Generalized Field Quantization and the Pauli Principle
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Probability and Statistics, Parastatistics, Boson, Fermion, Parafermion, Hausdorff Dimension, Percolation, Clusters
Applied Mathematics 2018, 8(1): 5-8 DOI: 10.5923/j.am.20180801.02 Why Fermions and Bosons are Observable as Single Particles while Quarks are not? Sencer Taneri Private Researcher, Turkey Abstract Bosons and Fermions are observable in nature while Quarks appear only in triplets for matter particles. We find a theoretical proof for this statement in this paper by investigating 2-dim model. The occupation numbers q are calculated by a power law dependence of occupation probability and utilizing Hausdorff dimension for the infinitely small mesh in the phase space. The occupation number for Quarks are manipulated and found to be equal to approximately three as they are Parafermions. Keywords Probability and Statistics, Parastatistics, Boson, Fermion, Parafermion, Hausdorff dimension, Percolation, Clusters There may be particles that obey some kind of statistics, 1. Introduction generally called parastatistics. The Parastatistics proposed in 1952 by H. Green was deduced using a quantum field The essential difference in classical and quantum theory (QFT) [2, 3]. Whenever we discover a new particle, descriptions of N identical particles is in their individuality, it is almost certain that we attribute its behavior to the rather than in their indistinguishability [1]. Spin of the property that it obeys some form of parastatistics and the particle is one of its intrinsic physical quantity that is unique maximum occupation number q of a given quantum state to its individuality. The basis for how the quantum states for would be a finite number that could assume any integer N identical particles will be occupied may be taken as value as 1<q <∞ (see Table 1). -
Physics Abstracts CLASSIFICATION and CONTENTS (PACC)
Physics Abstracts CLASSIFICATION AND CONTENTS (PACC) 0000 general 0100 communication, education, history, and philosophy 0110 announcements, news, and organizational activities 0110C announcements, news, and awards 0110F conferences, lectures, and institutes 0110H physics organizational activities 0130 physics literature and publications 0130B publications of lectures(advanced institutes, summer schools, etc.) 0130C conference proceedings 0130E monographs, and collections 0130K handbooks and dictionaries 0130L collections of physical data, tables 0130N textbooks 0130Q reports, dissertations, theses 0130R reviews and tutorial papers;resource letters 0130T bibliographies 0140 education 0140D course design and evaluation 0140E science in elementary and secondary school 0140G curricula, teaching methods,strategies, and evaluation 0140J teacher training 0150 educational aids(inc. equipment,experiments and teaching approaches to subjects) 0150F audio and visual aids, films 0150H instructional computer use 0150K testing theory and techniques 0150M demonstration experiments and apparatus 0150P laboratory experiments and apparatus 0150Q laboratory course design,organization, and evaluation 0150T buildings and facilities 0155 general physics 0160 biographical, historical, and personal notes 0165 history of science 0170 philosophy of science 0175 science and society 0190 other topics of general interest 0200 mathematical methods in physics 0210 algebra, set theory, and graph theory 0220 group theory(for algebraic methods in quantum mechanics, see -
The Conventionality of Parastatistics
The Conventionality of Parastatistics David John Baker Hans Halvorson Noel Swanson∗ March 6, 2014 Abstract Nature seems to be such that we can describe it accurately with quantum theories of bosons and fermions alone, without resort to parastatistics. This has been seen as a deep mystery: paraparticles make perfect physical sense, so why don't we see them in nature? We consider one potential answer: every paraparticle theory is physically equivalent to some theory of bosons or fermions, making the absence of paraparticles in our theories a matter of convention rather than a mysterious empirical discovery. We argue that this equivalence thesis holds in all physically admissible quantum field theories falling under the domain of the rigorous Doplicher-Haag-Roberts approach to superselection rules. Inadmissible parastatistical theories are ruled out by a locality- inspired principle we call Charge Recombination. Contents 1 Introduction 2 2 Paraparticles in Quantum Theory 6 ∗This work is fully collaborative. Authors are listed in alphabetical order. 