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Topic: Second-quantized

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Quantization (physics) According to the explanation a quantized theory deals with operators and normal wave functions while second quantization makes also the functions operators that makes the number of also quantized i.e. quantization is a special formalism of quantum suited to deal with variable number of It pertains to quantum field theory and draws its name from a understanding of the formalism as quantifying once an already quantized theory. Quantization in quantum theory is the taking of discrete rather than continuous values for some physical quantities (e.g. www.freeglossary.com /Quantization_%28physics%29

Definition of Quantization (physics) According to the formal explanation a quantized theory deals with operators and normal wave functions, while second quantization makes also the wave functions operators, that makes the number of particles also quantized, i.e. Second quantization is a special formalism of quantum theory suited to deal with variable numbers of particles. In this sense second quantization is a full quantization. www.wordiq.com /definition/Quantization_%28physics%29

Quantum field theory - Wikipedia, the free encyclopedia In contrast, in the second quantized approach we will simply list the number of particles in each of the single-particle states, with the understanding that the multi-particle wavefunction is symmetric. In second quantized form, we write this as Classical field theory is the same as classical mechanics of an infinite number of dynamical quantities (say, particles). en.wikipedia.org /wiki/Quantum_field_theory

On the Quantization of the Red-Shifted Light from Distant Galaxies It is therefore concluded that at least some classes of galaxy redshifts are quantized in steps that are simple fractions of 72 km per second. Even allowing for this change to a 36 km per second interval, the chance of accidentally producing such a preference is less than 4 in 1000. By far the most intriguing result of these initial studies was the suggestion that galaxy redshifts take on preferred or "quantized" values. www.ldolphin.org /tifftshift.html

Application of the second quantization method:Phonons The Hamiltonian modeling He3 is easily written down using our second quantized formalism: From its first quantized expression, we have to minimize the potential energy without worrying too much about kotliar6.rutgers.edu /udo/prof/ta/He/TAphonons2ab.htm

Second Quantization Here we will only summarize the anticommutation relations between creation and annihilation operators, and then proceed to express the Hamiltonian in second quantized form for spatial orbitals, rather than for spin orbitals. Szabo and Ostlund [ 1 ] give a good introduction to second-quantized operators. Then we will use these results to derive the Hamiltonian in terms of the unitary group generators. www.uam.es /docencia/quimcursos/Docs/Knowledge/Fundamental_Theory/ci/node22.html

Canonical quantization - Wikipedia, the free encyclopedia So the process of canonical quantization of a field theory was called second quantization in the early literature. This wavefunction is a field variable which could then be quantized to deal with the theory of many particles. The first corresponds to positive frequencies, and the second, to negative. en.wikipedia.org /wiki/Second_quantization

EP1033883 Matsushita european software patent - Video signal encoding method, video signal encoder, and program recorded medium - Gauss Thereafter, a quantizer is selected which, when the AC components are quantized and variable length coded in the first compression system and the second compression system, enables the code amount of both the AC components after the variable length codings to be set within the thus obtained allocated code amount for the AC components. Alternatively, the second system code amount may not be a total code amount, but a part of the total, for example, a code amount of a partial period immediately before the transformed signal which is the object of the quantization. The quantizer 503 quantizes AC components from the orthogonal transformer 502 by using the quantizer which is selected by the quantization estimator 505, and outputs the result to the variable length coder 504. gauss.ffii.org /PatentView/EP1033883

Oversampled A/D converter using filtered, cascaded noise shaping modulators (US4862169) 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. The second circuit portion functions to remove the error of the first circuit portion from an output signal by providing a signal component, which when added with the output of the first circuit portion cancels the error of the first circuit portion. www.delphion.com /details?pn=US04862169__

[8] What is color quantization? If the maker quantized to a different number of colors than what you can display, you'll either waste display capability or else have to requantize to reduce the number of colors (which usually results in much poorer image quality than quantizing once from a full-color image). Therefore quantization is always required to display a color JPEG on a colormapped display, regardless of the image source. Furthermore, you will be able to take advantage of future improvements in quantization algorithms, or purchase better display hardware, to get a better view of JPEG images you already have. www.faqs.org /faqs/jpeg-faq/part1/section-8.html

courses.html Second quantization for fermions: creation and destruction operators, field operators, representation of observables. Second quantization for bosons: creation and destruction operators, observables. One and two particle operators in second quantization. cabtep5.cnea.gov.ar /particulas/diploma/courses.html

A CONCEPT OF QUANTUM GRAVITY In this sense, the second orthodox stream is "more correct" than the first, but still even string theory begins as a fundamentally incorrect quantization of a classical model. The second rank symmetric gravimetric tensor field that generalizes the gravitational potential of Newtonian gravity theory can be seen, modulo locally operative coordinate transformations, as determining 1) a local lightcone structure and 2) a conformal factor. Such a quantization method starts with a mathematical formulation of the kinematics and dynamcis of a classical system and then applies quantization rules of transformation to express the quantized version of the kinematics and dynamcis of the same system. graham.main.nc.us /~bhammel/FCCR/qg.html

