available from October 2021
FORMAT: Paperback ISBN: 9781108972352 Hardback ISBN: 9781108838801
This collection of problems in Quantum Field Theory, accompanied by their complete solutions, aims to bridge
the gap between learning the foundational principles and applying them practically. The carefully chosen problems
cover a wide range of topics, starting from the foundations of Quantum Field Theory and the traditional methods in
perturbation theory, such as LSZ reduction formulas, Feynman diagrams and renormalization. Separate chapters are
devoted to functional methods (bosonic and fermionic path integrals; worldline formalism), to non-Abelian gauge theories
(Yang-Mills theory, Quantum Chromodynamics), to the novel techniques for calculating scattering amplitudes
and to quantum field theory at finite temperature (including its formulation on the lattice, and extensions to systems
out of equilibrium). The problems range from those dealing with QFT formalism itself to problems addressing specific
questions of phenomenological relevance, and they span a broad range in difficulty, for graduate students taking their first or second course in QFT.
Allows students to appreciate the 'big picture' connections of this vast subject by presenting aspects of QFT that are usually only treated in specialized texts
Explains the current methods for calculating scattering amplitudes in particle physics, which are outdated in the older, traditional textbooks
By solving these problems and reproducing their solutions, readers will have reached a level of proficiency far higher than
what one would get by just learning the 'theory', reducing the gap between taught courses and actual research tools
While this is a self-contained problems/solutions book, an online supplement provides explicit links between
the discussions presented and the content of the author's QFT textbook (ISBN 9781108480901)
Preface
Acknowledgements
Notations and Conventions
Part I. Quantum Field Theory Basics
Part II. Functional Methods
Part III. Non-Abelian Fields
Part IV. Scattering Amplitudes
Part V. Lattice, Finite T, Strong Fields
Index.
Contains insight into the polynomial stability phenomenon
Systematically presents recent results in the field
Serves as a self-contained volume
This brief investigates the asymptotic behavior of some PDEs on networks. The structures
considered consist of finitely interconnected flexible elements such as strings and beams (or
combinations thereof), distributed along a planar network.Such study is motivated by the need
for engineers to eliminate vibrations in some dynamical structures consisting of elastic bodies,
coupled in the form of chain or graph such as pipelines and bridges. There are other
complicated examples in the automotive industry, aircraft and space vehicles, containing rather
than strings and beams, plates and shells. These multi-body structures are often complicated,
and the mathematical models describing their evolution are quite complex. For the sake of
simplicity, this volume considers only 1-d networks
Due 2021-11-26
1st ed. 2021, X, 140 p. 16 illus., 12 illus. in color.
Softcover
ISBN 978-3-030-86350-0
Product category : Brief
Series : SpringerBriefs in Mathematics
Mathematics : Analysis
A Guided Approach to Algebra, Geometry, Topology and Analysis
Covers topics in abstract algebra, topology, analysis, and geometry in an innovative way
Explains core elementary subjects of undergraduate mathematics in plain English
Offers a rich set of exercises and references for self-study
This textbook covers topics of undergraduate mathematics in abstract algebra, geometry,
topology and analysis with the purpose of connecting the underpinning key ideas. It guides
STEM students towards developing knowledge and skills to enrich their scientific education. In
doing so it avoids the common mechanical approach to problem-solving based on the
repetitive application of dry formulas. The presentation preserves the mathematical rigour
throughout and still stays accessible to undergraduates. The didactical focus is threaded
through the assortment of subjects and reflects in the book’s structure. Part 1 introduces the
mathematical language and its rules together with the basic building blocks. Part 2 discusses
the number systems of common practice, while the backgrounds needed to solve equations
and inequalities are developed in Part 3. Part 4 breaks down the traditional, outdated barriers
between areas, exploring in particular the interplay between algebra and geometry. Two
appendices form Part 5: the Greek etymology of frequent terms and a list of mathematicians
mentioned in the book. Abundant examples and exercises are disseminated along the text to
boost the learning process and allow for independent work. Students will find invaluable
material to shepherd them through the first years of an undergraduate course, or to
complement previously learnt subject matters. Teachers may pick’n’mix the contents for
planning lecture courses or supplementing their classes.
Due 2021-11-17
1st ed. 2021, IV, 496 p. 153 illus., 115 illus. in color.
Hardcover
Product category : Undergraduate textbook
Mathematics : Linear Algebra
Covers both mathematical analysis and computational techniques for solving
direct and inverse problems
Addresses recent significant developments as near field imaging, nonlinear
optics, and optimal design problem
Presents preliminary materials for students on diffraction problems in
periodic structures and variational formulation
This book addresses recent developments in mathematical analysis and computational
methods for solving direct and inverse problems for Maxwell’s equations in periodic structures.
