Lie Theory and the Lauricella Functions FD

The purpose of this article is to outline a nonrigorous and highly intuitive introductory approach to the sort of group representation theory used in molecular and solid state physics. We examine the real three-space spanned by orthonormal polar basis vectors {‖i〉, i=1,2,3}; first it is shown that the familiar block diagonal ’’rotation matrix’’ is simply the {‖i〉} representation of the geometric transformation operator ?φ which causes a counterclockwise rotation of any three-space polar vector by the angle φ about the ‖3〉 axis. By applying this argument to the group of symmetry operators of the ammonia molecule, it becomes self-evident that the two irreducible representations obtainable from the {‖i〉} representation of C3v correspond to subspaces of real-space invariant relative to the six operators of that group. And the basis vectors which span these invariant subspaces (and which produce the corresponding irreducible representations) have clearly defined symmetry (A1 and E) properties under the operations of C3v. This idea is further illustrated in consideration of the representation produced by the in-plane normal modes of vibration of the three hydrogen atoms in ammonia. Finally, it is shown that the approach can readily be extended into function space.

The present article considers Giulio Racah’s contributions to general physical theory and his establishment of theoretical physics as a discipline in Israel. Racah developed mathematical methods that are based on tensor operators and continuous groups. These methods revolutionized spectroscopy. Currently, these are essential research tools in atomic, nuclear and elementary particle physics. He himself applied them to modernizing theoretical atomic spectroscopy. Racah laid the foundations of theoretical physics in Israel. He educated several generations of Israeli physicists, and put Israel on the world map of physics.

An exotic atom is formed when an electron in an “ordinary” atom is replaced by a heavier particle such as a muon, π or K-meson, antiproton or a ∑-hyperon. Studies of these exotic atoms cover a whole range of disciplines from atomic and solid-state physics to nuclear and elementary particle physics. From the nuclear point of view, the strongly interacting pions, kaons, antiprotons and sigma-hyperons give information about the very low energy hadron-nucleus interaction and can in principle give further information about the nucleus such as the matter distribution. Information about the properties of the hadron, such as its mass or magnetic moment, and about the hadron-nucleon interaction can also be obtained.

The eighteenth International Conference PhysicA.SPb was held 26-29 October 2015 in Saint- Petersburg, Russia. The Conference continues the tradition of Saint-Petersburg Seminars on Physics and Astronomy originating from mid-90s. Since then PhysicA.SPb maintains both the scientific and educational quality of contributions delivered to the young audience. This is the main feature of the Conference that makes it possible to combine the whole spectrum of modern Physics and Astronomy within one event.PhysicA.SPb/2015 has brought together about 300 students, young scientists and their colleague professors from many universities and research institutes across the whole of Russia as well as from Belarus, Ukraine, Finland, Netherlands, Iceland, and France. Oral and poster presentations were combined into well-defined sections among which one should name Astronomy and Astrophysics, Optics and spectroscopy, Atomic and elementary particles physics, Physics of ferroics, Nanostructured and thin-film materials, Mathematical physics and numerical methods, THz and UHF materials and devices, Biophysics, Optoelectronic devices, Surface effects, Physics and technology of energy conversion, Plasma physics, hydro- and aero-dynamics, and Physics of quantum structures.This issue of the Journal of Physics: Conference Series presents the extended contributions from participants of PhysicA.SPb/2015 that were peer-reviewed by expert referees through processes administered by the Presiders of the Organising and Programme Committees to the best professional and scientific standards. This was made possible by the efforts of the Sectional Editors of this Issue: Prof. Petr Arseev (Lebedev Physical Institute), Prof. Yuri Kusraev (Ioffe Institute), Prof. Alexander Ivanchik (Ioffe Institute), Prof. Polina Ryabochkina (Ogarev Mordova State University), Dr. Karina Litvinova (Aston University), Dr. Nikolay Bert (Ioffe Institute), Dr. Yana Kuznetsova (Ioffe Institute), Dr. Prokhor Alekseev (Ioffe Institute), Dr. Mikhail Dunaevskii (Ioffe Institute), Dr. Alexandra Kalashnikova (Ioffe Institute), Dr. Leonid Lutsev (Ioffe Institute).The Editors: Nikita S. Averkiev, Sergey A. Poniaev and Grigorii S. Sokolovskii

The representation of symmetry groups plays a crucial role in physics. In this chapter we discuss the elements of the representation theory of Lie groups and Lie algebras. In particular, we apply representations of the Lie group SU(3) and the Lie algebra su(3) to the quark model in strong interaction.

