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Topic: Vacuum expectation value

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	YablonVacuumForceMasses
		Jay Yablon who has a web page at http://home.nycap.rr.com/jry/FermionMass.htm is a patent lawyer (think of Einstein's patent clerk career) who has done a great piece of independent thinking that he probably would not have been able to do had he been an establishment postdoc instead of a patent lawyer who studied on his own.
		The vacuum expectation value v = 252.5 GeV and
		Maybe since the tauon is given in terms of the electromagnetic force strength and the vacuum, and since the W+/- Boson acts on both leptons and quarks, this version of the W+/- Boson mass comes from looking at the vacuum in terms of both electromagnetic (leptonic) and color (quark) charges.
	www.valdostamuseum.org /hamsmith/YablonVacuumForceMasses.html (956 words)

	Vacuum expectation value - Wikipedia, the free encyclopedia
		In quantum field theory the vacuum expectation value (also called condensate) of an operator is its average, expected value in the vacuum.
		The vacuum expectation value of an operator O is usually denoted by
		One of the best known examples of the vacuum expectation value of an operator leading to a physical effect is the Casimir effect.
	en.wikipedia.org /wiki/Vacuum_expectation_value (277 words)

	Vacuum state - Wikipedia, the free encyclopedia
		If the quantum field theory can be accurately described through perturbation theory, then the properties of the vacuum are analogous to the properties of the ground state of a quantum mechanical harmonic oscillator (or more accurately, the ground state of a QM problem).
		In the Standard Model, the non-zero vacuum expectation value of the Higgs field, arising from spontaneous symmetry breaking, is the mechanism by which the other fields in the theory acquire mass.
		The VEV may break some of the internal symmetries of the Lagrangian of the field theory.
	en.wikipedia.org /wiki/Vacuum_state (396 words)

	IngentaConnect Vacuum polarization of a massless scalar field in the background ... (Site not responding. Last check: 2007-10-19)
		Vacuum polarization of a massless scalar field in the background of a global monopole with finite core
		In this paper, we analyse the vacuum polarization effects of a massless scalar field in the background of a global monopole considering its inner structure.
		Specifically we investigate the effect of its structure on the vacuum expectation value of the square of the field operator, andlanglehat{Phi}ˆ2(x)rangle ;, admitting a non-minimal coupling between the field with the geometry: andxi {cal R}hat{Phi}ˆ2 ;.
	www.ingentaconnect.com /content/iop/cqg/2005/00000022/00000016/art00009 (234 words)

	2 From Semiclassical to Stochastic Gravity (Site not responding. Last check: 2007-10-19)
		The source here is the expectation value of the stress-energy operator for the matter fields in some quantum state in the spacetime, a classical observable.
		The final expectation value of the stress-energy operator using a reasonable regularization technique is essentially unique, modulo some terms which depend on the spacetime curvature and which are independent of the quantum state.
		The Einstein equation which has the expectation value of the stress-energy operator of the quantum matter field as the source is known as the semiclassical Einstein equation.
	www.univie.ac.at /EMIS/journals/LRG/Articles/lrr-2004-3/articlese2.html (410 words)

	Johann Rafelski, Homepage, Professor of Physics, University of Arizona
		Many features of the structured vacuum have been studied in the past 20 years with a variety of methods, but one aspect, the appearance of a glue `condensate' field, i.e vacuum expectation value (VEV) of the gluon field-correlator, in the vacuum state is of particular relevance.
		The VP effect is based in the response of the vacuum to highly inhomogeneous field-strength, and is in general interpreted as a dielectric particle-hole (electron-positron) photon polarizibility.
		Nonlinear QED vacuum effects were in depth explored in the limit that gradients of the electromagnetic fields are insignificant on the scale of the electron Compton wave length.
	www.physics.arizona.edu /~rafelski/vacuum.html (1895 words)

	Zero-point energy Summary
		In quantum field theory, it is a synonym for the vacuum energy, an amount of energy associated with the vacuum of empty space.
		In cosmology, the vacuum energy is taken to be the origin of the cosmological constant.
		In quantum perturbation theory, it is sometimes said that the contribution of one-loop and multi-loop Feynman diagrams to elementary particle propagators are the contribution of vacuum fluctuations or the zero-point energy to the particle masses.
	www.bookrags.com /Zero-point_energy (3494 words)

