harald borner - Academia.edu (original) (raw)

Papers by harald borner

arXiv (Cornell University), Jan 13, 2024

We realize the Pauli group P as Galois group of polynomials over the rational numbers. It is show... more We realize the Pauli group P as Galois group of polynomials over the rational numbers. It is shown by construction that it is possible to find pure polynomials of the form X 8 + k 2 for k ̸ = λ 2 , 2λ 2 ; k, λ ∈ N, that provide an infinite family of such Galois extensions. This form is also proven to be a necessary condition for a realization of P by an irreducible pure polynomial of degree 8. It automatically provides a realization of the quaternion group Q8 by pure polynomials over a quadratic extension of Q, whereas it is shown to be impossible to realize Q8 over Q by any pure polynomial of degree 8. We link the results to Witt's theory of embedding criteria for the quaternion group via ternary quadratic forms over Q. This provides for a connection to general realizability criteria for embeddings of some finite groups into the Pauli group, and the interesting subtleties therein, via the equivalence of certain quaternion algebras. We thus show how to extend Witt's result of 1936 to an embedding of Q8 into the Pauli group.

Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 1990

Abstract It is shown how neutrino neutral-current x -distribution, although inaccessible to direc... more Abstract It is shown how neutrino neutral-current x -distribution, although inaccessible to direct experimental determination, can be obtained by measuring the distribution in a different scaling variable.

Thesis University of Oxford 1990 Source Dissertation Abstracts International Volume 52 04 Section B Page 2099, 1990

In this thesis we investigate the scattering of neutrinos and antineutrinos off free protons in t... more In this thesis we investigate the scattering of neutrinos and antineutrinos off free protons in the deep inelastic region via the neutral weak current. In the BEBC experiment, a hybrid detector consisting of a large liquid hydrogen bubble chamber and electronic counters for muon and hadron identification, has been exposed to the CERN wide band beam of neutrinos with energies up to 300 GeV. The detector provides the possibility to discriminate efficiently between hadron-induced and neutrino-induced muonless events. We are interested in the structure of the proton as it is resolved by the neutral carrier ZQ of the electroweak force. The kinematical scaling variable X(BJ) that represents information about the proton structure cannot be reconstructed in an experiment using a hydrogen target. Thus the X(Bj) dependence of the cross section for free protons has so far not been accessible. We construct a method that links the measurable distribution in a new variable w, that incorporates the hadronic momentum longitudinal and transverse to the beam, to the one in £(#,;)> m a model-independent way. It is shown that even with the statistics of about a thousand events it is possible to recover the £(Bj) dependence fo the neutrino proton cross-section with appreciable precision. This method is then applied to the data that consists of 2200 neutrino and 1060 antineutrino neutral current events, after correcting for various backgrounds and cuts. We observe a neutral current proton structure that is consistent with the notion of parton universality. The results are compared to two other investigations which employ isoscalar heavy targets, and we find agreement in as far as they are comparable. Furthermore we study the connection between the neutral current structure functions and distributions in the hadronic scaling variable w. It is found that they are related by simple formulae which do not incorporate any dependence on further kinematical variables, in the scaling approximation. We advocate the use of the w dependence of the neutral current cross section as an important piece of information that can provide access to some quantities that are measured only indirectly in charged current and electromagnetic scattering, and to the behaviour of the structure functions at small values of their argument. Thesis submitted for tho degree of Doctor of Philosophy in the University of Oxford Michaelmas 1990 for my parents So bleibt die einfache Tatsache der Ubereinstimmung der Denkgesetze mit den Naturgesetzen als tin ewig wunderbares Geheimnis bestehen, dessen Reiz den forschenden Menschengeist unaufhorlich zu Bemuhungen antreiben wird, seinen Inhalt der Anschauung ndherzubringen. (M. Planck) J l4Thus the simple fact of the correspondence between the laws of thinking and the laws of Nature remains an eternal miraculous secret, which will incessantly stimulate our enquiring mind to strive to bring its content closer to our visualisation and perception.' For the opportunity to work in this Department, and for his interest in my work, I would like to thank Prof. D. H. Perkins, who let me participate in two experiments, DELPHI and BEBC, that have been at the adolescent and the mature stages of their long 'life', respectively. I always enjoyed his demonstrations of how lively (to say the least) a departmental seminar can be. I am grateful for generous support from the 'Studienstiftung des deutschen Volkes' in form of a 'Doktorandenstipendium', and from a 'European Florey Studentship' at 'The Queen's College', Oxford. Without these scholarships I could not have met the costs of the studies here. The research presented in this thesis would have been impossible without the expertise of many members of the staff. As more stimulating and valuable even than their competent help, I shall remember the friendly, informal and cooperative atmosphere of the whole department. I thus feel indebted to everybody under the roof of 1, Keble Road, for receiving and assisting a foreigner with such kind openness.