1 3 Theoretical Equivalence 11 3.1 Field systems in AQFT . 13 3.2 Equivalence of field systems . 17 4 A Brief History of the Equivalence Thesis 20 4.1 The Green Decomposition . 20 4.2 Klein Transformations . 21 4.3 The Argument of Dr¨uhl,Haag, and Roberts . 24 4.4 The Doplicher-Roberts Reconstruction Theorem . 26 5 Sharpening the Thesis 29 6 Discussion 36 6.1 Interpretations of QM . 44 6.2 Structuralism and Haecceities . 46 6.3 Paraquark Theories . 48 1 Introduction Our most fundamental theories of matter provide a highly accurate description of subatomic particles and their behavior. -
A Scientific Metaphysical Naturalisation of Information
1 A Scientific Metaphysical Naturalisation of Information With a indication-based semantic theory of information and an informationist statement of physicalism. Bruce Long A thesis submitted to fulfil requirements for the degree of Doctor of Philosophy Faculty of Arts and Social Sciences The University of Sydney February 2018 2 Abstract The objective of this thesis is to present a naturalised metaphysics of information, or to naturalise information, by way of deploying a scientific metaphysics according to which contingency is privileged and a-priori conceptual analysis is excluded (or at least greatly diminished) in favour of contingent and defeasible metaphysics. The ontology of information is established according to the premises and mandate of the scientific metaphysics by inference to the best explanation, and in accordance with the idea that the primacy of physics constraint accommodates defeasibility of theorising in physics. This metaphysical approach is used to establish a field ontology as a basis for an informational structural realism. This is in turn, in combination with information theory and specifically mathematical and algorithmic theories of information, becomes the foundation of what will be called a source ontology, according to which the world is the totality of information sources. Information sources are to be understood as causally induced configurations of structure that are, or else reduce to and/or supervene upon, bounded (including distributed and non-contiguous) regions of the heterogeneous quantum field (all quantum fields combined) and fluctuating vacuum, all in accordance with the above-mentioned quantum field-ontic informational structural realism (FOSIR.) Arguments are presented for realism, physicalism, and reductionism about information on the basis of the stated contingent scientific metaphysics. -
The Connection Between Spin and Statistics
Sudarshan: Seven Science Quests IOP Publishing Journal of Physics: Conference Series 196 (2009) 012011 doi:10.1088/1742-6596/196/1/012011 The connection between spin and statistics Luis J. Boya Departamento de Física Teórica, Universidad de Zaragoza E - 50 009, Zaragoza, Spain E-Mail: [email protected] Abstract. After some brief historical remarks we recall the first demonstration of the Spin-Statistics theorem by Pauli, and some further developments, like Streater- Wightman’s, in the axiomatic considerations. Sudarshan’s short proof then follows by considering only the time part of the kinetic term in the lagrangian: the identity SU(2)=Sp(1,C) is crucial for the argument. Possible generalization to arbitrary dimensions are explored, and seen to depend crucially on the type of spinors, obeying Bott´s periodicity 8. In particular, it turns out that for space dimentions (7, 8, or 9) modulo 8, the conventional result does not automatically hold: there can be no Fermions in these dimensions. 1. Introduction The idea of this work came from discussions with Sudarshan in Zaragoza some years ago. George was surprised to learn that the properties of spinors crucial for the ordinary connection between spin and statistics would not hold in arbitrary dimensions, because of periodicity 8 of real Clifford algebras. After many discussions and turnarounds, I am happy today to present this collaboration, and I also apologize for the delay, for which I am mainly responsible. In any case, the priviledge to work and discuss physics with Sudarshan is a unique experience, for which I have been most fortunate. -