	[No title]
		In a quantum-field representation the condensate is described by a field with non-vanishing vacuum expectation value $\phi_0$, possibly depending on the spacetime coordinate $x$.
		It is known that in general by moving a type II superconductor (of which the HTC are one example, that is, with a structure of superconducting and non-superconducting regions) in an external field or by applying to it an AC, one causes resistive phenomena, since the super-currents' pattern is unable to follow the fields variations.
		The existence of a critical threshold for the value of the induced cosmological term $\mu^2(x)$ is theoretically appealing and in reasonable agreement with the experimental observations.
	www.amasci.com /freenrg/jhs.txt (8135 words)

	The Pion Formfactor Experiment
		Fig.2 Change of expectation value of PHI (we use PHIbar to stand for this) due to a constant external matter source J. In case (a) PHIbar changes continuesly with J. In case (b), as J increases, there is a critical value at which PHIbar makes a sudden jump.
		Consequently, we have avoided the apportunity to study coherent phenomena which may be connected with vacuum.
		We know that Z0 mass is believed to be propotional to the expectation value of PHI(x) (we know that Higgs mechanism is also a good example of spontanious symmetry breaking), so it is a good testing of the formation of the domain or vacuum phase transition.
	www.jlab.org /~xu/vacuum.html (1725 words)

	ToyHiggs.nb
		An expectation value of zero is therefore forbidden, such that the potential energy has a delta function at zero.
		In this discrete model, the vacuum energy density, also called quantum fluctuations of the vacuum or zero-point energy, results from the position indeterminacy and apparent random vibration of each spacetime point within its small volume of virtual space.
		This uncertainty is determined by the vacuum expectation value of the Higgs field.
	home.earthlink.net /~dolascetta/ToyHiggs.html (2661 words)

	Rhett Herman-Chapter 1
		This is necessary since $\nu=0$, a value for which the generalized $\zeta$ function does not converge, is the value of interest in quantum field calculations.
		Candelas and Howard \cite{ch} calculated $\langle\phi^{2}\rangle_{ren}$ for the Hartle-Hawking vacuum in the Schwarzschild spacetime in the region exterior to the horizon.
		The point-splitting procedure is capable of yielding a DS approximation for both the vacuum polarization $\langle\phi^{2}\rangle$ (which is directly proportional to $G^{(1)}$) and the vacuum expectation value of the stress energy tensor $\langle T_{\mu\nu}\rangle$ (which is assembled from $G^{(1)}$ and its derivatives).
	www.runet.edu /~rherman/thesis/chap1.html (3687 words)

	Astronomical Glossary
		The vacuum is not simple, since the inherently probabilistic nature of quantum theory implies that unpredictable events, such as the chance materialization of an electron and its antiparticle, the positron, can occur at any time.
		The value of the Higgs field (a constant value different from zero) is called a system's Vacuum Expectation Value.
		The value of this depends only on the temperature, and is independent of the volume (unless all the vapor condenses or all the liquid evaporates).
	www.angelfire.com /stars5/astroinfo/gloss/v.html (3256 words)

	p-Adic Higgs mechanism
		The real counterpart for the thermal expectation value (obtained by canonical identification) for the mass squared is extremely sensitive to the statistical degeneracy of the state with given quantum numbers and in general the mass squared expectation value is of the order of CP_2 mass =about 10^(-4) Planck mass.
		Contrary to the simplest expectations, some of the elementary particle quantum numbers reside on boundaries of CP_2 type extremal and some in its interior: a crucial element of the model is the compensation of color quantum numbers giving rise to a correct correlation between color and electroweak quantum numbers.
		The value of k cannot be predicted at this state but for very natural choise of k the known masses of elementary particles can be reproduced in accuracy better than one percent.
	www.helsinki.fi /~matpitka/padmasses.html (1305 words)

