Spin-statistics theorem

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	Spin-statistics theorem - Wikipedia, the free encyclopedia
		The spin-statistics theorem in quantum mechanics relates the spin of a particle to the statistics obeyed by that particle.
		Pauli, The Connection Between Spin and Statistics, Phys.
		Spin is the intrinsic angular momentum of a particle such as an electron.
	www.wikipedia.org /wiki/Spin-statistics_theorem (340 words)

	Learn more about Spin (physics) in the online encyclopedia.
		Furthermore, the spin-statistics theorem states that particles with integer spin correspond to bosons, and particles with half-integer spin correspond to fermions.
		Also, unlike classical mechanical spinning, the spin is not described by a vector, but by a two-component object (for spin-1/2 particles): there is an observable difference in how it transforms under coordinate rotations.
		Unlike classical "spinning" objects, which derive their angular momentum from the rotation of their constituent parts, spin angular momentum is not associated with any rotating internal masses.
	www.onlineencyclopedia.org /s/sp/spin__physics_.html (727 words)

	Talk:Fermion - Wikipedia, the free encyclopedia
		According to the spin-statistics theorem, this is equivalent with having half-integer spin.
		In spin-statistics theorem, the only difference is the word "net" where fermions have a "net" energy rotation spin and bosons are particles where the "net" energy rotation cancels in the composite matter structures.
		Now that the spin equations have been corrected, the definitions for fermions and bosons are incorrect, and must be redefined as follows.
	en.wikipedia.org /wiki/Talk:Fermion (1196 words)

	Pauli exclusion principle - Wikipedia, the free encyclopedia
		According to the spin-statistics theorem, particles with integer spin occupy symmetric quantum states, and particles with half-integer spin occupy antisymmetric states; furthermore, only integer or half-integer values of spin are allowed by the principles of quantum mechanics.
		This does not violate the Pauli principle because spin is part of the quantum state of the electron, so the two electrons are occupying different quantum states.
		Another physical phenomenon for which the Pauli principle is responsible is ferromagnetism, in which the exclusion effect implies an exchange energy that induces neighboring electron spins to align (whereas classically they would anti-align).
	www.wikipedia.org /wiki/Pauli_exclusion_principle (849 words)

	H-atom p.8
		The Spin-Statistics Theorem concludes that the determining feature as to whether a particle is a boson or a fermion is the spin of the particle.
		That is to say that the Spin-Statistics Theorem says nothing about the exchange properties of different types of particles, only identical particles.
		Thus the spin angular momentum of a fundamental particle is an unchanging characteristic of the particle.
	www.physics.csbsju.edu /QM/H.08.html (679 words)

	PAULI AND THE SPIN-STATISTICS THEOREM
		In spite of its fundamental importance, it is only a slight exaggeration to say that "everyone knows the spin—statistics theorem, but no one understands it".
		This book makes broadly accessible an understandable proof of the infamous spin—statistics theorem.
		Evaluation of Intuitive Proofs of the Spin-Statistics Theorem
	www.worldscibooks.com /physics/3457.html (295 words)

	Re: Why does and electron have 1/2 spin???
		The reason why spin 1/2 particles must be fermions is explained by the "Spin-Statistics Theorem", which is usually considered to be a fundamental result of relativistic quantum theory.
		The reasons why the Spin-Statistics Theorem is true are a subject of continuing interest.
		The same theorem also explains why spinless particles must be "bosons", which have the property that the quantum mechanical wave-function is unchanged under the interchange of two of them.
	www.madsci.org /posts/archives/jun2000/962051189.Ph.r.html (354 words)

	Local fields with the wrong connection between spin and statistics, by R. F. Streater; quantum fields with infinitely many components.
		This shows that the well-known theorem on spin and statistics cannot be extended to general theories of local observables; it also shows that the assumptions made in `S-matrix theory' do not hold for the S-matrix of a theory of interacting infinite fields.
		The Bisognano-Wichmann theorem is needed for an algebraic proof of PCT and spin-statistics.
		They describe a mass-degenerate tower of particles with spins 1/2, 3/2, 5/2,..., but they commute at space-like separation, giving rise to Bose statistics for the particles.
	www.mth.kcl.ac.uk /~streater/rongspin.html (705 words)

	Spin, Statistics, and the TCP Theorem -- Schwinger 44 (2): 223 -- Proceedings of the National Academy of Sciences
		Spin, Statistics, and the TCP Theorem -- Schwinger 44 (2): 223 -- Proceedings of the National Academy of Sciences
	www.pnas.org /cgi/reprint/44/2/223 (19 words)

	Pauli, Heisenberg, and all that
		There is a deep theorem, called the spin-statistics theorem, which shows that in any quantum theory consistent with special relativity the exclusion principle has to hold for all particles whose spin is a half-integral number of units.
		The fundamental theorem here, due to Emmy Noether, is that so long as the same laws of physics apply at all times, the variable (frequency or energy) describing how things change in time must itself be conserved.
		Of course, the fermions are precisely these particles, so the formal theorem matches perfectly with observed behaviors.
	van.hep.uiuc.edu /Van/qa/section/New_and_Exciting_Physics/Quantum_Mechanics/20040114104603.htm (588 words)

