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Daintith, John, ed. (2009). "Landau ghost". A Dictionary of Physics (6thed.). Oxford: Oxford University Press. ISBN 9780199233991. OCLC 244417456. Archived from the original on 2017-12-28 . Retrieved 2018-04-25.

## The Ghost Fields by Elly Griffiths | Waterstones The Ghost Fields by Elly Griffiths | Waterstones

If a given theory is self-consistent by the introduction of ghosts, these states are labeled "good". Good ghosts are virtual particles that are introduced for regularization, like Faddeev–Popov ghosts. Otherwise, "bad" ghosts admit undesired non-virtual states in a theory, like Pauli–Villars ghosts that introduce particles with negative kinetic energy. A ghost condensate is a speculative proposal in which a ghost, an excitation of a field with a wrong sign of the kinetic term, acquires a vacuum expectation value. This phenomenon breaks Lorentz invariance spontaneously. Around the new vacuum state, all excitations have a positive norm, and therefore the probabilities are positive definite.The Landau pole is sometimes referred as the Landau ghost. Named after Lev Landau, this ghost is an inconsistency in the renormalization procedure in which there is no asymptotic freedom at large energy scales. [9] See also [ edit ]

## Elly Griffiths - Book Series In Order Elly Griffiths - Book Series In Order

Bad ghosts" represent another, more general meaning of the word "ghost" in theoretical physics: states of negative norm, [6] or fields with the wrong sign of the kinetic term, such as Pauli–Villars ghosts, whose existence allows the probabilities to be negative thus violating unitarity. [7] It is possible, however, to modify the action, such that methods such as Feynman diagrams will be applicable by adding ghost fields which break the gauge symmetry. The ghost fields do not correspond to any real particles in external states: they appear as virtual particles in Feynman diagrams – or as the absence of some gauge configurations. However, they are a necessary computational tool to preserve unitarity. Chen, W.F. (2008), "Quantum Field Theory and Differential Geometry", Int. J. Geom. Methods Mod. Phys., 10 (4): 1350003, arXiv: 0803.1340v2, doi: 10.1142/S0219887813500035, S2CID 16651244 The necessity for Faddeev–Popov ghosts follows from the requirement that quantum field theories yield unambiguous, non-singular solutions. This is not possible in the path integral formulation when a gauge symmetry is present since there is no procedure for selecting among physically equivalent solutions related by gauge transformation. The path integrals overcount field configurations corresponding to the same physical state; the measure of the path integrals contains a factor which does not allow obtaining various results directly from the action. Unfortunately, this theory allows for superluminal propagation of information in some cases and has no lower bound on its energy. This model doesn't admit a Hamiltonian formulation (the Legendre transform is multi-valued because the momentum function isn't convex) because it is acausal. Quantizing this theory leads to problems.An example of the need of ghost fields is the photon, which is usually described by a four component vector potential A μ, even if light has only two allowed polarizations in the vacuum. To remove the unphysical degrees of freedom, it is necessary to enforce some restrictions; one way to do this reduction is to introduce some ghost field in the theory. While it is not always necessary to add ghosts to quantize the electromagnetic field, ghost fields are strictly needed when dealing with non-Abelian Yang–Mills theory extensions to the Standard Model. [1] [2] Faddeev, Ludwig D.; Popov, Victor N. (1967). "Feynman diagrams for the Yang-Mills field". Physics LettersB. 25 (1): 29–30. Bibcode: 1967PhLB...25...29F. doi: 10.1016/0370-2693(67)90067-6. ISSN 0370-2693. Arkani-Hamed, Nima; Cheng, Hsin-Chia; Luty, Markus A.; Mukohyama, Shinji (2004-05-29). "Ghost Condensation and a Consistent Infrared Modification of Gravity". Journal of High Energy Physics. 2004 (5): 074. arXiv: hep-th/0312099. Bibcode: 2004JHEP...05..074H. doi: 10.1088/1126-6708/2004/05/074. ISSN 1029-8479. S2CID 16844964. Hawking, Stephen W.; Hertog, Thomas (2002). "Living with Ghosts". Physical Review D. 65 (10): 103515. arXiv: hep-th/0107088. Bibcode: 2002PhRvD..65j3515H. doi: 10.1103/PhysRevD.65.103515. S2CID 2412236.