Selected topics in the theory of elementary particles

Multiplicity One Theorems for Generalized Gelfand-Graev Representations of Semisimple Lie Groups and Whittaker Models for the Discrete Series

Science sets itself apart from other paths to truth by recognizing that even its greate practitioners sometimes err.

This introductory chapter discusses the general physical foundations of the Casimir effect as manifestation of the existence of zero-point vacuum oscillations. Connections between the Casimir force, the van der Waals force, and other physical phenomena of quantum electrodynamics caused by the existence of zero-point oscillations are considered. Specifically, it is explained that the Casimir force between material boundaries can be interpreted as simply a retarded van der Waals force. The Casimir effect is presented as a multidisciplinary subject which plays an important role in condensed matter physics, elementary particle physics, atomic physics, gravitation and cosmology, mathematical physics, and nanotechnology. The chapter ends with a guide to the book explaining the structure of the book, with brief detail on the content of each chapter, and the main notation.

The Nobel Foundation arranges on a regular basis special Nobel Symposia in scientific disciplines that are related to the Nobel prizes. Since 1965, when the series of symposia was first initiated, more than one hundred have been arranged. A Nobel symposium corresponds to a rather small meeting with leading scientists in their particular field, facilitating informal discussions, in plenum as well as in private, on critical issues and latest results. In addition to the specialists a small number graduate students, young researchers, and researchers from nearby fields are also invited to participate in the symposia.This time the Nobel Foundation has selected the field of quantum chaos for its 116th symposium. Thus "Quantum Chaos Y2K" was held in June 13-17, 2000, at the historic and beautiful Bäckaskogs Castle in the south of Sweden.Quantum chaos is becoming a very wide field that ranges from experiments to theoretical physics and purely mathematical issues. Because of this grand span we decided at an early stage of the planning of this symposium to focus on experiments and theory, and to encourage the interplay between them. We also wanted to stress the interdisciplinary character of the subject, and involved physics from a broad range of subjects, including condensed matter physics, nuclear physics, atomic physics, and elementary particle physics. The physics involved in quantum chaos has much in common with acoustics, microwaves, optics, etc. Therefore we choose to include also aspects of wave chaos in this broader sense. The program was structured according to the following headings: Manifestations of Classical Chaos in Quantum Systems Transport Phenomena Description of Quantal Spectra in Terms of Periodic Orbits Semiclassical and Random Matrix Approaches Quantum Chaos in Interacting Systems Chaos and Tunneling Wave-Dynamic Chaos The meeting at Bäckaskog was conducted in a truly interdisciplinary atmosphere with invited talks and poster presentations. There was ample time for discussions in which the chairmen played very important roles in summarising and highlighting the different sub-fields. In addition to invited talks and poster contributions the present proceedings therefore also contain informal contributions from some of the chairmen. In this way we hope the proceedings will convey some of the enthusiasm felt at Bäckaskog.Finally we wish to thank the Nobel Foundation for selecting the field of quantum chaos to be the topic of the 116th Nobel symposium and for its generous support. We also wish to thank the international program committee for all its help when designing the symposium.

We discuss some current problems in the relationship between elementary particle physics and gravitation, i.e., in the subject investigated by Prof.~K.~P.~Staniukovich half a century ago. Specifically, the inflationary stage of the Universe evolution, originating from the vacuum polarization and particle creation, corrections to Newton's gravitational law due to exchange of light elementary particles or spontaneous compactification of extra dimensions, and constraints on the parameters of axions as probable constituents of dark matter in our Universe are considered. It is pointed out that presently the relationship between elementary particles and gravitation has become an experimental science, and many experiments, directed towards resolution of all related problems, are performed in many countries.

