.
		Oh, right, so the quantization error is the error between the actual sin/cos and the value you get by quantizing the input angle to one of the angles in the table.
	www.gamedev.net /community/forums/topic.asp?topic_id=271283&whichpage=1& (309 words)

	MULTIPLE FACETS OF QUANTIZATION AND SUPERSYMMETRY
		Arkady Vainshtein is Professor of Physics and a member of the Theoretical Physics Institute at University of Minnesota.
		He is the author of 160 research papers in particle physics and quantum field theory.
		He is a Fellow of the American Physical Society and a recipient of the 1999 Sakurai Prize for Theoretical Particle Physics from this society.
	www.worldscibooks.com /physics/5025.html (307 words)

	FUN
		Here's a bunch of fun stuff, mostly written by me. It's mainly about math and physics, but there's also some about astronomy, biology, and other things.
		This is not for the faint-hearted; a less demanding version can be found in Jorge Pullin's newsletter, Matters of Gravity.
		octonions - an introduction to the octonions and their connections to geometry, topology, group theory, and mathematical physics.
	math.ucr.edu /home/baez/FUN.html#mathematics (1153 words)

	Books - "quantization physics" - Find, Compare, and Buy at Shopping.com
		Noncovariant Gauges: Quantization of Yang-Mills and Chern-Simons Theory in Axial-Type Gauges
		Quantization and Coherent States Methods: Proceedings of the XI Workshop on Geometric Methods in Physics Bialowieza, Poland 7-14 July 1992
		Quantization, Nonlinear Partial Differential Equations, and Operator Algebra: 1994 John Von Neumann Symposium on Quantization and Nonlinear Wave Equations June 7-11, 1994 Massachusetts Institute of Technology Cambridge
	www.shopping.com /xPP-Books-quantization_physics-~all-nonfiction_category_books (243 words)

	Einstein's Unknown Insight and the Problem of Quantizing Chaos - Physics Today August 2005
		Chaotic systems were beyond the reach of an ingenious coordinate-invariant quantization scheme developed by Albert Einstein, and to this day, their quantization remains a challenge.
		At the 11 May 1917 meeting of the German Physical Society, Albert Einstein, then a professor at the University of Berlin, presented the only research paper of his career that was written on the quantization of energy for mechanical systems.
		Douglas Stone is the Carl A. Morse Professor of Applied Physics and Physics at Yale University in New Haven, Connecticut.
	www.physicstoday.org /web_bin/pt/vol-58/iss-8/p37.shtml (4224 words)

	Abhay Ashtekar : Publications
		Ashtekar, Quantization of the Radiative Modes of the Gravitational Field, In: Quantum Gravity 2; Edited by C. Isham, R. Penrose, and D. Sciama (Oxford University Press, Oxford, 1981).
		Ashtekar and J. Winicour, Linkages and Hamiltonians at Null Infinity, Journal of Mathematical Physics, 23, 2410-2417 (1982).
		Ashtekar, Quantum Geometry and its Ramifications, In: The Future of Theoretical Physics and Cosmology, A volume in honor of Stephen Hawking's 60th birthday, edited by G. Gibbons, Paul Shellard and Stuart Ranking (Cambridge University Press, 2003).
	gravity.psu.edu /people/Ashtekar/publications_full.html (4019 words)

	No Title
		The self-energy effects on the rotation symmetry in the lightcone quantized scalar fields scattering, Phys.
		Higher-Fock States and the Covariance of the Light-Front Quark Model, in DPF 2000, to be published in International Journal of Modern Physics A (with H.M.Choi), Columbus,Ohio, August 9-12, 2000.
		Served as a Referee of the papers submitted to Physical Review Letters, Physical Review C and D, Nuclear Physics A and Journal of Physics G and the proposals submitted to Department of Energy (DOE), National Science Foundation (NSF), National Research Council (NRC) and Korea Science and Engineering Foundation (KOSEF).
	www.physics.ncsu.edu /ntg/crj2/vitae/ji1.html (4498 words)

	Many Body Physics 620 (Site not responding. Last check: 2007-10-22)
		Many body physics, 620, will be an introduction to the study of non relativistic systems containing a large number of degrees of freedom.
		It is an essential course for all students intending to study physics at the graduate level.
		Many body physics provides the right language to describe the results of experimental investigations and we will connect experimental results to theory via the notions of correlation and response functions.
	www.physics.rutgers.edu /~kotliar/course/620.html (447 words)

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