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• Introduction
• A Guess at the Riddle
• Physical Laws and Physical Things
• The Still More Basic Question.

• Prologue
• Paris, 1903: Cracks begin to appear
• Berlin, 1900: An act of desperation
• Bern, 1905: The patent serf
• Paris, 1906: The decline and fall of Pierre Curie
• Berlin, 1909: The end of the flying cigars
• Prague, 1911: Einstein says it with flowers
• Cambridge, 1911: A Dane grows up
• The North Atlantic, 1912: The sinking of infallibility
• Munich, 1913: A painter moves to Munich
• Munich, 1914: On tour with the atom
• Berlin, 1915: Good at theory, bad at relationships
• Germany, 1916: War and peace
• Berlin, 1917: Einstein breaks down
• Berlin, 1918: Pandemic
• The Mid-Atlantic, 1919: The moon obscures the sun
• Munich, 1919: A young man reads Plato
• Berlin, 1920: Great minds meet
• Göttingen, 1922: A son finds his father
• Munich, 1923: A highflier almost crashes
• Copenhagen, 1923: Bohr and Einstein take the tram
• Copenhagen, 1924: One last try
• Paris, 1924: A prince makes atoms sing
• Heligoland, 1925: The vastness of the sea and the tininess of atoms
• Cambridge, 1925: The quiet genius
• Leiden, 1925: The prophet of spin
• Arosa, 1925: A late erotic outburst
• Copenhagen, 1926: Waves and particles
• Berlin, 1926: A visit with the demigods
• Berlin, 1926: The Plancks throw a party
• Göttingen, 1926: The abolition of reality
• Munich, 1926: A turn war
• Copenhagen, 1926: Exquisitely carved marble statues falling out of the sky
• Copenhagen, 1926: A game with sharpened knives
• Copenhagen, 1927: The world goes fuzzy
• Como, 1927: The great debate
• Berlin, 1930: Germany flourishes; Einstein falls ill
• Brussels, 1930: KO in the second round
• Zurich, 1931: Pauli's dreams
• Copenhagen, 1932: Faust in Copenhagen
• Berlin, 1933: Some flee; some stay
• Amsterdam, 1933: A sad end
• Oxford, 1935: The cat that isn't there
• Princeton, 1935: Einstein puts the world back in focus
• Garmisch, 1936: Dirty snow
• Moscow, 1937: On the other side
• Berlin, 1938: Bursting nuclei
• The Atlantic, 1939: Terrible news
• Copenhagen, 1941: Estrangement
• Berlin, 1942: No bomb for Hitler
• Stockholm, 1943: Flight
• Princeton, 1943: Einstein mellows
• England, 1945: The impact of the explosion
• Epilogue.

"The epic true story of how a global team of physics luminaries-Einstein, Curie, Schrödinger, and more-toppled the Newtonian universe amid the turmoil of two World Wars"-- Provided by publisher.

What is 'the void'? What remains when you take all the matter away? Can empty space - 'nothing' - exist? This text explores the science & history of the elusive void - from Aristotle's theories to black holes & quantum particles, & why our very latest discoveries about the vacuum can tell us extraordinary things about the cosmos

• Intro
• ANHA Series Preface
• En guise de préface
• Contents
• Contributors
• The Making of a Physicist
• Alex Grossmann, a Rinascimento Multidisciplinary Man
• 1 A Jubilee of Multifold Research
• 2 Quantum Physics and Related Fields
• 3 Wavelets
• 4 Genomics
• 5 How to Conclude Such a Short But Mind-Boggling Overview?
• 6 Postlude: A Geometric Existentialist Way of Thinking
• Generalized Affine Signal Analysis with Time-Delay Thresholds