In recent years there has been considerable growth in research in so-called 'interface' areas where nuclear physics, particle physics and astrophysics meet; sharing common goals and language, as well as instrumentation techniques. Examples include: Probing the standard model by measuring elements of the CKM matrix The use of colliders and detectors with access to the highest energies to search for the underlying structure of matter and energy Fundamental interactions at the nuclear and particle level required to understand processes from solar burning to supernovae Neutrino physics; including oscillations, mass and interactions probing the standard solar model Hadronic physics dealing with the interactions, binding and structure of the strongly interacting particles under various conditions The increased use of 4 detectors in low-energy nuclear physics to select specific processes of interest. These are only a few examples of what has become a major meeting place for much of the exciting physics of the early 21st Century. In today's science, the spectrum of particles, the nucleus as well as the large-scale components of the universe, are our laboratories for testing and understanding nature.These exciting areas of cross-over require much further research and exploration. The Editorial Board and staff of Journal of Physics G: Nuclear and Particle Physics wish to strengthen their support for physicists working in such areas of intersection. To make our coverage of these interconnections more explicit, we have redrafted our scope statement as follows:Theoretical and experimental topics in the physics of elementary particles and fields, intermediate-energy physics and nuclear physics. The particle astrophysics section includes all aspects of experimental and theoretical research into cosmic rays, nuclear and particle astrophysics, gamma ray astronomy, neutrino astrophysics and dark matter. We also welcome articles from all areas of interface between these fields.We would like to invite all physicists working on these topics to publish their work in the pages of J.Phys.G. Naturally we shall continue to welcome outstanding research in our core nuclear and particle physics areas.Since its launch in 1975, J.Phys.G has had a broad scope covering all aspects of the physics of elementary particles, nuclear physics, and nuclear and particle astrophysics. We have always felt this provides the journal's authors and readers with a unique overview of these increasingly interconnected subjects.When you publish in J.Phys.G you'll benefit from fast and impartial peer review, with an average receipt-to-first decision time for papers of 58 days. We strive to provide outstanding author service with online article submission, tracking of manuscripts and electronic refereeing. Publishing with us provides your paper with wide international visibility in print and online at www.iop.org/journals/jphysg. As well as being accessible to our subscribers, each new paper is freely available to all for 30 days on our Website

The number of women physicists doing research in Armenia is far less than the number of men, because women put their family and children ahead of their careers. Only a small number of women physicists who try to combine family life and career are successful. Armenia is a small country with few research positions; in spite of this there are several women physicists in Armenia. They are working very well in various areas of physics such as theoretical physics, nuclear physics, elementary particle physics, biophysics, and solid-state physics. Due to hard and fruitful work, some women physicists occupy high positions; for example, A. Danagulyan is the Chair of Nuclear Physics of Yerevan State University. In the three years since the First IUPAP International Conference on Women in Physics, female scientists of Armenia have worked very effectively. Four defended their PhD theses (Candidate) and one defended her Doctorate thesis during this period. Many papers of female scientists were presented at international conferences and printed in refereed journals. The women scientists at Yerevan State University (Dr. Prof. A. Danagulyan, Dr. A. Balabekyan, PhD student J. Drnoyan, and young researcher G. Hovhannisyan) have participated in six international conferences devoted to the problems of nuclear physics: International Seminar on Heavy Ion Physics. Joint Institute for Nuclear Research, Dubna, 2002 25th International Colloquium on Group Theoretical Methods in Physics, Cocoyoc, Mexico 2004 52nd, 53rd, and 54th International Conference on Nuclear Spectroscopy and Nuclear Structure, Moscow 2002, St. Petersburg 2003, and Belgorod 2004 VI Conference of Young Scientists of JINR, Dubna 2002 The main results are presented in 11 scientific papers published in refereed journals such as Nuclear Physics and Physics of Atomic Nuclei. Along with their research activities, these women scientists also have wide teaching experience. They are lecturers in nuclear physics, nuclear reactions, and elementary particle physics. Gohar Haroutunyan, the Doctor of Science at the Chair of Theoretical Physics of Yerevan State University, investigates the theory of gravitation and its astrophysical application. Six of her papers were published from 2002 to 2005. She teaches theoretical mechanics, statistical physics, and Green’s functions. Dr. Prof. Yeva Dalyan is a specialist in macromolecular physics, the physics of nucleic acids, and structural biology, and works in molecular pharmacology as well. Her papers are published in Biomolecular Structure and Dynamics, Experimental and Molecular Medicine, Molecular and Cellular Proteomics, and Biophysics. Dr. Prof. Dalyan reported the results of her work at the international conference “URM-2004” in Yerevan in 2004 and at the “International Symposium on Hydration and Thermodynamics of Molecular Recognition” in Armenia in 2005. She teaches courses in molecular physics, introduction to biophysics, and the physics of proteins and nucleic acids. Two female scientists (Dr. A. Djotyan and Sh. Gasparyan) participated in the International Women’s Conference on BIEN-Technology in Daejeon, Korea, in 2003 and presented two scientific reports. The papers are included in the proceedings of the conference in a special issue of the journal Key Engineering Materials. Dr. I.G. Aznauryan (Yerevan Institute of Physics) works in the field of quantum chromodynamics (QCD), which is the fundamental theory accepted now for the description of strong interactions of elementary particles. Dr. Aznauryan works in close cooperation with experimental physicists at Jefferson Lab in the United States. Her investigation of experimental data obtained at Jefferson Lab led to the determination that up to a momentum transfer of 5 GeV, there is no indication of an approaching perturbative region of QCD. The results of her work were published in Physical Review C67 and C68 (2003) and C71 (2005).

