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...ing of identical particles, and does not require Lorentz covariance, locality, or other properties of quantum field theory In theories with noncommutative spacetime coordinates the Drinfel’d “twists” =-=[19]-=- can convert fermi→fermi or bose→bose transitions to the opposite type, but cannot produce bose→fermi transitions or vice versa. 5.3 Theoretical possibilities for quantum statistics Three types of sta...

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...he photon. I will conclude with some brief remarks about Héctor’s last interests–cosmology and astroparticle physics. 3. Quarks and aces As we all know, the quark model was introduced by George Zweig =-=[1]-=- and Murray GellMann [2] in 1964. Zweig focussed on the constituent aspect of what he called “aces.” Gell-Mann focussed on the algebraic properties of his “quarks.” Zweig was struck by the dominance o...

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...e→fermi transitions or vice versa. 5.3 Theoretical possibilities for quantum statistics Three types of statistics [20] can occur in 3 or more space dimensions: parabose statistics of integer order p, =-=[21]-=- parafermi statistics of integer order p, [21] and infinite statistics. [22] (In fewer than 3 dimensions, fractional statistics (anyons) can occur.) The rule we all know and love, that bose statistics...

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...de with some brief remarks about Héctor’s last interests–cosmology and astroparticle physics. 3. Quarks and aces As we all know, the quark model was introduced by George Zweig [1] and Murray GellMann =-=[2]-=- in 1964. Zweig focussed on the constituent aspect of what he called “aces.” Gell-Mann focussed on the algebraic properties of his “quarks.” Zweig was struck by the dominance of φ → KK̄ over φ → ρpi ....

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...e symmetric group cannot be coherent, i.e. cannot interfere, because no observable connects such states. This incoherence leads to a primitive superselection rule that Messiah and I first pointed out =-=[17]-=- and that R. Amado and H. Primakoff [18] also emphasized: States in inequivalent representations of the symmetric group are separated by this superselection rule. Corollaries of this are that no trans...

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...ymmetry. That was not to be the way. What worked was to take quarks as real, but change their statistics. I realized that the Pauli exclusion principle is valid if quarks are parafermions of order 3. =-=[8]-=- I predicted the spectrum of excited states of baryons using parafermi quarks of order 3 and the fact that 3 quarks can be in a symmetric state in the visible degrees of freedom, space, spin and flavo...

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...te, “We compare this process to a method sometimes employed in French cuisine: a piece of pheasant meat is cooked between two slices of veal, which are then discarded.” Feza Gürsey and Luigi Radicati =-=[4]-=-, were the first to introduce spin in the quark model in an intrinsic way. Choosing spin 1/2 for the quarks is the simplest way to account for baryons of spin 1/2. Gürsey and Radicati went much furthe...

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...ic theory. Some physicists hoped that a fully relativistic version of SU(6) would wrap up particle physics. No-go theorems, culminating in Coleman and Mandula [6] and in Haag, Lopuszanski and Sohnius =-=[7]-=- proved that the only way to incorporate an internal symmetry with Poincaré symmetry is supersymmetry. That was not to be the way. What worked was to take quarks as real, but change their statistics. ...

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...block of lead and looked for the x-rays from transitions into the K shell. They did not find such x-rays and found a qualitative bound on violations of the exclusion principle. E. Ramberg and G. Snow =-=[25]-=- repeated this type of experiment running a 30 A current in a thin copper strip for one month and looking for the slightly displaced x-rays. They had Avogadro’s number on their side and found a null r...

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... atomic barium. These transtions are forbidden by the LandauYang bose-einstein selection rule. They found the bound ν forbidden/ν allowed ≤ 4.0×10−11. In two papers in 2010, A.P. Balachandran, et al, =-=[28]-=- studied the possibility of violations of statistics in theories with noncommutative space coordinates. They found that the Drinfel’d “twists” can induce bose → bose transitions between two-electron s...

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...in order to make SU(6) a fully relativistic theory. Some physicists hoped that a fully relativistic version of SU(6) would wrap up particle physics. No-go theorems, culminating in Coleman and Mandula =-=[6]-=- and in Haag, Lopuszanski and Sohnius [7] proved that the only way to incorporate an internal symmetry with Poincaré symmetry is supersymmetry. That was not to be the way. What worked was to take quar...

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...e. cannot interfere, because no observable connects such states. This incoherence leads to a primitive superselection rule that Messiah and I first pointed out [17] and that R. Amado and H. Primakoff =-=[18]-=- also emphasized: States in inequivalent representations of the symmetric group are separated by this superselection rule. Corollaries of this are that no transitions can occur between SP-obeying and ...

