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Robert J. Finkelstein

Bio: Robert J. Finkelstein is an academic researcher from University of California, Los Angeles. The author has contributed to research in topics: Electroweak interaction & Gauge theory. The author has an hindex of 12, co-authored 66 publications receiving 429 citations.


Papers
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Journal ArticleDOI
TL;DR: A review of a small set of papers that correlate the properties of quantized knots with empirical properties of the elementary particles can be found in this paper, where the present review is intended to present the model in its current form.
Abstract: The idea that the elementary particles might have the symmetry of knots has had a long history. In any modern formulation of this idea, however, the knot must be quantized. The present review is a summary of a small set of papers that began as an attempt to correlate the properties of quantized knots with empirical properties of the elementary particles. As the ideas behind these papers have developed over a number of years, the model has evolved, and this review is intended to present the model in its current form. The original picture of an elementary fermion as a solitonic knot of field, described by the trefoil representation of SUq(2), has expanded into its present form in which a knotted field is complementary to a composite structure composed of three preons that in turn are described by the fundamental representation of SLq(2). Higher representations of SLq(2) are interpreted as describing composite particles composed of three or more preons bound by a knotted field. This preon model unexpectedly agrees in important detail with the Harari–Shupe model. There is an associated Lagrangian dynamics capable in principle of describing the interactions and masses of the particles generated by the model.

31 citations

Journal ArticleDOI
TL;DR: In this paper, the states of maximum localization are smeared δ-functions dependeing on q, and the q-commutators are realized by difference operators.
Abstract: As oen would anticipate from the realization of the q-commutators by difference operators, the states of maximum localization are smeared δ-functions dependeing on q.

29 citations

Journal ArticleDOI
TL;DR: In this paper, the states of maximum localization are smeared delta functions depending on q and the q-commutators are realized by difference operators, where q is defined by the difference operator.
Abstract: As one would anticipate from the realization of the q-commutators by difference operators, the states of maximum localization are smeared delta functions depending on q.

27 citations

Journal ArticleDOI
TL;DR: The simplest neutral geometry with variable torsion is derived from a Lagrangian in which a pseudoscalar Yukawa field is coupled by pseudovector coupling to ψ (+) and ψ(−), and the hypercharge and parity of this charge doublet are determined by the weight of the spinor under general coordinate transformations as discussed by the authors.

21 citations

Journal ArticleDOI
TL;DR: In this paper, the authors explore a knot model of the elementary particles that is compatible with electroweak physics, where the knots are quantized and their kinematic states are labeled by, irreducible representations of SUq(2), where j = N/2, m = w/2 and m′ = (r+1)/2 and (N, w, r) designate respectively the number of crossings, the writhe, and the rotation of the knot.
Abstract: We explore a knot model of the elementary particles that is compatible with electroweak physics. The knots are quantized and their kinematic states are labeled by , irreducible representations of SUq(2), where j = N/2, m = w/2, m′ = (r+1)/2 and (N, w, r) designate respectively the number of crossings, the writhe, and the rotation of the knot. The knot quantum numbers (N, w, r) are related to the standard isotopic spin quantum numbers (t, t3, t0) by (t = N/6, t3 = -w/6, t0 = -(r+1)/6), where t0 is the hypercharge. In this model the elementary fermions are low lying states of the quantum trefoil (N = 3) and the gauge bosons are ditrefoils (N = 6). The fermionic knots interact by the emission and absorption of bosonic knots.