في هذه الورقة نتحدث عن مجموعة Heisenberg ، المثال الأكثر معرفة من مجموعات الكذب. بعد ذلك نناقش نظرية التمثيل لهذه المجموعة ، والعلاقة بين نظرية التمثيل لمجموعة Heisenberg وعوامل الموضع والزخم و عوامل الزخم. العلاقة بين نظرية التمثيل لمجموعة Heisenberg والموقف والمؤمن ، وهذا يوضح كيف سنقوم بالربط بين مجموعة Heisenberg والفيزياء. لقد نظرنا فقط في صورة Schr dinger. أي أن جميع التمثيلات التي أخذناها في الاعتبار يتم تحقيقها في فضاء هيلبرت. نحدد مجموعة تحويل فورييه في مجموعة هايزنبرغ كدالة ذات قيمة للمشغل ، وحقائق وخصائص أخرى. الهدف الرئيسي من بحثنا هو الحصول على صيغة Schr dinger Representation التي تربط الفيزياء بمجموعة Heisenberg. اعتمادًا على هذا التمثيل ، سوف ندرس الصيغ الجديدة لبعض المفاهيم الرياضية مثل تحويل فورييه و.

عرّفنا في بحثنا هذا زمرة هايزنبرغ، وهي الزمرة الأكثر شهرةً من زمر لي. ثمّ ناقشنا نظريّة التمثيل لهذه الزمرة، إضافةً إلى العلاقة بين نظريّة التمثيل لزمرة هايزنبرغ، ومؤثرات كميّة الحركة والموضع. وهذا ما يُبيّن لنا كيفية تحقيق الترابط بين زمرة هايزنبرغ والفيزياء. وسنأخذ في بحثنا هذا بوجهة نظر شرودنجر Schr dinger، التي تعتبر أنّ جميع التمثيلات التي نفرضها تتحقق على فضاء هيلبرت . ثمّ نُعرّف زمرة تحويل فورييه على زمرة هايزنبرغ. إضافةً إلى مفاهيم أخرى ذات أهميّة في الأبحاث المشابهة. وقد اعتمدنا في بحثنا هذا على صيغ جديدة لبعض المفاهيم الرياضيّة مثل تحويل فورييه وتحويل وايل. إنَ الهدف الرئيس من بحثنا هذا هو تقديم مبرهنة Paley_ Wiener لأجل تحويل فورييه على زمرة هايزنبرغ. وسوف نُبيّن أنّ مبرهنة Paley_ Wiener التقليديّة لتحويل فورييه التقليدي، تُميّز الدوال ذات الدعامة المتراصّة من خلال سلوك تحويل فورييه لها. وسنهتم بإنشاء النتائج لأجل زمرة تحويل فورييه، وتحويل وايل.