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	Wightman axioms - Wikipedia, the free encyclopedia
		The first theorem of Wigner is that under these conditions, we can express invariance more conveniently in terms of linear or anti-linear operators (indeed, unitary or antiunitary operators); the symmetry operator on the projective space of rays can be lifted to the underlying Hilbert space.
		PCT theorem — there is general symmetry under change of parity, particle-antiparticle reversal and time inversion (none of these symmetries alone exists in nature, as it turns out)
		Haag's theorem says that there can be no interaction picture — that we cannot use the Fock space of noninteracting particles as a Hilbert space — in the sense that we would identify Hilbert spaces via field polynomials acting on a vacuum at a certain time.
	en.wikipedia.org /wiki/Wightman_axioms (1923 words)

	CPT symmetry - Wikipedia, the free encyclopedia
		There is a theorem that derives the preservation of CPT symmetry for all of physical phenomena assuming the correctness of quantum laws.
		Specifically, the CPT theorem, by John Stewart Bell, states that any Lorentz invariant local quantum field theory with a Hermitian Hamiltonian must have CPT symmetry.
		The CPT theorem can be generalized to take into account pin groups.
	en.wikipedia.org /wiki/PCT_theorem (420 words)

	[No title]
		It is shown that the geometric action of the modular conjugation J associated with the von Neumann algebra of a wedge region and the vacuum implies the PCT theorem for superselection sectors of a net of local algebras.
		It is shown that the geometric action of the modular conjugation, hence the PCT theorem, is a consequence of the geometric action of the modular group.
		The proof of the spin and statistics connection is given for conformal nets on a circle, namely it is shown that the statistical phase of an irreducible sector with finite Jones' index coincides with the value of the corresponding group representation for the rotation of 2π.
	axp.mat.uniroma2.it /~guido/research/themes.html (942 words)

	[No title] (Site not responding. Last check: 2007-10-25)
		To test the invariance of PCT, imagine making a movie of an experiment's mirror image in which all the particles have been replaced by their corresponding antiparticles.
		One consequence of PCT invariance is that the circular cyclotron frequencies of the antiproton and proton in a magnetic field should be identical.
		Another consequence of PCT invariance is that the structure of antihydrogen and hydrogen should be identical.
	hussle.harvard.edu /~atrap/Goals/CptTests/Cpt.html (447 words)

	CERN Courier - Ettore Majorana: genius and - IOP Publishing - article
		The spin-statistics theorem has an interesting and long history, the main players of which are some of the most distinguished theorists of the 20th century.
		It cannot be accidental that the first suggestion of the existence of the PCT invariance law came from the same people engaged in the study of the spin-statistics theorem, Lüders and Zumino.
		The validity of PCT invariance for quantum field theories was obtained in 1951 by Julian Schwinger, a great admirer of Majorana (Schwinger 1951).
	cerncourier.com /main/article/46/6/19 (2587 words)

	[No title]
		It has to be remarked, however, that not all such examples violate PCT symmetry {\it for the algebra of observables} generated by the field.
		PCT symmetry, on the other hand, requires that $M(p)$ can be written as $L(p)^{*} M^{\prime}(p)L(p)$ with $M^{\prime}(p)$ satisfying \eqref{pctsymmfield} and $L(p)$ polynomial in $p$.
		One may ask whether Poincar\'e covariance, spectrum condition and nuclearity (which implies the split property) are sufficient to derive the PCT theorem.
	www.ma.utexas.edu /mp_arc/html/papers/00-497 (4022 words)

	An Algebraic Spin And Statistics Theorem. I - Guido, Longo (ResearchIndex)
		A spin-statistics theorem and a PCT theorem are obtained in the context of the superselection sectors in Quantum Field Theory on a 4-dimensional space-time.
		Such a property, satisfied by the local algebras generated by Wightman fields because of the Bisognano-Wichmann theorem, is regarded as a natural...
		4 the converse of the Reeh-Schlieder theorem (context) - Borchers - 1968
	citeseer.ist.psu.edu /guido94algebraic.html (944 words)