	94-211
		PCT and Spin and Statistics theorems for superselection sectors with finite statistics} In this section we shall prove the Spin and Statistics theorem in the framework of local observable algebras [\rfr(Haag1)], i.e.
		From the mathematical point of view the spin-statistics correspondence is a relation between two quantities of different nature, the univalence and the statistics phase, and one is led to tie up these concepts on a general ground, somehow in the spirit of an index theorem.
		PCT, Spin and Statistics on the field algebras} In this section we consider a pre-cosheaf $\O\to\F(\O)$ of von~Neumann algebras acting on a Hilbert space $\H$, where $\O$ is any open region of the $4$-dimensional Minkowski space $M$.
	www.ma.utexas.edu /mp_arc/html/papers/94-211 (3788 words)

	A New Approach to Spin & Statistics - Kuckert (ResearchIndex)
		11 An Algebraic Spin and Statistics Theorem - Guido, Longo - 1994
		It is expected to be a progress towards a general spin-statisticstheorem includingalso (1+2)-dimensionaltheories with braid group statistics.
		Modular Covariance, PCT, Spin and Statistics - Guido (1995)
	citeseer.ist.psu.edu /36132.html (777 words)

	Dream 2047 Jan 2002 issue
		To find the relation between particle type and the statistics which is obeyed was left to Pauli (1936, 1940), who showed that integral spin particles obeyed Bose statistics and half integral spin particles obeyed Fermi statistics.
		Bose-Einstein statistics : The statistical mechanics of a system of indistinguishable particles for which there is no restriction on the number of particles that may exist in the same state simultaneously.
		Identical particles of any spin that are sufficiently widely separated to be distinguished, The molecules of a gas are particles of this kind.
	www.vigyanprasar.com /dream/jan2002/article1.htm (6557 words)

	QUANTUM UNIVERSE AS ALGEBRA
		If one wanted to consider a neccesarily Q approach to the statistics of such an ensemble, it would probably have to be a mixture of Fermionic and Bose type objects where the patches with n even are Fermionic and patches with n odd are Bosonic.
		) also vanishes, showing by Stokes Theorem that the phase function is well defined at every point.
		The first key to dealing statistically with large numbers of objects in the context of quantum theory is that unlike the way it is done in classical statistical mechanics (Maxwell-Boltzman), the objects if the same, cannot be distinguished, even in principle, which is to say that artifically distinguishing them with labels is forbidden.
	graham.main.nc.us /~bhammel/PHYS/algu.html (11111 words)

	Spin and Statistics
		The spin-statistics theorem of quantum field theory says that particles with half-odd-integer spin (like the electron) must be fermions, while particles with integer spin (like the photon) must be bosons.
		Fermions obey Fermi-Dirac statistics, and hence obey the Pauli exclusion principle.
		The difference in statistics stems from the properties of the exchange operator.
	math.ucr.edu /home/baez/lie/node16.html (116 words)

	Re: Why is tritium radioactive?
		The Spin-Statistics Theorem says that particles of odd half-integer spin are fermions, and no more than one fermion may occupy a given quantum state.
		When applied to electrons, which are also spin one-half fermions, the Spin-Statistics Theorem yields the Pauli Exclusion Principle: No two electrons in an atom can be at the same time in the same state or configuration.
		Neutrons have an intrinsic (as opposed to orbital) angular momentum of one half Planck's constant divided by 2pi; in the jargon of particle physics, neutrons have "spin* one half".
	www.madsci.org /posts/archives/Jun2003/1054474286.Ph.r.html (700 words)

	spin-statistics theorem -- Encyclopædia Britannica
		in quantum mechanics, fundamental mathematical proof that subatomic particles having integral values of spin (such as photons and helium-4 atoms) must be described by Bose-Einstein statistics (q.v.
		The Pythagorean Theorem is used to calculate the relationship between the legs and angles of a triangle.
		Statistics appear in the claims of advertisers, in predictions of election results and opinion polls, in cost-of-living indexes, and in reports of business...
	www.britannica.com /eb/article-9069133 (735 words)

	Spin, Statistics, CPT and All That Jazz
		Streater and A. Wightman, PCT, Spin and Statistics, and All That, reprinted by Addison-Wesley, New York, 1989.
		This is a little grab-bag of proofs of the spin-statistics relations, with some stuff about CPT thrown in.
		Because the CPT theorem is an almost-consequence of Lorentz invariance.
	math.ucr.edu /home/baez/spin_stat.html (1908 words)

	Fundamental Theory Group: Elementary Particles & Fields
		Spin and Statistics (Balachandran) A fundamental theorem in Quantum Field Theory (for flat background metrics) concerns the relation between spin and statistics.
		A program is underway to understand the spin-statistics theorem in this more general setting.
		Balachandran and coworkers have been studying this theorem using an approach based on certain algebras.
	www-hl.syr.edu /depts/Physics/FTGElementary.htm (1744 words)

