Symmetries in Atomic Nuclei: From Isospin to Supersymmetry (Springer Tracts in Modern Physics Book 230)

__Symmetries in Atomic Nuclei__ aims to present an overview of recent applications of symmetry to the description of atomic nuclei. Special care is given to a pedagogical introduction of symmetry concepts using simple examples. After a historical overview of the applications of symmetry in nuclear physics, progress in the field during the last decade is reviewed. Special emphasis is put on the introduction of neutron-proton and boson-fermion degrees of freedom. Their combination leads to a supersymmetric description of pairs and quartets of nuclei. Both theoretical aspects and experimental signatures of dynamical (super)symmetries are carefully discussed. Case studies show how these symmetries are displayed by real atomic nuclei which have been studied experimentally using state-of-the art spectroscopy. __Symmetries in Atomic Nuclei__ focuses on nuclear structure physics and has been written by active investigators in the field, but its scope is wider and is intended for final-year or post-graduate students and researchers interested in understanding the power and beauty of symmetry methods in physics. This Text Was Originally Written For A Capstone Course At Michigan State University. A Capstone Course Is Intended For Undergraduate Mathematics Majors, As One Of The Final Courses Taken In Their Undergraduate Curriculum. Its Purpose Is To Bring Together Different Topics Covered In The Undergraduate Curriculum And Introduce Students To Current Developments In Mathematics And Their Applications. Basic Wavelet Theory Seems To Be A Perfect Topic For Such A Course. As A Subject, It Dates Back Only To 1985. Since Then There Has Been An Explosion Of Wavelet Research, Both Pure And Applied. Wavelet Theory Is On The Boundary Between Mathematics And Engineering. In Particular It Is A Good Topic For Demonstrating To Students That Mathematics Research Is Thriving In The Modern Day: Students Can See Non-trivial Mathematics Ideas Leading To Natural And Important Applications, Such As Video Compression And The Numerical Solution Of Differential Equations. The Only Prerequisites Assumed Are A Basic Linear Algebra Background And A Bit Of Analysis Background. This Text Is Intended To Be As Elementary An Introduction To Wavelet Theory As Possible. It Is Not Intended As A Thorough Or Authoritative Reference On Wavelet Theory. Preface -- Acknowledgements -- Prologue: Compression Of The Fbi Fingerprint Files -- Background: Complex Numbers And Linear Algebra -- The Discrete Fourier Transform -- Wavelets On Zn -- Wavelets On R -- Wavelets And Differential Equations -- Bibliography -- Index. Michael W. Frazier. Includes Bibliographical References (p. 484-490) And Index. Mathematics majors at Michigan State University take a “Capstone” course near the end of their undergraduate careers. The content of this course varies with each offering. Its purpose is to bring together different topics from the undergraduate curriculum and introduce students to a developing area in mathematics. This text was originally written for a Capstone course. Basicwavelettheoryisanaturaltopicforsuchacourse. Byname, wavelets date back only to the 1980s. On the boundary between mathematics and engineering, wavelet theory shows students that mathematics research is still thriving, with important applications in areas such as image compression and the numerical solution of differential equations. The author believes that the essentials of wavelet theory are suf?ciently elementary to be taught successfully to advanced undergraduates. This text is intended for undergraduates, so only a basic background in linear algebra and analysis is assumed. We do not require familiarity with complex numbers and the roots of unity. These are introduced in the?rst two sections of chapter 1. In the remainder of chapter 1 we review linear algebra. Students should be familiar with the basic de?nitions in sections 1. 3 and 1. 4. From our viewpoint, linear transformations are the primary object of study; v Preface vi a matrix arises as a realization of a linear transformation. Many students may have been exposed to the material on change of basis in section 1. 4, but may bene?t from seeing it again. In section 1. "Symmetries in Atomic Nuclei aims to present an overview of recent applications of symmetry to the description of atomic nuclei. Special care is given to a pedagogical introduction of symmetry concepts using simple examples. After a historical overview of the applications of symmetry in nuclear physics, progress in the field during the last decade is reviewed. Special emphasis is put on the introduction of neutron-proton and boson-fermion degrees of freedom. Their combination leads to a supersymmetric description of pairs and quartets of nuclei." "Both theoretical aspects and experimental signatures of dynamical (super)symmetries are carefully discussed. Case studies show how these symmetries are displayed by real atomic nuclei which have been studied experimentally using state-of-the art spectroscopy." "Symmetries in Atomic Nuclei focuses on nuclear structure physics and has been written by active investigators in the field, but its scope is wider and is intended for final-year or post-graduate students and researchers interested in understanding the power and beauty of symmetry methods in physics."--Jacket Symmetries in Atomic Nuclei aims to present an overview of recent applications of symmetry to the description of atomic nuclei. Special care is given to a pedagogical introduction of symmetry concepts using simple examples. After a historical overview of the applications of symmetry in nuclear physics, progress in the field during the last decade is reviewed. Special emphasis is put on the introduction of neutron-proton and boson-fermion degrees of freedom. Their combination leads to a supersymmetric description of pairs and quartets of nuclei. Both theoretical aspects and experimental signatures of dynamical (super)symmetries are carefully discussed. Case studies show how these symmetries are displayed by real atomic nuclei which have been studied experimentally using state-of-the art spectroscopy. This book focuses on nuclear structure physics and has been written by active investigators in the field, but its scope is wider and is intended for final-year or post-graduate students and researchers interested in understanding the power and beauty of symmetry methods in physics. "This introduction to wavelets assumes a basic background in linear algebra (reviewed in Chapter 1) and real analysis at the undergraduate level. Fourier and wavelet analyses are first presented in the finite-dimensional context, using only linear algebra. Then Fourier series are introduced in order to develop wavelets in the infinite-dimensional, but discrete context. Finally, the text discusses Fourier transform and wavelet theory on the real line. The computation of the wavelet transform via filter banks is emphasized, and applications to signal compression and numerical differential equations are given."--BOOK JACKET. "This text is ideal for a topics course for mathematics majors, because it exhibits an emerging mathematical theory with many applications. It also allows engineering students without graduate mathematics prerequisites to gain a practical knowledge of wavelets."--BOOK JACKET. Wavelet theory is on the boundary between mathematics and engineering, making it ideal for demonstrating to students that mathematics research is thriving in the modern day. Students can see non-trivial mathematics ideas leading to natural and important applications, such as video compression and the numerical solution of differential equations. The only prerequisites assumed are a basic linear algebra background and a bit of analysis background. Intended to be as elementary an introduction to wavelet theory as possible, the text does not claim to be a thorough or authoritative reference on wavelet theory. Front Matter....Pages I-XII Symmetry and Supersymmetry in Quantal Many-Body Systems....Pages 1-27 Symmetry in Nuclear Physics....Pages 29-78 Supersymmetry in Nuclear Physics....Pages 79-104 Symmetries with Neutrons and Protons....Pages 105-121 Supersymmetries with Neutrons and Protons....Pages 133-153 Supersymmetry and Supersymmetric Quantum Mechanics....Pages 155-170 Conclusion....Pages 171-172 Back Matter....Pages 173-185 When your local police arrest somebody on a minor charge, they would like to check whether that person has an outstanding warrant, possibly in another state, for a more serious crime. A. Frank, J. Jolie, P. Van Isacker. Includes Bibliographical References (p. 173-181) And Index.