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...ical properties of identical particles, (iv) Stability of matter. The pioneering experiment to search for transitions between anomalous states was carried out by M. Goldhaber and G. Scharff-Goldhaber =-=[24]-=- in 1947. They pointed out that if the electrons in beta decay were not quantum-mechanically identical to the electrons in atoms, then beta decay electrons could fall into the K shell of an atom in vi...

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...or aces was mixed. Zweig took them as real. Gell-Mann’s attitude was ambivalent. Gell-Mann’s response to Zweig when Zweig returned from CERN was “Oh, the concrete quark model. That’s for blockheads!” =-=[3]-=- Many physicists were deeply skeptical of the quark model, and even more of color. Oppenheimer’s response to me when 3 Quarks and quantum statistics O.W. Greenberg I showed him my paper in 1964 was “G...

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... recovered the Gell-Mann–Okubo mass relations for the baryon octet and decuplet and found a new relation between the masses of the octet and decuplet. Mirza A. Baqi Bég, Benjamin Lee and Abraham Pais =-=[5]-=- calculated the magnetic moment ratio, µp/µn, using this symmetry, another success. Gürsey and Radicati assigned the ground state baryons to the symmetric quark state. This assignment was paradoxical,...

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...Oppenheimer’s response to me when 3 Quarks and quantum statistics O.W. Greenberg I showed him my paper in 1964 was “Greenberg, it’s beautiful, but I don’t believe a word of it.” Steven Weinberg wrote =-=[9]-=-, “At that time (1967) I didn’t have any faith in the existence of quarks.” In contrast to Gell-Mann, Oppenheimer, Weinberg and many other physicists, Héctor wholeheartedly embraced the idea of quarks...

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...Quark Model” [11] “Dynamical Derivation of Baryon Masses in the Quark Model” [12] “Electromagnetic Properties of Hadrons in the Quark Model” [13] “Nucleon-Antinucleon Annihilation in the Quark Model” =-=[14]-=- “A Dynamical Quark Model for Hadrons.” [15] This impressive output makes clear that Hector completely invested in the idea that quarks are real, not just a mechanism to get group theory results. He d...

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...aryon Masses in the Quark Model” [12] “Electromagnetic Properties of Hadrons in the Quark Model” [13] “Nucleon-Antinucleon Annihilation in the Quark Model” [14] “A Dynamical Quark Model for Hadrons.” =-=[15]-=- This impressive output makes clear that Hector completely invested in the idea that quarks are real, not just a mechanism to get group theory results. He did realize that quarks could be used to get ...

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...vert fermi→fermi or bose→bose transitions to the opposite type, but cannot produce bose→fermi transitions or vice versa. 5.3 Theoretical possibilities for quantum statistics Three types of statistics =-=[20]-=- can occur in 3 or more space dimensions: parabose statistics of integer order p, [21] parafermi statistics of integer order p, [21] and infinite statistics. [22] (In fewer than 3 dimensions, fraction...

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... statistics Three types of statistics [20] can occur in 3 or more space dimensions: parabose statistics of integer order p, [21] parafermi statistics of integer order p, [21] and infinite statistics. =-=[22]-=- (In fewer than 3 dimensions, fractional statistics (anyons) can occur.) The rule we all know and love, that bose statistics occur for particles having integer spin and fermi statistics occur for part...

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...ept for q = ±1. An analog of Wick’s theorem holds. In contrast to the bose and fermi cases, the terms have coefficients that are powers of q rather than the ±1 that occur in the bose and fermi cases. =-=[23]-=- For a state with n quons, all representation of Sn occur, with weights dependent on q. For q→ −1 the more antisymmetric representations dominate, and for q→ 1 the more symmetric representations domin...

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... precision. With the two-body density matrix in the form ρ = (1− vF)ρA+ vFρS (5.3) Ramberg and Snow found the bound vF ≤ 1.7× 10−26. This bound was improved by the VIP experiment of Bartalucci, et al =-=[26]-=- in (2010), which gave the bound vF ≤ 6×10−29 This improvement came from three factors, (i) using CCD detectors that give greater sensitivity, (ii) running 6 Quarks and quantum statistics O.W. Greenbe...

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...er run which give greater statistics. High-precision tests of bose-einstein statistics for photons are more difficult because we don’t have bound states with many photons. In 2010, D. English, et al, =-=[27]-=- looked for bose-einstein forbidden two-photon transitions in atomic barium. These transtions are forbidden by the LandauYang bose-einstein selection rule. They found the bound ν forbidden/ν allowed ≤...