	Abstract
		Two uniqueness theorems concerning the Bisognano-Wichmann symmetries whose P_1_CT-part is used in the discussion of the spin-statistics theorem are presented for the algebraic setting.
		Using a special version of the PCT-theorem which was found by Bisognano and Wichmann for finite-component Wightman fields, a proof of the spin-statistics theorem is given within the algebraic framework for quantum field theory.
		Spin & Statistics, Localization Regions, and Modular Symmetries in Quantum Field Theory
	www.lqp.uni-goettingen.de /lqp/papers/98/10/98100100.html (214 words)

	Addendum to Spin, Statistics, and the TCP Theorem -- Schwinger 44 (6): 617 -- Proceedings of the National Academy of Sciences
		Addendum to Spin, Statistics, and the TCP Theorem -- Schwinger 44 (6): 617 -- Proceedings of the National Academy of Sciences
	www.pnas.org /cgi/reprint/44/6/617 (21 words)

	FUN
		spin_stat - a sketch of the proof of the spin-statistics theorem.
		spin - an introduction to the theory of spin in quantum mechanics, by Michael Weiss.
		harmonic - discreteness and the role of compact groups and double covers in the quantum mechanics of spin and the harmonic oscillator.
	math.ucr.edu /home/baez/FUN.html (1153 words)

	Articles - Boson
		The spin-statistics theorem identify bosons as having integer spin.
		The spin-statistics theorem identifies the structural properties that differentiate fermions and bosons.
		Bosons obey Bose-Einstein statistics and are also the only particles in which any number can share the same quantum state.
	www.lastring.com /articles/Boson (526 words)

	1s, 2s, 2p, 3s, 3p, 4s, 4p, 3d...: Archive Entry From Brad DeLong's Webjournal
		The connection between spin and 'statistics' (aka The Spin-Statistics Theorem) is one of those frustrating truths that are fundamental but don't appear to have a non-technical explanation-- at least I've never heard one.
		The fact that particles with integer spin obey Bose-Einstein statistics (multiple particles can occupy the same quantum state--no Pauli exclusion) while particles with half-integer spin obey Fermi-Dirac statistics (only 1 particle per quantum state--Pauli exclusion) is generally called the spin-statistics theorem and was first seriously established by Wolfgang Pauli.
		The famous spin-statistics theorem tells you that half-integer spin particles can only be quantized with Fermi-Dirac statistics and that integral spin particles need Bose-Einstein statistics.
	www.j-bradford-delong.net /movable_type/2004_archives/000302.html (5322 words)

	References - symmetrization postulate of quantum mechanics
		Guido and R. Longo, "An Algebraic Spin and Statistics Theorem," Comm.
		Berry and J. Robbins, "Indistinguishability for quantum particles: spin, statistics and the geometric phase," Proc.
		Jaroszewicz and P. Kurzepa, "Spin, Statistics, and Geometry of Random-Walks," Ann.
	physics.nist.gov /MajResFac/EBIT/peprefs.html (5006 words)

	QCD and the structure of matter
		As a consequence of this spin-statistics theorem, an odd number of
		Now, there is an old theorem that says particles with spin
		spin 1/2 quarks cannot be combined to form a completely symmetric state.
	conferences.fnal.gov /lp2003/forthepublic/qcd (2607 words)

	Faculty Member Prize for Research at an Undergraduate Institution Lecture: Experimental Tests of the Spin-Statistics Theorem
		The spin-statistics theorem of relativistic quantum field theory seems to provide a theoretical basis for this connection.
		Faculty Member Prize for Research at an Undergraduate Institution Lecture: Experimental Tests of the Spin-Statistics Theorem
		The connection between the spin of particles and the permutation symmetry ("statistics") of multiparticle states lies at the heart of much of atomic, molecular, condensed matter, and nuclear physics.
	flux.aps.org /meetings/YR97/BAPSAPR97/abs/S290005.html (199 words)

	List of theorems
		In some fields, theorem can be considered as a courtesytitle, given to major results, although with a content that would not satisfy a mathematician.
		No attempt is made here tocomment on that aspect of usage: this is a list of results known as theorems.
		Stone's representation theorem for Boolean algebras (mathematical logic)
	www.therfcc.org /list-of-theorems-239671.html (186 words)

	American Journal of Physics 1995 April
		Poincare invents an ``inverse statistical mechanics'' that allows him to prove a crucial result that no one had proved before: The hypothesis of quanta is both a sufficient and a necessary condition to account for Planck's law of radiation.
		Given the significant impact of Poincare's memoir on quantum theory and statistical physics, it is surprising that most physicists are not aware of its valuable mathematical and physical ideas.
		A unique formulation of statistical mechanics, based on the calculus of probabilities, Fourier's integral, and complex analysis, logically unfolds throughout the memoir.
	www.acs.appstate.edu /orgs/tptindex/files/AJP1990s/1995/3696_6304_ajp1995_apr.html (1465 words)

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