FRACTIONAL CALCULUS
An Introduction for Physicists
by Richard Herrmann (GigaHedron, Germany)
276pp
978-981-4340-24-3: US$85 / £53 US$59.50
/ £37.10
Table
of Contents (119k)
Foreword
(106k)
Chapter
1: Introduction (247k)
Fractional calculus is undergoing rapid and ongoing
development. We can already recognize, that within its framework new
concepts and strategies emerge, which lead to new challenging insights
and surprising correlations between different branches of physics.
This book is an invitation both to the interested student and
the professional researcher. It presents a thorough introduction to the
basics of fractional calculus and guides the reader directly to the
current state-of-the-art physical interpretation. It is also devoted to
the application of fractional calculus on physical problems, in the
subjects of classical mechanics, friction, damping, oscillations, group
theory, quantum mechanics, nuclear physics, and hadron spectroscopy up
to quantum field theory.
Contents:
- Functions
- The Fractional Derivative
- Friction Forces
- Fractional Calculus
- The Fractional Harmonic Oscillator
- Wave Equations and Parity
- Nonlocality and Memory Effects
- Quantum Mechanics
- Fractional Spin: A Property of Particles
Described with the Fractional Schrödinger Equation
- Factorization
- Symmetries
- The Fractional Symmetric Rigid Rotor
- q-Deformed Lie Algebras and Fractional Calculus
- Fractional Spectroscopy of Hadrons
- Higher Dimensional Fractional Rotation Groups
- Fractors: Fractional Tensor Calculus
- Fractional Fields
- Gauge Invariance in Fractional Field Theories
- Outlook
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