	Special Analysis Seminar
		It is a generalization of the notion of a graph, where all the edges are of size 2.
		We prove a generalization of Hall's theorem to families of hypergraphs, namely give sufficient conditions for a family of hypergraphs to have a system of disjoint representatives (a choice of edges from each hypergraph, such that two edges chosen from different hypergraphs are disjoint).
		One of the main advantages of the new approach to the theorem is that it gives very greatly improved bounds for the dependence of $N$ on $k$ and $\delta$.
	www.math.princeton.edu /~seminar/2000-2001-sem/10-23-00weekly.htm (1174 words)

	Wightman axioms Did You Mean wightman_axioms (Site not responding. Last check: 2007-10-25)
		This being done for each group element (a,L), we get a family of unitary or antiunitary operators U(a,L) on our Hilbert space, such that the ray Psi transformed by (a,L) is the same as the ray containing U(a,L)psi.
		Connection between spin and statistic - fields which transform according to half integer spin anticommute, while those with integer spin commute (axiom W3) There are actually technical fine details to this theorem.
		Streater and A. Wightman, PCT, Spin and Statistics and All That, Princeton University Press, Landmarks in Mathematics and Physics, 2000.
	www.did-you-mean.com /Wightman_axioms.html (1861 words)

	PCT, spin and statistics, and all that, by R. F. Streater and A. S. Wightman (Site not responding. Last check: 2007-10-25)
		PCT, spin and statistics, and all that, by R. Streater and A. Wightman
		This avoids the assumption, made in Wightman theory, that unobservable fields either commute or anticommute at space-like separation.
		This is a natural axiom, since (1) it leads to a unique action of the Poincaré group on the observables and (2) it leads to the split property, that an algebra of type I lies between the local algebra of a double cone and that of any properly larger cone.
	www.mth.kcl.ac.uk /~streater/PCT.html (409 words)

	Eric Trees
		The LP Matrix Partition Theorem and its use with Fractional Domination and Domatic Parameters
		The property that results is described as the Partition Class Theorem (PCT).
		We show that the PCT is a generalization of the ACT.
	www.math.uah.edu /dissertations/trees.html (164 words)

	Jens Karl Heinz Mund, PhDThesis, FU Berlin (Site not responding. Last check: 2007-10-25)
		Further, model-independent results concerning the PCT operator and the connection of spin and statistics are obtained.
		Assuming the observable algebra to satisfy the Bisognano-Wichmann theorem, a PCT theorem for plektons is derived.
		The structure of the Hilbert space of scattering states of plektons and anyons is further clarified.
	www.diss.fu-berlin.de /1999/7/indexe.html (483 words)

	Wolfgang Pauli, great theoretical physicist (Site not responding. Last check: 2007-10-25)
		On the left was a proof of the PCT theorem, and on the right was a proof of the spin-statistics theorem.
		He then looked at the time, and said, oh, there seemed to be fifty minutes left, so he would take the opportunity to talk about new work that might be of more interest (than these old results).
		I realised that Pauli did not want the PCT and spin-statistics theorems published; they were five-minute talks on old stuff.
	www.mth.kcl.ac.uk /~streater/pauli.html (1039 words)

	Namit Mahajan (Site not responding. Last check: 2007-10-25)
		In [1], some phenomenological aspects were investigated while in [2], PCT theorem, one of the pillars of quantum field theory, was investigated in such a set up.
		PCT THEOREM IN FIELD THEORY ON NONCOMMUTATIVE SPACE, Namit Mahajan, Phys.
		Seminar on "PCT theorem and its status in Non-commutative Field Theory", August 2003.
	www.mri.ernet.in /~anlweb/annlrep/yr03_04/acadrep_phys/p0304_mahajan_namit/p0304_mahajan_namit.html (329 words)

	Converse of the PCT Theorem
		PCT, a fundamental symmetry of particle physics, is derived assuming
		What happens if we assume only Lorentz invariance and PCT symmetry?
		Hamiltonians having this property need not be Hermitian, but, except when PCT is
	www.pma.caltech.edu /PhysColl/abstracts/98-03/bender.html (110 words)

	John N's Web - Space-time diagrams for particles and photons
		Then naturally also follows the PCT theorem; this is the combination of space, time and charge inversion.
		The PCT trio gives a recipe for the change of entering neutrinos for out going anti neutrinos in the space-time diagrams.
		The beta decay, where a neutron changes in a proton under simultaneous emission of an electron and it's anti neutrino, is characterizing for the weak interaction.
	home.tiscali.nl /nentjes/time-e.htm (2561 words)

