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Topic: Fock space

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Quantum field theory

	Fock Space
		In this context, it is known as (bosonic) Fock space.
		Fock space is used to analyze such quantum phenomena as the annihilation and creation of particles.
		By considering fermionic Fock space on the category of finite-dimensional vector spaces, we obtain a model of full propositional linear logic, although the model is somewhat degenerate in that certain connectives are equated.
	www.cis.upenn.edu /~bcpierce/types/archives/1994/msg00090.html (354 words)

	Fock space -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-11-06)
		Technically the Fock space is the Hilbert space made from the (A union of two disjoint sets in which every element is the sum of an element from each of the disjoint sets) direct sum of
		is the operator which symmetrize or antisymmetrize the space, whereby providing the Fock space describing particles obeying (additional info and facts about bosonic) bosonic (ν=+) or (additional info and facts about fermionic) fermionic (ν=-) algebra respectively.
		Fock space does not describe finite temperature physics as well.
	www.absoluteastronomy.com /encyclopedia/f/fo/fock_space.htm (694 words)

	Fock state - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-11-06)
		A Fock state, in quantum mechanics, is any state of the Fock space with a well-defined number of particles in each state.
		If we limit to a single mode for simplicity (doing so we formally describe a mere harmonic oscillator), a Fock state is of the type
		Fock states form the most convenient basis of the Fock space.
	en.wikipedia.org /wiki/Fock_state (149 words)

	Encyclopedia: Fock space
		Technically the Fock space is the Hilbert space made from the direct sum of tensor products of single-particle Hilbert spaces: In abstract algebra, the direct sum is a construction which combines several vector spaces (or groups, or abelian groups, or modules) into a new, bigger one.
		is the operator which symmetrize or antisymmetrize the space, whereby providing the Fock space describing particles obeying bosonic (Î½=+) or fermionic (Î½=-) algebra respectively.
		In quantum mechanics, the wavefunction associated with a particle such as an electron, is a complex-valued function Ïˆ defined over a portion of space and normalized in such a way that In Max Borns probabilistic interpretation of the wavefunction, the amplitude squared of the wavefunction Ïˆ(x)2 is the...
	www.nationmaster.com /encyclopedia/Fock-space (874 words)

	The Wavelet Digest :: View topic - Preprint: "Wavelet representations and Fock space on positive matrices" by ...
		We show that every biorthogonal wavelet determines a representation by operators on Hilbert space satisfying simple identities, which captures the established relationship between orthogonal wavelets and Cuntz-algebra representations in that special case.
		This is accomplished by showing that each of these wavelets yields a collection of operators acting on Hilbert space which satisfy simple identities, and which contain the Cuntz relations [J. Cuntz, Simple C*-algebras generated by isometries, Communications in Mathematical Physics 57 (1977), 173-185] as a special case.
		Toward this end, we introduce a general Fock space Hilbert space construction which reduces to unrestricted Fock space in the familiar cases.
	www.wavelet.org /phpBB2/viewtopic.php?t=5116&view=next (358 words)

	A calculus on Fock space and its probabilistic interpretations - Privault (ResearchIndex) (Site not responding. Last check: 2007-11-06)
		A calculus on Fock space and its probabilistic interpretations - Privault (ResearchIndex)
		A calculus on Fock space and its probabilistic interpretations (1999)
		A calculus on Fock space and its probabilistic interpretations.
	citeseer.ist.psu.edu /56642.html (538 words)

	Banach Spaces & Linear Logic
		Fock space was introduced in quantum field theory as a framework for modelling the annihilation and creation of particles.
		Finally, the Fock space associated to a Banach space or Hilbert space has a concrete representaton as a space of holomorphic functions, suitably defined.Thus, the Kleisli category can reasonably be thought of as a category of generalized holomorphic functions.
		The point of the second paragraph is that Banach spaces and Hilbert spaces have a notion of norm, whereas ordinary vector spaces do not.
	www.cis.upenn.edu /~bcpierce/types/archives/1993/msg00110.html (302 words)