19 citations


Cited by
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TL;DR: In this article, a generalization of Einstein's gravitational theory is discussed in which the spin of matter as well as its mass plays a dynamical role, and the theory which emerges from taking this coupling into account, the ${U}_{4}$ theory of gravitation, predicts, in addition to the usual infinite-range gravitational interaction medicated by the metric field, a new, very weak, spin contact interaction of gravitational origin.
Abstract: A generalization of Einstein's gravitational theory is discussed in which the spin of matter as well as its mass plays a dynamical role. The spin of matter couples to a non-Riemannian structure in space-time, Cartan's torsion tensor. The theory which emerges from taking this coupling into account, the ${U}_{4}$ theory of gravitation, predicts, in addition to the usual infinite-range gravitational interaction medicated by the metric field, a new, very weak, spin contact interaction of gravitational origin. We summarize here all the available theoretical evidence that argues for admitting spin and torsion into a relativistic gravitational theory. Not least among this evidence is the demonstration that the ${U}_{4}$ theory arises as a local gauge theory for the Poincar\'e group in space-time. The deviations of the ${U}_{4}$ theory from standard general relativity are estimated, and the prospects for further theoretical development are assessed.

2,421 citations

Journal ArticleDOI
A. Bandyopadhyay1, Sandhya Choubey1, Raj Gandhi1, Srubabati Goswami1, B.L. Roberts2, J. Bouchez, I. Antoniadis3, John Ellis3, Gian F. Giudice3, T. Schwetz3, S. Umasankar, G. Karagiorgi4, Alexis A. Aguilar-Arevalo4, Janet Conrad4, M. H. Shaevitz4, Silvia Pascoli5, S. Geer6, J.E. Campagne7, Mark Rolinec8, A. Blondel9, Manuela Campanelli9, Joachim Kopp10, Manfred Lindner10, J.T. Peltoniemi, P. J. Dornan11, Kenneth Long11, Takashi Matsushita11, C. Rogers11, Y. Uchida11, Marcos Dracos, K. Whisnant12, David William Casper13, Mingshui Chen13, B. A. Popov14, Juha Äystö15, Danny Marfatia16, Y. Okada17, H. Sugiyama17, Klaus-Peter Jungmann18, Julien Lesgourgues, Michael S. Zisman19, Mariam Tórtola20, Alexander Friedland21, Sacha Davidson22, Stefan Antusch23, C. Biggio23, Andrea Donini23, Enrique Fernandez-Martinez23, Belen Gavela23, Michele Maltoni23, Jacobo Lopez-Pavon23, Stefano Rigolin23, N. K. Mondal24, V. Palladino, Frank Filthaut, Carl H. Albright25, A. de Gouvea26, Yoshitaka Kuno27, Y. Nagashima27, M. Mezzetto, S. Lola28, Paul Langacker29, A. Baldini, Hiroshi Nunokawa30, Davide Meloni31, Michel Diaz32, Stephen F. King33, Kai Zuber34, A.G. Akeroyd35, Y. Grossman36, Yasaman Farzan, Kazuhiro Tobe37, Mayumi Aoki38, Hitoshi Murayama39, Hitoshi Murayama19, Hitoshi Murayama40, N. Kitazawa41, Osamu Yasuda41, S.T. Petcov42, Andrea Romanino42, P. Chimenti43, Andrea Vacchi43, A. Yu. Smirnov44, Elena Couce45, J.J. Gómez-Cadenas45, Pilar Hernández45, M. Sorel45, José W. F. Valle45, Paul Fraser Harrison46, Cecilia Lunardini47, J.K. Nelson48, Vernon Barger49, Lisa L. Everett49, Patrick Huber49, Walter Winter50, W. Fetscher51, A. van der Schaaf52 
Harish-Chandra Research Institute1, Boston University2, CERN3, Columbia University4, Durham University5, Fermilab6, University of Paris-Sud7, Technische Universität München8, University of Geneva9, Max Planck Society10, Imperial College London11, Iowa State University12, University of California, Irvine13, Joint Institute for Nuclear Research14, University of Jyväskylä15, University of Kansas16, KEK17, University of Groningen18, Lawrence Berkeley National Laboratory19, Instituto Superior Técnico20, Los Alamos National Laboratory21, Lyon College22, Autonomous University of Madrid23, Tata Institute of Fundamental Research24, Northern Illinois University25, Northwestern University26, Osaka University27, University of Patras28, University of Pennsylvania29, Pontifical Catholic University of Rio de Janeiro30, Sapienza University of Rome31, Pontifical Catholic University of Chile32, University of Southampton33, University of Sussex34, National Cheng Kung University35, Technion – Israel Institute of Technology36, Tohoku University37, University of Tokyo38, University of California, Berkeley39, Institute for the Physics and Mathematics of the Universe40, Tokyo Metropolitan University41, International School for Advanced Studies42, University of Trieste43, International Centre for Theoretical Physics44, Spanish National Research Council45, University of Warwick46, University of Washington47, College of William & Mary48, University of Wisconsin-Madison49, University of Würzburg50, ETH Zurich51, University of Zurich52
TL;DR: The conclusions of the Physics Working Group of the International Scoping Study of a future Neutrino Factory and super-beam facility (the ISS) are presented in this article.
Abstract: The conclusions of the Physics Working Group of the International Scoping Study of a future Neutrino Factory and super-beam facility (the ISS) are presented. The ISS was carried out by the international community between NuFact05, (the 7th International Workshop on Neutrino Factories and Super-beams, Laboratori Nazionali di Frascati, Rome, 21–26 June 2005) and NuFact06 (Ivine, CA, 24–30 August 2006). The physics case for an extensive experimental programme to understand the properties of the neutrino is presented and the role of high-precision measurements of neutrino oscillations within this programme is discussed in detail. The performance of second-generation super-beam experiments, beta-beam facilities and the Neutrino Factory are evaluated and a quantitative comparison of the discovery potential of the three classes of facility is presented. High-precision studies of the properties of the muon are complementary to the study of neutrino oscillations. The Neutrino Factory has the potential to provide extremely intense muon beams and the physics potential of such beams is discussed in the final section of the report.