• Introductory Note on the Draft Paper ``Generalized Affine Signal Analysis with Time-Delay Thresholds'', by Jan W. Dash, Alex Grossmann and Thierry Paul
• 1 Wavelets in the Mid-1980s
• 1.1 The Group-Theoretic View of Wavelets
• 1.2 Overcompleteness Can Be a Virtue
• 1.3 Comments on the First Sentence: ``A Class of Functions Recently Introduced by Dash and Paul ...''
• 1.4 Phase
• 2 Specific Comments on the Text
• 3 Le Baron de Prony's Overcomplete Set of ``Wavelets à la Neanderthal''
• 4 Alex
• 5 Addendum/Corrigendum

• Alex Grossmann's PhD Thesis (Harvard 1959): Covariant Functions of Quantum Fields
• Table of Contents and Introduction
• Part I Quantum Mechanics and Theoretical Physics
• Alex Grossmann, from Nested Hilbert Spaces to Partial Inner Product Spaces and Wavelets
• 1 Introduction: Some History
• 2 Rigged Hilbert Spaces
• 3 Nested Hilbert Spaces
• 4 Towards Partial Inner Product Spaces
• 5 Operators on PIP-Spaces
• 5.1 General Definitions
• 5.2 Homomorphisms and Orthogonal Projections
• 5.3 Symmetric Operators and Self-Adjointness
• 6 Applications in Quantum Mechanics

• 6.1 General Formulation
• 6.2 Resonances, Analyticity Properties
• 6.3 Condensed Matter Physics
• 7 The Legacy: Operator Partial Algebras
• 8 Towards 2D Wavelets
• 9 Epilogue
• References
• Combining Quantum Mechanical Languages (A Tribute to Alex Grossmann)
• 1 Introduction
• 2 The kq-Representation
• 3 Bloch-Like Functions
• 4 Phase of the Bloch Function
• 5 kq-Space
• 6 Conclusion
• References
• Alex Grossmann, Scattering Amplitude, Fermi Pseudopotential, and Particle Physics
• 1 Harvard and Scattering Amplitude
• 2 Marseille and Fermi Pseudopotential
• 3 Particle Physics

• References
• Sixty Years of Hadronic Vacuum Polarization
• 1 Introduction
• 2 What Is Hadronic Vacuum Polarization-- 3 HVP and the Muon μ-Particle
• 4 Mellin-Barnes Representation of aμHVP
• 5 The Time Momentum Representation
• 6 Limitations of the LQCD Evaluations
• 7 Mellin-Barnes Approximants
• 7.1 Euler Beta-Function Approximants
• 8 Time Momentum Representation Approximants
• 8.1 Heaviside Spectral Function Approximants
• 9 Conclusion
• References
• Standard Model, and Its Standard Problems
• 1 Prologue
• 2 A Short Introduction to the Standard Model A.D. 2021

• 2.1 The Neutrino Mass Sector Sν

Over the course of a scientific career spanning more than fifty years, Alex Grossmann (1930-2019) made many important contributions to a wide range of areas including, among others, mathematics, numerical analysis, physics, genetics, and biology. His lasting influence can be seen not only in his research and numerous publications, but also through the relationships he cultivated with his collaborators and students. This edited volume features chapters written by some of these colleagues, as well as researchers whom Grossmanns work and way of thinking has impacted in a decisive way. Reflecting the diversity of his interests and their interdisciplinary nature, these chapters explore a variety of current topics in quantum mechanics, elementary particles, and theoretical physics; wavelets and mathematical analysis; and genomics and biology. A scientific biography of Grossmann, along with a more personal biography written by his son, serve as an introduction. Also included are the introduction to his PhD thesis and an unpublished paper coauthored by him. Researchers working in any of the fields listed above will find this volume to be an insightful and informative work.

• Frontmatter
• Contents
• 1 Introduction
• 2 Nonlinear maps
• 3 Dynamical systems
• 4 Ordinary differential equations I, initial value problems
• 5 Ordinary differential equations II, boundary value problems
• 6 Ordinary differential equations III, memory, delay and noise
• 7 Partial differential equations I, basics
• 8 Partial differential equations II, applications
• 9 Monte Carlo methods
• A Matrices and systems of linear equations
• B Program library
• C Solutions of the problems
• D README and a short guide to FE-tools
• Index