	Fock Space (Site not responding. Last check: 2007-11-06)
		This construction arose independently in quantum physics, where it is considered as a canonical model of quantum field theory.
		In this context, the construction is known as (bosonic) Fock space.
		When considering Banach or Hilbert spaces, the Fock construction provides a model of weakening cotriple in the sense of Jacobs.
	www.math.mcgill.ca /rags/fock/fock.abstract.html (258 words)

	sciforums.com - what is Fock space?
		the textbooks say that a fock space is the multiparticle extension of a hilbert space.
		(Q) H represents the space of states of one particle of mass m and spin s; in short, H is then called the "one-particle Hilbert space".
		there is a separate hilbert space for all the kets with the same excitation number, and the fock space is the direct product of all those hilbert spaces.
	www.sciforums.com /printthread.php?t=13578 (235 words)

	Fock Space - index page - Free MP3 downloads, CDs, Bio Info, Tour Dates, Lyrics and More!" (Site not responding. Last check: 2007-11-06)
		In Fock Space, music can be neither created nor destroyed, just transformed into different shapes.
		In Fock Space balance to each note is its inversion, balance to each note lenth is eternal silence minus the note lenth and balance to each note dynamics is the Fourier Transform of a duck.
		Fragments of sound are sampled across all Fock Space and creates a mixture of many different musical styles.
	artists.iuma.com /IUMA/Bands/Fock_Space (85 words)

	Re: Fock space
		> "The Fock space F is an (integrable) module for the quantum group > U_q(widehat{sl}_{}) of the affine special linear group.
		Start with your favourite Hilbert space, H. (For quantum phsics, it is always a complex Hilbert space.) 2.
		In physics, variants of this Fock space are in use, namely the symmetric and the antisymmetric Fock spaces, F_{+}(H) and F_{-}(H); they're suited to the description of bosons resp.
	www.lns.cornell.edu /spr/1999-09/msg0018305.html (920 words)

	Kevin Costello (Site not responding. Last check: 2007-11-06)
		This is a line in the Fock space associated to periodic cyclic homology, which is a symplectic vector space.
		On the field theory side, the BV operator has an interpretation as the quantised differential on the Fock space for periodic cyclic chains.
		A modular operad is constructed from moduli spaces of Riemann surfaces with boundary; this modular operad is shown to be the modular envelope of the A-infinity cyclic operad.
	www.ma.ic.ac.uk /~kcostell (627 words)

	Project 2301-1 (Site not responding. Last check: 2007-11-06)
		T are to be interpreted as the Fock space upto random time T and after T respectively, (ii) the semigroup property of composition of Stop-time etc. However, a strong short-coming of these formulations were noted soon after by Accardi-Sinha, viz.
		A "truely infinite toy fock space" was developed which approximates the usual Bosonic Fock Space.
		In this toy Fock space, one can describe a 'random walk' and stop (both-sided) using Poisson jump-times and then take the appropriate limit to get the required result.
	www.iconsoftec.com /cefipra/CEFIPREN/project/th01/prj23011.htm (724 words)

	No Title
		We discussed the Fock space of the quantized Klein-Gordon field, then canonical quantization of other boson fields.
		The Fock space, which contains all physical states of the quantum field, is spanned by the energy eigenstates.
		With that done, canonical quantization goes through as usual, giving a Fock space of multiphoton states of both polarizations, with photons being bosons.
	www.emory.edu /PHYSICS/Faculty/Benson/380-96/notes/33/33.html (426 words)

	Re: Fock space
		More precisely, instead of using L^2(R^n) as our Hilbert >> space of states, we use HL^2(C^n), the Hilbert space of holomorphic >> functions on C^n that are square-integrable with respect to a Gaussian >> measure centered at the origin.
		Well, there are indeed situations where phase space is more important than configuration space, and even lots of situations where phase space isn't the cotangent bundle of any configuration space - and in these situations, geometric quantization (the description of quantum states as sections of a line bundle over phase space) becomes very important.
		But there are also lots of situations where both configuration space and phase space are important, and then it's lots of fun to relate geometric quantization to the good old "Schroedinger representation", where quantum states are treated as functions on configuration space.
	www.lns.cornell.edu /spr/1999-10/msg0018699.html (814 words)

