The Ghost Fields: The Dr Ruth Galloway Mysteries 7

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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] 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. Faddeev, Ludwig D. (2009). "Faddeev-Popov ghosts". Scholarpedia. 4 (4): 7389. Bibcode: 2009SchpJ...4.7389F. doi: 10.4249/scholarpedia.7389. ISSN 1941-6016. 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 ]

ghost - Wikipedia Faddeev–Popov ghost - Wikipedia

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] 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 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. 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. 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.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. 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. 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. A field with a negative ghost number (the number of ghosts excitations in the field) is called an anti-ghost. 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 ]

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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) 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. 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. 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. 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]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.