TMPh V. P. Maslov - Ultra-second quantization and ``ghosts" in quantized entropy Maslov – Ultra-second quantization and ``ghosts" in quantized entropy TMPh V. Maslov - Ultra-second quantization and ``ghosts" in quantized entropy Here we show that in both the bosonic and fermionic cases, the quantized entropy introduced as an operator in special Fock spaces containing a new variable, called the statistical spin, depends on some variables that do not affect any physical results and are hence called “ghosts." math.ras.ru /tmph/scripts/tmph2.cgi?paperinfo=866

Second quantization in a quon-algebra The explicit form of the normal ordered expansion series for a second quantized observable is a quadratic form of the creation and annihilation operators. From the early days of quantum field theory it has been known that observables from quantum mechanics can be extended to observables in quantum fields: the so-called process of second quantization. In particular, reselling and systematic downloading of files is prohibited. stacks.iop.org /0305-4470/26/4643

Dr. Donald H. Kobe D.H. Kobe, "Gauge invariance in second quantization: applications to Hartree-Fock and generalized random-phase approximations," Phys. D.H. Kobe, “A relativistic-Schrödinger equation for a photon and its second quantization,” Foundations of Physics 29, 1203-1231 (1999). D.H. Kobe and J.Q. Liang, "Aharonov-Bohm Scattering as Due to the Lorentz Force of the Return Flux," Second International Symposium on the Foundations of Quantum Mechanics--In the Light of the New Technology, Topical Meeting on the Aharonov-Bohm Effect, Tokyo, Japan, 31 August - 4 September, 1986. www.phys.unt.edu /faculty/Kobe.htm

nth quantization One easy answer is that it's the Hilbert space for a second quantized string, i.e. This is not as silly as it may seem, since if we take the harmonic oscillator Hamiltonian N = dK(1) on K(K(0)) and second quantize it, we get a Hamiltonian dK(N) on K(K(K(0))) which is precisely the usual Hamiltonian for a massless scalar quantum field on a cylindrical spacetime! As Edward Nelson said, " first quantization is a mystery, but second quantization is a functor "! math.ucr.edu /home/baez/nth_quantization.html

Path Integrals Prague 2005 Abstract: Systems with constraints pose problems when they are quantized. class constraints that invalidate conventional Dirac constraint quantization procedures. path integrals, enables one to directly impose a regularized form of the quantum constraints. bimbo.fjfi.cvut.cz /~pathintegrals/participants.php?pkey=6   (52 words)

Normal-Ordered Second-Quantized Operators 21, §4), a normal-ordered string of second-quantization operators is one in which we find ``all annihilation operators standing to the right of all creation operators.'' Normal ordering of such strings provides a bookkeeping system by which the nonzero matrix elements of second-quantized operators may be more easily identified. [4.1] which produces a nonzero result is the one containing no second-quantized operators; all other terms involve application of an annihilation operator to By rearranging a given string of annihilation and creation operators into a normal-ordered form, matrix elements of such operators between determinantal wavefunctions may be evaluated in a relatively algorithmic manner. zopyros.ccqc.uga.edu /lec_top/cc/html/node12.html   (352 words)

Units: P The pascal is the standard pressure unit in the MKS metric system, equal to one newton per square meter or one "kilogram per meter per second per second." Sounds impressive, but in traditional English terms a pascal is only 0.000 145 pounds per square inch (0.020 885 lbf/ft Since one pound of mass is 0.453 592 kilograms and the acceleration of gravity averages 9.806 65 meters per second per second at the surface of the Earth, one pound force equals the product of these two numbers, 4.448 221 615 newtons. This is the shortest time that is meaningful in our understanding of the laws of physics, representing the scale at which time itself may become quantized (discrete) rather than continuous. www.unc.edu /~rowlett/units/dictP.html   (9494 words)

Connexions You will compare the response of the filter having unquantized coefficients with that of a filter having coefficients quantized as a single, fourth-order stage and with that of a filter having coefficients quantized as a cascade of two, second-order stages. You will implement a fourth-order, elliptical, low-pass infinite impulse-response (IIR) filter as a cascade of two second-order sections. Infinite impulse response (IIR) filters are an alternative to finite impulse response (FIR) filters. cnx.org /content/similarity?b_start:int=10&objectId=m10479   (443 words)

nth quantization One easy answer is that it's the Hilbert space for a second quantized string, i.e. It should now be clear that we are dealing with the Hilbert space of the quantized harmonic oscillator! So let us apply the second quantization functor K: Hilb -> Hilb to our Hilbert space 0, and see what happens. math.ucr.edu /home/baez/nth_quantization.html   (443 words)