	Calculation of Cosmological Baryon Asymmetry in Grand Unified Gauge Models (1982)
		-violating vacuum expectation value, which may be associated either with a complex field or with a pseudoscalar real field.
		Symmetry restoration usually occurs at a temperature of the same order as the vacuum expectation value of the Higgs condensate and the mass of the corresponding Higgs boson [15,6].
		In general, the presence of a large vacuum expectation value for a Higgs field in a complex representation of the gauge group lowers the rank of the effective gauge symmetry by breaking at least one of the U(1) invariances associated with the Cartan subalgebra.
	www.stephenwolfram.com /publications/articles/cosmology/82-calculations/4/text.html (1763 words)

	Normal ordering and VEV subtraction (Site not responding. Last check: 2007-10-19)
		Since the\nfield operators are actually operator valued distributions, this product\nis expected to be divergent (pp.86-87).\n\nA general prescription for regulating this divergence is normal\nordering.
		Although the product\nphi(x)phi(x) and its expectation value andlt;phi(x)phi(x)andgt; with respecto to\nany chosen state are ill defined, the product phi(x)phi(y) and its\nexpectation value andlt;phi(x)phi(y)andgt; is a well defined bidistribution on\ntest functions in spacetime.
		This state is often called a \'vacuum state\',\nthough this is not quite appropriate, unless you allow the vacuum\nto carry gravitational and electromagnetic fields.
	www.physicsforums.com /showthread.php?t=76288 (3294 words)

	Citebase - Vacuum Expectation Value of the Higgs Field and Dyon Charge Quantisation from Spacetime Dependent Lagrangians (Site not responding. Last check: 2007-10-19)
		Citebase - Vacuum Expectation Value of the Higgs Field and Dyon Charge Quantisation from Spacetime Dependent Lagrangians
		Vacuum Expectation Value of the Higgs Field and Dyon Charge Quantisation from Spacetime Dependent Lagrangians
		This is then used to obtain an estimate of the vacuum expectation value of the Higgs field,it viz.
	www.citebase.org /abstract?id=oai:arXiv.org:hep-th/0210174 (209 words)

	Holism and Nonseparability in Physics (Stanford Encyclopedia of Philosophy)
		In Newtonian spacetime, the kinematical behavior of a system of point particles under the action of finite forces is supervenient upon ascriptions of particular values of position and momentum to the particles along their trajectories during the collision.
		In that case, it would rather be the probability distribution conditional on a complete specification of the values of the hidden variables that should be taken to constitute irreducible dispositions of the system concerned.
		But it is not clear that vacuum expectation values of products of field operators defined at n-tuples of distinct spacetime points represent either qualitative intrinsic physical properties of these n-tuples or physical relations between them.
	plato.stanford.edu /entries/physics-holism (8216 words)

	Electroweak interaction Summary
		Unlike other fields, which have the value zero when there are no particles present, the Higgs field has a constant nonzero component, called its vacuum expectation value, or VEV.
		This unification of two seemingly unrelated interactions is one of the most important accomplishments in theoretical physics in the twentieth century, and it sparked a whole industry of physicists trying to further unify the remaining fundamental forces.
		It is possible to construct theories in which the vacuum does not share all the symmetries of the theory; this is called spontaneous symmetry breaking.
	www.bookrags.com /Electroweak_interaction (3394 words)

	PowerPedia:Zero point energy - PESWiki
		Despite the definition, the concept of zero-point energy, and the hint of a possibility of extracting "free energy" from the vacuum, has attracted the attention of amateur inventors.
		For almost all quantum-mechanical systems, the lowest possible expectation value that this operator can obtain is not zero; this lowest possible value is called the zero-point energy.
		One obvious difficulty with this association is that the zero-point energy of the vacuum is absurdly large.
	peswiki.com /index.php/Zero_Point_Energy (1813 words)

	Zero Point Energy
		In reality, the motionless system generally has plenty of energy: potential, internal, gravitational, etc. Only at the theoretical zero point, which could only possibly be found in the furthest reaches of space vacuum, would a quantum physical system have no tappable energy.
		In science and science fiction, zero point energy is sometimes referred to in the concept of extracting energy from the vacuum.
		Zero point energy is sometimes referred to as the vacuum expectation value, with the energy at that point called the vacuum energy.
	www.iscid.org /encyclopedia/Zero_Point_Energy (221 words)

