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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. 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) 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] 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.
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Faddeev, Ludwig D. (2009). "Faddeev-Popov ghosts". Scholarpedia. 4 (4): 7389. Bibcode: 2009SchpJ...4.7389F. doi: 10.4249/scholarpedia.7389. ISSN 1941-6016.
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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.
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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. A field with a negative ghost number (the number of ghosts excitations in the field) is called an anti-ghost. 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 ] 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
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} 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.