	[No title]
		The purpose of this paper is to point out that, if we consider the massless Nelson model in a non-Fock representation of the CCR for time-zero fields, then it has a ground state even in the case where no infrared cutoff is made.
		\subsection{The SNM} The coordinate of the configuration space $\R^{dN}$ of the $N$ particles is denoted $q=(q_1, \cdots,$ $q_N) \in \R^{dN}$ with $q_j:=(q_{j1}, \cdots, q_{jd}) \in \R^d$ ($j=1, \cdots,N$).
		\end{description} The Hilbert space for state vectors of the quantum scalar field of the SNM is given by \begin{equation} {\cal F}_{\rm b} :=\oplus_{n=0}^{\infty} \otimes_{\rm s}^nL^2(\R^d), \end{equation} the Boson Fock space over $L^2(\R^d)$, where $\otimes_{\rm s}^nL^2(\R^d)$ is the symmetric tensor product of $L^2(\R^d)$ ($\otimes_{\rm s}^0L^2(\R^d):=\C$).
	www.ma.utexas.edu /mp_arc/papers/00-478 (3084 words)

	Fock space - TheBestLinks.com - Algebra, Boson, Fermion, Hilbert space, ... (Site not responding. Last check: 2007-11-06)
		Fock space - TheBestLinks.com - Algebra, Boson, Fermion, Hilbert space,...
		Fock space, Algebra, Boson, Fermion, Hilbert space, Identical particles, Pauli...
		You can add this article to your own "watchlist" and receive e-mail notification about all changes in this page.
	www.thebestlinks.com /Fock_space.html (560 words)

	Physics Help and Math Help - Physics Forums - View Single Post - Degenerate vacua in QFT
		Therefore, the transformed vacuum\nandgt; vac\'andgt; of the "alpha,beta" Fock space cannot be a linear combination\nandgt; of any vectors in the "a,b" Fock space.
		This is what we mean when we say\nandgt; that the two Fock spaces are orthogonal, and what we mean when we say that\nandgt; they\'re "unitarily inequivalent".\nandgt;\nandgt; Hopefully, it\'s now clear what is meant by "the different vacua are not\nandgt; states in the same hilbert space".\nandgt;\nandgt; ------------------------------------------------------------\nandgt;\nandgt; Ref [1] Umezawa, Matsumoto and Tachiki.
		After all, you\ndo have the unitary transformation G between the two Fock spaces that\npreserves the CCRs.
	www.physicsforums.com /showpost.php?p=404754&postcount=3 (585 words)

	Vortrag Wysoczanski (Site not responding. Last check: 2007-11-06)
		We introduce the \textit{weakly monotone Fock space}, on which these operators act.
		This space in a natural way one derives from the papers by Pusz and Woronowicz on twisted second quantization.
		It was observed by Bo{\.z}ejko that, by taking $q=0$, for the $q-CAR$ relations one obtains the Muraki's monotone Fock space, while for the $q-CCR$ relations one obtains the weakly monotone Fock space.
	www.math-inf.uni-greifswald.de /sonstiges/wysoczanski.html (129 words)

	ipedia.com: Vladimir Aleksandrovich Fock Article (Site not responding. Last check: 2007-11-06)
		Vladimir Aleksandrovich Fock was a Soviet physicist, who did foundational work on quantum mechanics.
		His primary scientific contribution lies in the development of quantum physics, although he also contributed significanly to the fields of mechanics, theoretical optics, theory of gravitation, physics of continous medium.
		He gave his name to Fock space, the Fock representation and Fock state, and developed the Hartree-Fock method in 1930.
	www.ipedia.com /vladimir_aleksandrovich_fock.html (190 words)