Curriculum Vitae
DAVID JOHN BAKER CURRICULUM VITAE Department of Philosophy [email protected] 2215 Angell Hall http://www-personal.umich.edu/~djbaker 435 S State St. Ann Arbor, MI 48109-1003 APPOINTMENTS Associate Professor of Philosophy, University of Michigan, 2014-present. Assistant Professor of Philosophy, University of Michigan, 2008-2014. EDUCATION PhD. in Philosophy, Princeton University, September 2008. Advisor: Hans Halvorson. B.S. in Philosophy (with Highest Honors) and Physics, University of Michigan, April 2003. AREAS OF SPECIALIZATION Philosophy of Physics, Philosophy of Science, Metaphysics. AREAS OF COMPETENCE Moral Philosophy, Logic, Philosophy of Religion, Epistemology. PUBLICATIONS “Does String Theory Posit Extended Simples?” Philosophers’ Imprint 16 (2016): Issue 18. “The Philosophy of Quantum Field Theory.” Oxford Handbooks Online (2016): DOI 10.1093/oxfordhb/9780199935314.013.33 “The Conventionality of Parastatistics,” with Hans Halvorson and Noel Swanson. The British Journal for the Philosophy of Science 66 (2015): 929-976. “How is spontaneous symmetry breaking possible? Understanding Wigner’s theorem in light of unitary inequivalence,” with Hans Halvorson. Studies in History and Philosophy of Modern Physics 44 (2013): 464-469. “Identity, Superselection Theory and the Statistical Properties of Quantum Fields.” Philosophy of Science 80 (2013): 262-285. “‘The Experience of Left and Right’ Meets the Physics of Left and Right.” Nous 46 (2012): 483-498. “Broken Symmetry and Spacetime.” Philosophy of Science 78 (2011): 128-148. “Symmetry and the Metaphysics of Physics.” Philosophy Compass 5 (2010): 1157-1166. “Antimatter,” with Hans Halvorson. The British Journal for the Philosophy of Science 61 (2010): 93-121. DAVID JOHN BAKER – CURRICULUM VITAE 2 “Against Field Interpretations of Quantum Field Theory.” The British Journal for the Philosophy of Science 60 (2009): 585-609. -
Arxiv:0805.0285V1
Generalizations of Quantum Statistics O.W. Greenberg1 Center for Fundamental Physics Department of Physics University of Maryland College Park, MD 20742-4111, USA, Abstract We review generalizations of quantum statistics, including parabose, parafermi, and quon statistics, but not including anyon statistics, which is special to two dimensions. The general principles of quantum theory allow statistics more general than bosons or fermions. (Bose statistics and Fermi statistics are discussed in separate articles.) The restriction to Bosons or Fermions requires the symmetrization postu- late, “the states of a system containing N identical particles are necessarily either all symmetric or all antisymmetric under permutations of the N particles,” or, equiv- alently, “all states of identical particles are in one-dimensional representations of the symmetric group [1].” A.M.L. Messiah and O.W. Greenberg discussed quantum mechanics without the symmetrization postulate [2]. The spin-statistics connec- arXiv:0805.0285v1 [quant-ph] 2 May 2008 tion, that integer spin particles are bosons and odd-half-integer spin particles are fermions [3], is an independent statement. Identical particles in 2 space dimensions are a special case, “anyons.” (Anyons are discussed in a separate article.) Braid group statistics, a nonabelian analog of anyons, are also special to 2 space dimensions All observables must be symmetric in the dynamical variables associated with identical particles. Observables can not change the permutation symmetry type of the wave function; i.e. there is a superselection rule separating states in inequivalent representations of the symmetric group and when identical particles can occur in states that violate the spin-statistics connection their transitions must occur in the same representation of the symmetric group. -
${\Mathbb Z} 2\Times {\Mathbb Z} 2 $-Graded Parastatistics In