290 citations

Journal ArticleDOI
TL;DR: From physical arguments space-time is assumed to possess a connection between time and space as mentioned in this paper, which is a common assumption in most of the existing metric definitions, including the one presented in this paper.
Abstract: From physical arguments space-time is assumed to possess a connection % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFepeea0de9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaacbaGaa83Kdm% aaDaaajeaObaGaa8xAaiaa-PgaaeaacaWFRbaaaOGaa8xpamaacmaa% baqbaeqabiqaaaqaaiaa-TgaaeaacaWFPbGaa8NAaaaaaiaawUhaca% GL9baacaWFRaGaam4uamaaDaaaleaacaWFPbGaa8NAaaqaaiaa-bca% caWFRbaaaOGaa8xlaiaadofadaqhaaWcbaGaa8NAaiaa-bcacaWFGa% Gaa8hiaiaa-LgaaeaacaWFGaGaa83Aaaaakiaa-TcacaWGtbWaa0ba% aSqaaiaa-bcacaWFGaGaa8hiaiaa-LgacaWFQbaabaGaa83Aaaaaki% aa-1dadaGadaqaauaabeqaceaaaeaacaWFRbaabaGaa8xAaiaa-Pga% aaaacaGL7bGaayzFaaGaa8xlaiaadUeadaqhaaWcbaGaa8xAaiaa-P% gaaeaacaWFGaGaa8hiaiaa-Tgaaaaaaa!5E41! $$\Gamma _{ij}^k = \left\{ {\begin{array}{*{20}c} k \\ {ij} \\ \end{array} } \right\} + S_{ij}^{ k} - S_{j i}^{ k} + S_{ ij}^k = \left\{ {\begin{array}{*{20}c} k \\ {ij} \\ \end{array} } \right\} - K_{ij}^{ k} $$ . % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFepeea0de9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaiWaaeaafa% qabeGabaaabaacdaGaa83Aaaqaaiaa-LgacaWFQbaaaaGaay5Eaiaa% w2haaaaa!3AEE! $$\left\{ {\begin{array}{*{20}c} k \\ {ij} \\ \end{array} } \right\}$$ is Christoffel's symbol built up from the metric g ij and already appearing in General Relativity (GR). Cartan's torsion tensor % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFepeea0de9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaacdiGaa83uam% aaBaaajeaObaacdaGaa4xAaiaa+PgaaeqaaOWaaWbaaKqaGgqabaGa% a43Aaaaakiabg2da9maaleaaleaacaaIXaaabaGaaGOmaaaakiaacI% cajaaqcqqHtoWrkmaaDaaajeaObaGaa4xAaiaa+PgaaeaacaGFRbaa% aOGaeyOeI0scaaKaeu4KdCKcdaqhaaqcbaAaaiaa+PgacaGFPbaaba% Gaa43AaaaakiaacMcaaaa!4AC0! $$S_{ij} ^k = \tfrac{1}{2}(\Gamma _{ij}^k - \Gamma _{ji}^k )$$ and the contortion tensor K ij k , in contrast to the theory presented here, both vanish identically in conventional GR. Using the connection introduced above in this series of articles, we will discuss the consequences for GR in the framework of a consistent formalism. There emerges a theory describing, in a unified way, gravitation and a very weak spin-spin contact interaction. In section 1 we start with the well-known dynamical definition of the energy-momentum tensor σ ij ∼ δℒ/δg ij , where ℒ represents the Lagrangian density of matter (section1.1). In sections1.2,3 we will show that due to geometrical reasons, the connection assumed above leads to a dynamical definition of the spin-angular momentum tensor according to τk ji ∼ δℒ/δK ij k . In section1.4, by an ideal experiment, it will become clear that spin prohibits the introduction of an instantaneous rest system and thereby of a geodesic coordinate system. Among other things in section1.5 there are some remarks about the role torsion played in former physical theories. In section 2 we sketch the content of the theory. As in GR, the action function is the sum of the material and the field action function (sections2.1,2). The extension of GR consists in the introduction of torsion S ij k as a new field. By variation of the action function with respect to metric and torsion we obtain the field equations in a general form (section2.3). They are also valid for matter described by spinors; in this case, however, one has to introduce tetrads as anholonomic coordinates and slightly to generalize the dynamical definition of energy-momentum (sections2.4,5).