	Special topic course
		Fundamental observables as operators in the Fock’s space (energy-momentum, charge, projection of spin, number of particles and antiparticles).
		Definition of the path integral for a quantum system with one degree of freedom: state space (Hamiltonian) form of the path integral formula for the matrix element of the quantum evolution operator.
		Derivation of the state space version of the path integral using Weyl’s quantization.
	www.math.ttu.edu /~vshubov/outline_quantum.html (518 words)

	Unlooping the LQG string \| The String Coffee Table
		But it is legitimate and you obtain a different Hilbert space (that is is not separable because the orthonormal system is labelled by intervals rather than integers but this is only a consequence but not essential).
		So usually this pathological Hilbert space realization is ruled out by the assumption of weak continuity but Thomas has promised to give me a reference to a paper that discusses the relevance of this pathological Hilbert space in some condensed matter system.
		really is in the Fock space state and check that the diffeomorphism group is really only represented projectively (that is with the phase from the central charge) thus establishing that as one would expect the usually construction can also be rewritten in this GNS formalism.
	golem.ph.utexas.edu /string/archives/000369.html (2393 words)

	GAP Manual: 71 The Specht Share Package
		The Fock space F is an (integrable) module for the quantum group U_q(widehat{sl}_{}) of the affine special linear group.
		) of the Fock space corresponding to the
		All of these functions can also be applied to elements of the Fock space (see Specht); in which case they correspond to the action of the generators E_i and F_i of U_q(widehat{sl_e}) on F.
	schmidt.ucg.ie /gap/CHAP071.htm (7123 words)

	[No title] (Site not responding. Last check: 2007-11-06)
		More precisely: not all symplectic linear transformations on the classical phase space H can be implemented as unitary operators on the corresponding Fock space F(H) - only those that are "close to unitary".
		Remember, the classical phase space H starts out life as a symplectic vector space, but we must make it into a complex Hilbert space before we can define the Fock space F(H) as a Hilbert space.
		Once H has been made into a complex Hilbert space, it makes sense to ask whether a symplectic linear transformation T: H -> H is unitary or not.
	www.math.niu.edu /~rusin/known-math/00_incoming/fock (418 words)

	PhilSci Archive - Year: 2002
		Frigg, Roman (2002) On the Property Structure of Realist Collapse of Quantum Mechanics and the So-Called "Counting Anomaly".
		Holland, Peter and Brown, Harvey R. (2002) The non-relativistic limits of the Maxwell and Dirac equations: the role of Galilean and gauge invariance.
		Kryukov, Alexey (2002) Coordinate formalism on abstract Hilbert space: Kinematics of a quantum measurement.
	philsci-archive.pitt.edu /view/year/2002.html (2467 words)

	Citebase - Wavelet representations and Fock space on positive matrices
		Stavropoulos, Multiresolution analyses of abstract Hilbert spaces and wandering subspaces, The Functional and Harmonic Analysis of Wavelets and Frames (San Antonio, 1999) (L.W. Baggett and D.R. Larson, eds.), Contemp.
		Samolenko, The kernel of Fock representations of Wick algebras with braided operator of coecients, Pacic J. Math.
		We construct representations of a q-oscillator algebra by operators on Fock space on positive matrices.
	www.citebase.org /cgi-bin/citations?id=oai:arXiv.org:math/0204034 (1709 words)

	Citebase - On the Fock space for nonrelativistic anyon fields and braided tensor products
		Authors: Goldin, G. Majid, S. We realize the physical N-anyon Hilbert spaces, introduced previously via unitary representations of the group of diffeomorphisms of the plane, as N-fold braided-symmetric tensor products of the 1-particle Hilbert space.
		This perspective provides a convenient Fock space construction for nonrelativistic anyon quantum fields along the more usual lines of boson and fermion fields, but in a braided category.
		In particular we show how the algebraic structure of our anyonic Fock space leads to a natural anyonic exclusion principle related to intermediate occupation number statistics, and obtain the partition function for an idealised gas of fixed anyonic vortices.
	www.citebase.org /cgi-bin/citations?id=oai:arXiv.org:hep-th/0307168 (1169 words)

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