From Strategy to Execution

The consulting firm McKinsey & Company is a trend-setter in the business world. Their examina... more The consulting firm McKinsey & Company is a trend-setter in the business world. Their examination of “excellent” US companies in the early 1980’s became a “search for excellence” that produced one of the best-selling business books of all time — In Search of Excellence: Lessons from America’s Best-Run Companies — and turned a former McKinsey consultant — Tom Peters — into a business pop-guru.

arXiv (Cornell University), Jan 13, 2024

We realize the Pauli group P as Galois group of polynomials over the rational numbers. It is show... more We realize the Pauli group P as Galois group of polynomials over the rational numbers. It is shown by construction that it is possible to find pure polynomials of the form X 8 + k 2 for k ̸ = λ 2 , 2λ 2 ; k, λ ∈ N, that provide an infinite family of such Galois extensions. This form is also proven to be a necessary condition for a realization of P by an irreducible pure polynomial of degree 8. It automatically provides a realization of the quaternion group Q8 by pure polynomials over a quadratic extension of Q, whereas it is shown to be impossible to realize Q8 over Q by any pure polynomial of degree 8. We link the results to Witt's theory of embedding criteria for the quaternion group via ternary quadratic forms over Q. This provides for a connection to general realizability criteria for embeddings of some finite groups into the Pauli group, and the interesting subtleties therein, via the equivalence of certain quaternion algebras. We thus show how to extend Witt's result of 1936 to an embedding of Q8 into the Pauli group.

Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 1990

Abstract It is shown how neutrino neutral-current x -distribution, although inaccessible to direc... more Abstract It is shown how neutrino neutral-current x -distribution, although inaccessible to direct experimental determination, can be obtained by measuring the distribution in a different scaling variable.

Thesis University of Oxford 1990 Source Dissertation Abstracts International Volume 52 04 Section B Page 2099, 1990

In this thesis we investigate the scattering of neutrinos and antineutrinos off free protons in t... more In this thesis we investigate the scattering of neutrinos and antineutrinos off free protons in the deep inelastic region via the neutral weak current. In the BEBC experiment, a hybrid detector consisting of a large liquid hydrogen bubble chamber and electronic counters for muon and hadron identification, has been exposed to the CERN wide band beam of neutrinos with energies up to 300 GeV. The detector provides the possibility to discriminate efficiently between hadron-induced and neutrino-induced muonless events. We are interested in the structure of the proton as it is resolved by the neutral carrier ZQ of the electroweak force. The kinematical scaling variable X(BJ) that represents information about the proton structure cannot be reconstructed in an experiment using a hydrogen target. Thus the X(Bj) dependence of the cross section for free protons has so far not been accessible. We construct a method that links the measurable distribution in a new variable w, that incorporates the hadronic momentum longitudinal and transverse to the beam, to the one in £(#,;)> m a model-independent way. It is shown that even with the statistics of about a thousand events it is possible to recover the £(Bj) dependence fo the neutrino proton cross-section with appreciable precision. This method is then applied to the data that consists of 2200 neutrino and 1060 antineutrino neutral current events, after correcting for various backgrounds and cuts. We observe a neutral current proton structure that is consistent with the notion of parton universality. The results are compared to two other investigations which employ isoscalar heavy targets, and we find agreement in as far as they are comparable. Furthermore we study the connection between the neutral current structure functions and distributions in the hadronic scaling variable w. It is found that they are related by simple formulae which do not incorporate any dependence on further kinematical variables, in the scaling approximation. We advocate the use of the w dependence of the neutral current cross section as an important piece of information that can provide access to some quantities that are measured only indirectly in charged current and electromagnetic scattering, and to the behaviour of the structure functions at small values of their argument. Thesis submitted for tho degree of Doctor of Philosophy in the University of Oxford Michaelmas 1990 for my parents So bleibt die einfache Tatsache der Ubereinstimmung der Denkgesetze mit den Naturgesetzen als tin ewig wunderbares Geheimnis bestehen, dessen Reiz den forschenden Menschengeist unaufhorlich zu Bemuhungen antreiben wird, seinen Inhalt der Anschauung ndherzubringen. (M. Planck) J l4Thus the simple fact of the correspondence between the laws of thinking and the laws of Nature remains an eternal miraculous secret, which will incessantly stimulate our enquiring mind to strive to bring its content closer to our visualisation and perception.' For the opportunity to work in this Department, and for his interest in my work, I would like to thank Prof. D. H. Perkins, who let me participate in two experiments, DELPHI and BEBC, that have been at the adolescent and the mature stages of their long 'life', respectively. I always enjoyed his demonstrations of how lively (to say the least) a departmental seminar can be. I am grateful for generous support from the 'Studienstiftung des deutschen Volkes' in form of a 'Doktorandenstipendium', and from a 'European Florey Studentship' at 'The Queen's College', Oxford. Without these scholarships I could not have met the costs of the studies here. The research presented in this thesis would have been impossible without the expertise of many members of the staff. As more stimulating and valuable even than their competent help, I shall remember the friendly, informal and cooperative atmosphere of the whole department. I thus feel indebted to everybody under the roof of 1, Keble Road, for receiving and assisting a foreigner with such kind openness.

From Strategy to Execution

The consulting firm McKinsey & Company is a trend-setter in the business world. Their examina... more The consulting firm McKinsey & Company is a trend-setter in the business world. Their examination of “excellent” US companies in the early 1980’s became a “search for excellence” that produced one of the best-selling business books of all time — In Search of Excellence: Lessons from America’s Best-Run Companies — and turned a former McKinsey consultant — Tom Peters — into a business pop-guru.