Z2 ˆ Z2-graded parastatistics in multiparticle quantum Hamiltonians Francesco Toppan∗ August 27, 2020 CBPF, Rua Dr. Xavier Sigaud 150, Urca, cep 22290-180, Rio de Janeiro (RJ), Brazil. Abstract The recent surge of interest in Z2 Z2-graded invariant mechanics poses the challenge of ˆ understanding the physical consequences of a Z2 Z2-graded symmetry. In this paper it is shown that non-trivial physicsˆ can be detected in the multiparticle sector of a theory, being induced by the Z2 Z2-graded parastatistics obeyed by the particles. ˆ The toy model of the N 4 supersymmetric/ Z2 Z2-graded oscillator is used. In this set-up the one-particle energy“ levels and their degenerationsˆ are the same for both supersymmetric and Z2 Z2-graded versions. Nevertheless, in the multiparticle sector, a measurement of an observableˆ operator on suitable states can discriminate whether the system under consideration is composed by ordinary bosons/fermions or by Z2 Z2-graded ˆ particles. Therefore, Z2 Z2-graded mechanics has experimentally testable consequences. ˆ Furthermore, the Z2 Z2-grading constrains the observables to obey a superselection rule. ˆ As a technical tool, the multiparticle sector is encoded in the coproduct of a Hopf algebra defined on a Universal Enveloping Algebra of a graded Lie superalgebra with a braided tensor product. arXiv:2008.11554v1 [hep-th] 26 Aug 2020 CBPF-NF-007/20 ∗E-mail: [email protected] 1 1 Introduction This paper presents a theoretical test of the physical consequences of the Z2 Z2-graded paras- ˆ tatistics in a toy model case of a quantum Hamiltonian. -
Appendixes Appendix I Physical Constants and Conversion Factors
Appendixes Appendix I Physical Constants and Conversion Factors Numerical values for the constants are from B. N. Taylor, W. H. Parker, and D. N. Langenberg, Revs. Mod. Phys., 41, 375 (1969). Units are quoted in mksa (Systeme International) and in cgs. Physical Quantity Symbol Value Units (51) Units (cgs) I. Speed of light c 2.9979250 108 meters sec-I 10 10 cm sec-I 2. Electron charge e 1.6021918 10-19 C 10-20 emu 4.803250 10-10 esu 3. Planck's constant h 6.6261965 10-34 joule sec 10-27 erg sec n = h/27T 1.05459198 10-34 joule sec I 0-27 erg sec 4. Avogadro's number No 6.022169 1026 kmole-' 10 23 mole-I 5. Electron rest mass me 9.109559 10-31 kg 10-28 gm 0.5110041 MeV 6. Proton rest mass mp 1.672614 10-27 kg 10-24 gm 938.2592 MeV 7. Neutron rest mass mn 1.674920 10-27 kg 10-24 gm 939.5528 MeV 8. Faraday's constant F 9.648671 107 coul kmole-' 10 3 emu mole-I 2.892599 1014 esu mole-I 9. Gas constant R 8.31434 103 joule kmole-' K-' 10 7 erg mole-I K-I 10. Boltzmann's constant k 1.380623 10-23 joule K-I 10-16 erg K-' II. Gravitational constant G 6.6732 IO- llnewt meter2 kgm-2 10-8 dyne cm 2 gm-2 Clusters of Constants In many atomic and nuclear calculations the above constants appear in clusters, the evaluation of which can become tedious. -
Intermediate Statistics, Parastatistics, Fractionary Statistics and Gentilionic Statistics
Intermediate Statistics, Parastatistics, Fractionary Statistics and Gentilionic Statistics. M. Cattani (*) and J. M. F. Bassalo (**) (*) Instituto de Física da Universidade de São Paulo. C.P. 66318, CEP 05315 - 970 São Paulo, SP, Brasil. E-mail < [email protected] > (**)Fundação Minerva,R.Serzedelo Correa 347,1601-CEP 66035-400 Belém-Pará -Brasil E-mail < [email protected] > Abstract We made in this paper a brief analysis of the following statistics: Intermediate Statistics, Parastatistics, Fractionary Statistics and Gentilionic Statistics that predict the existence of particles which are different from bosons, fermions and maxwellons. We shown the fundamental hypothesis assumed in each one of the above mentioned statistics and their main predictions and compared them with experimental results. Taking into account the works done about these statistics we could say that there is a tendency to believe that real particles, that is, those that can be observed freely, can be only bosons, fermions and maxwellons and that all other particles, different from these would be quasiparticles. Up to date in 3-dim systems only bosons, fermions and maxwellons have been detected freely. Recently in 2-dim systems have been detected the quasiparticles named anyons that have fractionary charges and spins. (1)Introduction. Many works have been published about statistics that are different from the traditional bosonic, fermionic and maxwellonic. We do not intend to perform an extensive analysis about this theme but only to do a brief review of the following statistics: Intermediate , Parastatistics , Fractionary and Gentileonic. Since in these works we study systems composed by “particles” it is necessary to define what we understand by this word. -