	Untitled Document: (Site not responding. Last check: 2007-10-25)
		Continuing with the previous work in this direction, along with my collaborators, two more decay modes were explored [3,4].\\ Non-commutative field theories have attracted a lot of interest and activity in the recent past.
		In [1], some phenomenological aspects were investigated while in [2], PCT theorem, one of the pillars of quantum field theory, was investigated in such a set up.\\ The unitarity violation in Littlest Higgs models was studied in preprint [1].
		\item[2.]Seminar on "PCT theorem and its status in Non-commutative Field Theory", August 2003.
	www.mri.ernet.in /~anlweb/annlrep/yr03_04/acadrep_phys/p_mahajan_namit.html (428 words)

	[No title]
		Among other results in perturbayive string theory, the PCT theorem for strings has been proven.
		Morbidelli and A. Giorgilli, "On a connection between KAM and Nekoroshev's theorem", Physica D, 86, 514-516 (1995) 5.
		Giorgilli and U. Locatelli, "A classical self-contained proof of Kolmogorov's theorem on invariant tori, to be published on the proceedings of the Nato ASI school in Sagaro" (1995) 8.
	www.mi.infn.it /DIP/SEZIONI/teorica.html (4322 words)

	Amazon.com: PCT, Spin and Statistics, and All That: Books: Raymond F. Streater,Arthur S. Wightman (Site not responding. Last check: 2007-10-25)
		PCT, Spin and Statistics, and All That is the classic summary of and introduction to the achievements of Axiomatic Quantum Field Theory.
		Today, a realistic quantum field theory must be given a distance scale, and all quantities are calculated with respect to this scale.
		Then follow general theorems for local field theory, like spin-statistics, CPT (and all that...).
	www.amazon.com /exec/obidos/tg/detail/-/0691070628?v=glance (1822 words)

	Amazon.ca: Relativistic Quantum Mechanics and Field Theory: Books (Site not responding. Last check: 2007-10-25)
		All of these discussions are interesting but they leave the reader wanting for an explanation of how bound states can form in a fully relativistic quantum field theory.
		In part three, the author delves more deeply into the theoretical aspects of quantum field theory, and proves the famous PCT theorem.
		An entire chapter is spent on renormalization, wherein Wick's theorem is proved.
	www.amazon.ca /exec/obidos/ASIN/0471353868 (3338 words)

	Physics News Update Number 218 - CPT CONSERVATION, SPECIAL RELATIVITY AND THE SINGLE ANTIPROTON (Site not responding. Last check: 2007-10-25)
		In separate measurements of a single proton in their trap, they confirmed that the cyclotron frequency of antiprotons and protons is identical to one part in a billion--a factor of 40 improvement over their previous measurements involving many trapped particles and 45,000 times more precise than earlier measurements with hot antiprotons.
		This is the first exact test of CPT theory for baryonic matter (precision tests of the PCT theorem have already been performed for leptons and pions).
		In separate measurements, the researchers then applied a brief radio pulse to add energy to the antiproton, increasing its velocity and consequently its mass according to special relativity.
	www.aip.org /enews/physnews/1995/split/pnu218-1.htm (257 words)

	9 Jan. 2004 - Brookhaven: New g-2 Measurement Deviates Further From Standard Model
		The precision of the new result matches the combined precision of the previously reported results.
		All three results are in good agreement with one another and with a long-standing theoretical prediction of the so-called PCT Theorem that particles and antiparticles should wobble at the same rate in a magnetic field.
		But when compared with the latest Standard Model predictions for the g-2 value, the new experimental result differs from the most direct theory calculation by 2.8 standard deviations, and from a somewhat more indirect theory calculation by 1.7 standard deviations, making this the most significant deviation to date between experiment and theory.
	www.interactions.org /cms?pid=1009159 (1107 words)