JCE 2004 (81) 1423 [Oct] Galileo's Finger: The Ten Great Ideas of Science (Peter Atkins) Atkins finesses the interesting phenomenon of zero-point energy in quantized systems by showing the quantized levels with the continuous classical ones, but not pointing out that there is not an allowed level at zero energy. I found his discussion of entropy to be especially good, in the same way as his excellent book The Second Law gets to the heart of thermodynamics. Atkins, P. The Second Law; Freeman: New York, 1994. jchemed.chem.wisc.edu /Journal/Issues/2004/Oct/abs1423_1.html   (789 words)

Classical Covariant Field Theory It explores the limits of what can be achieved with purely classical notions, and shows how these classical notions have a deep and important connection with the second quantized field theory, which follows on from the Schwinger Action Principle. It explores the limits of what can be achieved with purely classical notions, and shows how these have a deep and important connection with the second quantized field theory, which follows on from the Schwinger Action Principle. Its pragmatic view of field theory focuses on issues which are usually omitted from quantum field theory texts and catalogs results which are often hard to find in the literature. isbn.nu /0521813638   (494 words)

source Be sure to print out graphs showing the differences between the filter responses of the unquantized notch filter, the notch filter quantized as a single fourth-order section, and the notch filter quantized as two second-order sections. One important issue that must be considered when IIR filters are used on a fixed-point processor is that the filter coefficients that are actually used are quantized from the "exact" (high-precision floating point) values computed by Matlab. Since, unlike with FIR filters, this quantization can actually have significant impacts in the response of the filter, it is worth examining the effects of quantizing the filter coefficients on the actual filter response. cnx.rice.edu /content/m10623/2.1/source   (832 words)

Graduate Calendar 2005-2006 Angular momentum and rotation operations; Wigner and Racah coefficients; several and many electron problem in atoms; variational and Hartree-Fock formalism; introduction to second quantized field theory; scattering theory. Relativistic quantum field theory; second quantization of Bose and Fermi fields; reduction and LSZ formalism; perturbation expansion and proof of renormalizability of quantum electrodynamics; calculations of radiative corrections and applications. Phenomenology This course will consist of a variety of seminars and short lecture courses, and will cover topics of immediate interest to the research program of the department. www.gs.carleton.ca /calendars/current/sci/oc_physics.html   (832 words)

Technical Reports 2002 In this paper we show that there is a link between the combinatorics of the canonical basis of a quantized enveloping algebra and the monomial bases of the second author arising from representations of quivers. We prove that some reparametrization functions of the canonical basis, arising from the link between Lusztig's approach to the canonical basis and the string parametrization of the canonical basis, are given on a large region of linearity by linear functions arising from these monomial bases for a quantized enveloping algebra. The seemingly distinct areas of group theory, formal language theory, and complexity theory interact in an important way when one considers decision problems in groups, such as the question of whether a word in the generators of the group represents the identity or not. www.mcs.le.ac.uk /techreports/TechReports02.html   (832 words)

The Physics of a Global Episodic Quantum Frequency Change For example, consider the mass ratio M. This begins with Newton’s second law: F = MA solved for M. Next, work W divided by length L is substituted for force F, and V Thus, the apparent expansion of the universe can be explained by a sequence of infrequent but real episodic quantized contractions of the observer’s rulers and atomic length scales that result in quantized mass and density gains as his atoms age. If the invariant frequency model is true, then energy is conserved but the speed of light changes in the same ratio as the length scale, and Einstein’s postulate regarding the universal constancy of the speed of light is false. home1.gte.net /res00bfl/redshift_physics.htm   (6257 words)

A Fundamental Introduction to the Compact Disc Player It is the difference between the actual voltage to be represented and the quantized voltage level that induces quantization error. The residual signal is also fed into the second order noise shaper, where the output of the second quantizer, Q2, is differentiated and then summed with the output of the first noise shaper to create the final output signal [6]. However, quantization error becomes quite significant when a low-level signal approaches the level of the LSB, then the quantizing error actually becomes the signal, and therefore is an audible component of the output. www.tc.umn.edu /%7Eerick205/Papers/paper.html   (6257 words)

Signal (information theory) - Wikipedia, the free encyclopedia As a result, the values of such a signal are restricted to belong to a finite set; in other words, it is quantized. CDs contain discrete signals representing sound, recorded at 44,100 samples per second. In short, the difference between them is that digital signals are discrete and quantized, as defined below, while analog signals possess neither property. en.wikipedia.org /wiki/Signal_(information_theory)   (855 words)

On the Quantization of the Red-Shifted Light from Distant Galaxies It is therefore concluded that at least some classes of galaxy redshifts are quantized in steps that are simple fractions of 72 km per second. The redshift differences bunch up near multiples of 72 km per second. Large-scale redshift quantization needed to be confirmed by analyzing redshifts of an entirely different class of objects. www.ldolphin.org /tifftshift.html   (855 words)

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