248 citations

01 Jan 2000
TL;DR: In this paper, the authors considered the problem of additive number theory for the Riemann surface and showed that the solution of the problem can be expressed as a polynomial series.
Abstract: Riemann surface, 29 addition theorem for sn(u), 28 additive number theory, 15 algebraic function, 29 balanced hypergeometric series, 18 Bell number, 17, 107 Bernoulli counting scheme, 111 Bernoulli number, 17 Bernoulli polynomial, 17 beta integral, 19 binomial series, 18 branched covering map, 28 branchpoint, 29 Catalan number, 16 Chu-Vandermonde summation formula, 19 commutative ordinary differential operators, 117 complete symmetric polynomial, 12 completely multiplicative, 15 complex structure, 29 conformally equivalent, 29 conjugate partition, 5 contiguous relation, 20 Dedekind sum, 107 digamma function, 21 Dirichlet region, 26 double gamma function, 27 Eisenstein series, 26 elementary symmetric polynomial, 12 elliptic function, 26 elliptic integral, 25 Euler number, 22 Euler product, 15 Euler’s dilogarithm, 19 Euler’s transformation formula, 19 Euler-Maclaurin summation formula, 15, 21 Eulerian number, 17, 107 Fermat measure, 53 Fermat’s last theorem, 27 fractional differentiation, 18 function element, 28 fundamental region, 26 Galois field, 65, 121 Gauss second summation theorem, 21 Gauss summation formula, 20 Gegenbauer polynomial, 51 generalised Stirling number, 16 generalised Stirling polynomial, 16 generalized hypergeometric series, 18 generalized Laguerre polynomial, 22 generalized Vandermonde determinant, 125 Genocchi number, 17

245 citations

Journal ArticleDOI
TL;DR: In this article, a constructive approach based on gauge invariant description of massive high spin particles was used for investigation of possible interactions of massive spin 2 particle. But the approach was limited to the case of constant curvature (A ) dS d background, which allows us carefully consider all flat space, massless or partially massless limits.

126 citations