	Table of contents for Library of Congress control number 00061116
		Table of contents for PCT, spin and statistics, and all that / R.F. Streater, A.S. Wightman.
		The Reconstruction Theorem: Recovery of a Theory from its Vacuum Expectation Values 117 3-5.
		Some General Theorems of Relativistic Quantum Field Theory 134 4-1.
	www.loc.gov /catdir/toc/fy054/00061116.html (184 words)

	2003-04 UC Irvine Catalogue: Physical Sciences
		Perturbation theory, selection rules, crystal tensors, molecular vibrations, Jahn-Teller theorem, directed valence, time reversal symmetry, double groups, crystal field splittings of atomic levels.
		Full rotation group, Clebsch-Gordon coefficients, the Wigner-Eckart theorem, Racah coefficients, the Lorentz group, unitary groups.
		235B: Feynman graph techniques, renormalization, symmetries, PCT theorem, connection between spin and statistics.
	www.editor.uci.edu /03-04/ps/ps.8.htm (3184 words)

	Citebase - A General PCT Theorem for the Operator Product Expansion in Curved Spacetime
		A General PCT Theorem for the Operator Product Expansion in Curved Spacetime
		We propose that this result should be viewed as a replacement of the usual PCT theorem in Minkowski spacetime, at least in as far as the algebraic structure of the quantum fields at short distances is concerned.
		Users are cautioned not to use it for academic evaluation yet.
	www.citebase.org /cgi-bin/citations?id=oai:arXiv.org:gr-qc/0212028 (136 words)

	Pre-Calculus Class
		Investigate and sketch, with and without appropriate technology, the graphs of polynomia l and rational functions using the characteristics of domain and range, upper and lower bounds, maximum and minimum points, asymptotes and end behavior, zeros, multiplicity of zeros, y-intercepts, and symmetry.
		Solve, with and without appropriate technology, polynomial equations utilizing techniques such as Descartes' Rule of Signs, upper and lower bounds, Intermediate Value Theorem and Rational Root Theorem.
		Describe, with and without appropriate technology, the fundamental characteristics of rational functions: zeros, discontinuities (including vertical asymptotes), and end behavior (including horizontal asymptotes).
	www.punchard.com /classes/precalc/frworks.htm (1598 words)

	Metanexus Institute (Site not responding. Last check: 2007-10-25)
		In particle physics there is a close relationship between particles and anti-particles, namely, particles have all of their charges opposite, except mass which is identical.
		Even when discrete symmetries are broken, this correspondence comes from the PCT theorem.
		Aspect, A., Granger, P., Roger, G., Experimental Tests of realistic local theories via Bell's Theorem, Physical Review Letters, vol.
	www.metanexus.net /metanexus_online/printer_friendly.asp?ID=8023 (1554 words)

	Physics Timeline - Kansas Regent's Honor's Academy Cheetah Project
		The results allow us to classify all relativistic wave equations and the transformation properties of quantum fields.
		1940 Pauli proves the spin-statistics theorem: particles with half-integer spin have Fermi-Dirac statistics, those with integer spin are Bosons.
		1954-5 The PCT theorem is proved by Lüders and Pauli, involving space inversion (P), charge conjugation (C) and time reversal (T): in a local quantum field theory the product PCT of these transformations is always a symmetry.
	www.randyjohnston.com /johnston/KRHAphysics.htm (4079 words)

	OUP: UK General Catalogue (Site not responding. Last check: 2007-10-25)
		The flat tube theorem for vector valued functions, C.
		Notes for a quantum index theorem introduction, R.
		On the distance between MASA's in type II$_1$ factors, S.
	www.oup.com /uk/catalogue/?ci=9780821828144 (650 words)

	Curriculum Vitae of IBR Members
		REVIEW (relativistic extension of the Galilean symmetry with P. Roman; extension of the PCT theorem to all discrete symmetries with C, N. Ktorides, inapplicability of Pauli’s exclusion principle under open-nonconservative strong interactions with H. Myung; isotopic breaking of gauge symmetries; and several other papers);
		[57] Generalization of the PCT theorem to all discrete space-time symmetries in quantum field theories, with C.N. Ktorides Phys.
		Isotopies of the Pythagorean theorem, Global Analysis, Differential geometry and Lie Algebras, Gr.
	www.i-b-r.org /Ruggero-Maria-Santilli.htm (8211 words)

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