The fundamental importance of the fields is clear, since they are related to technology with
significant applications in optics and electromagnetics. The book provides both introductory
materials and in-depth discussion to the areas in diffractive optics that offer rich and
challenging mathematical problems. It is also intended to convey up-to-date results to
students and researchers in applied and computational mathematics, and engineering
disciplines as well.
1st ed. 2022, XI, 355 p. 32 illus., 17 illus. in color.
Hardcover
ISBN 978-981-16-0060-9
Product category : Monograph
Series : Applied Mathematical Sciences
Mathematics : Partial Differential Equations
An Introduction to the General Algebraic Study of Non-classical Logics
Presents an introduction to the algebraic study of non-classical logics
Details a powerful methodology to understand logics with implication
Includes many particular logics as examples for the theory
This monograph presents a general theory of weakly implicative logics, a family covering a vast
number of non-classical logics studied in the literature, concentrating mainly on the abstract
study of the relationship between logics and their algebraic semantics. It can also serve as an
introduction to (abstract) algebraic logic, both propositional and first-order, with special
attention paid to the role of implication, lattice and residuated connectives, and generalized
disjunctions. Based on their recent work, the authors develop a powerful uniform framework
for the study of non-classical logics. In a self-contained and didactic style, starting from very
elementary notions, they build a general theory with a substantial number of abstract results.
The theory is then applied to obtain numerous results for prominent families of logics and
their algebraic counterparts, in particular for superintuitionistic, modal, substructural, fuzzy, and
relevant logics. The book may be of interest to a wide audience, especially students and
scholars in the fields of mathematics, philosophy, computer science, or related areas, looking
for an introduction to a general theory of non-classical logics and their algebraic semantics.
Due 2021-12-13
1st ed. 2021, XXII, 466 p. 17 illus.
Hardcover
ISBN 978-3-030-85674-8
Product category : Monograph
Series : Trends in Logic
Other renditions
Philosophy : Logic
https://doi.org/10.1142/12364 | August 2021
Pages: 712
ISBN: 978-981-124-005-8 (hardcover)
ISBN: 978-981-124-145-1 (softcover)
How to see physics in its full picture? This book offers a new approach: start from math, in its simple
and elegant tools: discrete math, geometry, and algebra, avoiding heavy analysis that might obscure the true picture.
This will get you ready to master a few fundamental topics in physics:
from Newtonian mechanics, through relativity, towards quantum mechanics.
Thanks to simple math, both classical and modern physics follow and make a complete vivid picture of physics.
This is an original and unified point of view to highlighting physics from a fresh pedagogical angle.
Each chapter ends with a lot of relevant exercises.
The exercises are an integral part of the chapter: they teach new material and are followed by complete solutions.
This is a new pedagogical style: the reader takes an active part in discovering the new material, step by step, exercise by exercise.
The book could be used as a textbook in undergraduate courses such as Introduction to Newtonian mechanics
and special relativity, Introduction to Hamiltonian mechanics and stability, Introduction to quantum physics and chemistry,
and Introduction to Lie algebras with applications in physics.
Introduction to Newtonian Physics:
Introduction to Newtonian Mechanics: Energy-Work
Angular Momentum and Its Conservation
Stability in Geometrical Optics
Towards Stability in Classical Mechanics:
Poincare Stability in Classical Mechanics
Cantor Set and Its Applications
Is The Universe Infinite?
Binary Trees and Chaos Theory
The Binomial Formula and Quantum Statistical Mechanics:
Newton's Binomial and Trinomial Formulas
Applications in Quantum Statistical Mechanics
Introduction to Relativity:
Introduction to Special Relativity: Momentum-Energy
Towards General Relativity: Spacetime and Its Coordinates
Introduction to Quantum Physics and Chemistry:
Introduction to Quantum Mechanics: Energy Levels and Spin
Quantum Chemistry: Electronic Structure
Introduction to Lie Algebras and Their Applications:
Jordan Form and Algebras
Design Your Lie Algebra
Ideals and Isomorphism Theorems
Exercises: Solvability and Nilpotency
Nilpotency and Engel's Theorems
Weight Space and Lie's Lemma and Theorem
Cartan's Criterion for Solvability
Killing Form and Simple Ideal Decomposition
Hamiltonian Mechanics: Energy and Angular Momentum
Lie Algebras in Quantum Mechanics and Special Relativity
Appendix: Background in Calculus:
Functions and Their Derivatives
Polynomials and Partial Derivatives
Matrices and Their Eigenvalues
References
Index
Undergraduate and graduate students in Mathematics, Physics, and Chemistry.