2 Jul 2015 Symmetries, Symmetry Breaking, Gauge Symmetries
Symmetries, Symmetry Breaking, Gauge Symmetries∗ F. Strocchi INFN, Sezione di Pisa, Pisa, Italy Abstract The concepts of symmetry, symmetry breaking and gauge symmetries are discussed, their operational meaning being dis- played by the observables and the (physical) states. For infinitely extended systems the states fall into physically disjoint phases characterized by their behavior at infinity or boundary condi- tions, encoded in the ground state, which provide the cause of symmetry breaking without contradicting Curie Principle. Global gauge symmetries, not seen by the observables, are nev- ertheless displayed by detectable properties of the states (su- perselected quantum numbers and parastatistics). Local gauge symmetries are not seen also by the physical states; they ap- pear only in non-positive representations of field algebras. Their role at the Lagrangian level is merely to ensure the validity on the physical states of local Gauss laws, obeyed by the currents which generate the corresponding global gauge symmetries; they are responsible for most distinctive physical properties of gauge quantum field theories. The topological invariants of a local gauge group define superselected quantum numbers, which ac- arXiv:1502.06540v2 [physics.hist-ph] 2 Jul 2015 count for the θ vacua. ∗Talk at the Triennial International Conference “New Developments in Logic and Philosophy of Science”, Rome 18-20 June, 2014 1 2 1 Introduction The concepts of symmetries, symmetry breaking and gauge symme- tries, at the basis of recent developments in theoretical physics, have given rise to discussions from a philosophical point of view.1 Critical issues are the meaning of spontaneous symmetry breaking (appearing in conflict with the Principle of Sufficient Reason) and the physical or operational meaning of gauge symmetries. -
Quarks, Partons and Quantum Chromodynamics
Quarks, partons and Quantum Chromodynamics A course in the phenomenology of the quark-parton model and Quantum Chromodynamics 1 Jiˇr´ıCh´yla Institute of Physics, Academy of Sciences of the Czech Republic Abstract The elements of the quark-parton model and its incorporation within the framework of perturbative Quantum Chromodynamics are laid out. The development of the basic concept of quarks as fundamental constituents of matter is traced in considerable detail, emphasizing the interplay of experimental observations and their theoretical interpretation. The relation of quarks to partons, invented by Feynman to explain striking phenomena in deep inelastic scattering of electrons on nucleons, is explained. This is followed by the introduction into the phenomenology of the parton model, which provides the basic means of communication between experimentalists and theorists. No systematic exposition of the formalism of quantized fields is given, but the essential differences of Quantum Chromodynamics and the more familiar Quantum Electrodynamics are pointed out. The ideas of asymptotic freedom and quark confinement are introduced and the central role played in their derivation by the color degree of freedom are analyzed. Considerable attention is paid to the physical interpretation of ultraviolet and infrared singularities in QCD, which lead to crucial concepts of the “running” coupling constant and the jet, respectively. Basic equations of QCD–improved quark–parton model are derived and the main features of their solutions dis- cussed. It is argued that the “pictures” taken by modern detectors provide a compelling evidence for the interpretation of jets as traces of underlying quark–gluon dynamics. Finally, the role of jets as tools in searching for new phenomena is illustrated on several examples of recent important discoveries.