## ghost - Wikipedia Faddeev–Popov ghost - Wikipedia

A field with a negative ghost number (the number of ghosts excitations in the field) is called an anti-ghost. Faddeev, Ludwig D. (2009). "Faddeev-Popov ghosts". Scholarpedia. 4 (4): 7389. Bibcode: 2009SchpJ...4.7389F. doi: 10.4249/scholarpedia.7389. ISSN 1941-6016. In the terminology of quantum field theory, a ghost, ghost field, ghost particle, or gauge ghost is an unphysical state in a gauge theory. Ghosts are necessary to keep gauge invariance in theories where the local fields exceed a number of physical degrees of freedom. Ghost particles could obtain the symmetry or break it in gauge fields. The "good ghost" particles actually obtain the symmetry by unchanging the " gauge fixing Lagrangian" in a gauge transformation, while bad ghost particles break the symmetry by bringing in the non-abelian G-matrix which does change the symmetry, and this was the main reason to introduce the gauge covariant and contravariant derivatives. The chilling discovery of a downed World War II plane with a body inside leads Ruth and DCI Nelson to uncover a wealthy family’s secrets in this Ruth Galloway mystery.The exact form or formulation of ghosts is dependent on the particular gauge chosen, although the same physical results must be obtained with all gauges since the gauge one chooses to carry out calculations is an arbitrary choice. The Feynman–'t Hooft gauge is usually the simplest gauge for this purpose, and is assumed for the rest of this article. D [ A ] exp i ∫ d 4 x ( − 1 4 F μ ν a F a μ ν ) . {\displaystyle \int {\mathcal {D}}[A]\exp i\int \mathrm {d} Goldstone bosons are sometimes referred to as ghosts. Mainly, when speaking about the vanishing bosons of the spontaneous symmetry breaking of the electroweak symmetry through the Higgs mechanism. These good ghosts are artifacts of gauge fixing. The longitudinal polarization components of the W and Z bosons correspond to the Goldstone bosons of the spontaneously broken part of the electroweak symmetry SU(2)⊗ U(1), which, however, are not observable. Because this symmetry is gauged, the three would-be Goldstone bosons, or ghosts, are "eaten" by the three gauge bosons ( W ± and Z) corresponding to the three broken generators; this gives these three gauge bosons a mass, and the associated necessary third polarization degree of freedom. [5] Bad ghosts [ edit ] Faddeev–Popov ghosts are extraneous anticommuting fields which are introduced to maintain the consistency of the path integral formulation. They are named after Ludvig Faddeev and Victor Popov. [3] [4] Goldstone bosons [ edit ]

## The Ghost Fields: The Dr Ruth Galloway Mysteries 7 - WHSmith

This section needs additional citations for verification. Please help improve this article by adding citations to reliable sourcesin this section. Unsourced material may be challenged and removed. ( January 2017) ( Learn how and when to remove this template message) Becchi, Carlo Maria; Imbimbo, Camillo (2008-10-26). "Becchi-Rouet-Stora-Tyutin symmetry". Scholarpedia. 3 (10): 7135. Bibcode: 2008SchpJ...3.7135B. doi: 10.4249/scholarpedia.7135. ISSN 1941-6016. Griffiths, David J. (1987). Introduction to elementary particles. New York: Wiley. ISBN 0471603864. OCLC 19468842. In physics, Faddeev–Popov ghosts (also called Faddeev–Popov gauge ghosts or Faddeev–Popov ghost fields) are extraneous fields which are introduced into gauge quantum field theories to maintain the consistency of the path integral formulation. They are named after Ludvig Faddeev and Victor Popov. [1] [2]