	Bosonization (Site not responding. Last check: 2007-10-19)
		The reason\nnormal ordering is necessary is to regularize and eliminate some\ndivergences that arise in some ground state expectation values.
		The\nsimplest example is the infinite charge density or energy contributed\nto the vacuum by the "Dirac sea" when the Dirac field is quantized.\n\nNow, I\'ve seen many claims about normal ordering in the literature, and\nit is not obvious to me that they are equivalent or follow one another.\nHere are the normal ordering prescriptions that I\'ve run into:\n\nA,B,C,...
		Vacuum expectation values are defined _only_ for power series in\nthe a(x),a^*(x) with all terms in normally ordered form, and then they\nare defined as their constant term.\n\n\nArnold Neumaier\n\n\n\n\n

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Igor Khavkine wrote:

www.physicsforums.com /showthread.php?t=27677 (3145 words)

	Higgs Fields? - Advanced Physics Forums (Site not responding. Last check: 2007-10-19)
		At lower energies, the doublet of scalar fields gets a non-zero vacuum expectation value (a phase change of the vacuum) and appear to be massless in this vauum.
		I believe that the acceleration of a particle is resisted by the zero-point vacuum energy and this is the basis for inertia.
		Indeed, the non-zero value of that field, coupled with an interaction term between that field and, say, the electron field, gave a term in the lagrangian which DID respect the symmetries required, but mimicked, at low energies, as a term that was essentially the same as a mass term.
	www.advancedphysics.org /forum/showthread.php?t=514 (1080 words)

	6.1 Perturbations around Minkowski spacetime (Site not responding. Last check: 2007-10-19)
		The fact that the vacuum expectation value of the renormalized stress-energy operator in Minkowski spacetime should vanish was originally proposed by Wald [283], and it may be understood as a renormalization convention [100, 113].
		Note that other possible solutions of semiclassical gravity with zero vacuum expectation value of the stress-energy tensor are the exact gravitational plane waves, since they are known to be vacuum solutions of Einstein equations which induce neither particle creation nor vacuum polarization [107, 73, 104].
		), their values in the two-point coincidence limit, and the products of derivatives of two of such functions appearing in expressions (38
	www.univie.ac.at /EMIS/journals/LRG/Articles/lrr-2004-3/articlesu9.html (550 words)

	OSU Physics: Calendar of Events
		Description: We calculate the critical value of the hopping parameter, κc, in O(a) improved lattice QCD, to two loops in perturbation theory.
		The quantity which we study is a typical case of a vacuum expectation value resulting in an additive renormalization; as such, it is characterized by a power (linear) divergence in the lattice spacing, and its calculation lies at the limits of applicability of perturbation theory.
		The dependence of our results on the number of colors N, the number of fermionic flavors Nf, and the clover parameter cSW, is shown explicitly.
	www.physics.ohio-state.edu /calendar/event.php3?id=259 (126 words)

	Neutrino Mass and Mixing (Site not responding. Last check: 2007-10-19)
		Although we know that the neutrino mass is small, there is no reason to expect it to vanish.
		Indeed, in the standard model, the lepton masses originate from a Yukawa-type coupling of the lepton fields to the vacuum expectation value of the Higgs field.
		These oscillations can be investigated while the neutrinos are propagating in vacuum, in atomic and nuclear matter, involving in each case very different theoretical and experimental physics.
	www.phy.duke.edu /~rps/coll99/ludwig.html (191 words)

	Quantum Motion
		The value of the field at a spacetime point contributes as much to the definition of the 'state' of a system as does the position of the particle.
		the expectation value of the kinetic energy and total angular momentum operators are not equal to the ensemble averages of just the kinetic energy and total angular momentum, respectively, as in classical mechanics, but also include additional quantum terms.
		The picture of the quantum vacuum (12.5) is static in Bohm's theory (in a preferred frame) unlike Wheeler's picture of dynamical fluctuations leading to Hawking's "quantum foam" on the Planck scale of 10^-33 cm.
	www.qedcorp.com /pcr/pcr/qmotion.html (18595 words)

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