4 edition of **Geometrical and algebraic aspects of nonlinear field theory** found in the catalog.

- 29 Want to read
- 40 Currently reading

Published
**1989**
by North-Holland, Sole distributors for the U.S.A. and Canada, Elsevier Science Pub. Co. in Amsterdam, New York, New York, N.Y., U.S.A
.

Written in English

- Quantum field theory -- Congresses.,
- Nonlinear theories -- Congresses.,
- Geometry, Differential -- Congresses.

**Edition Notes**

Statement | edited by S. De Filippo ... [et al.]. |

Series | North-Holland delta series |

Contributions | De Filippo, S., Università degli studi di Salerno. |

Classifications | |
---|---|

LC Classifications | QC174.45.A1 I578 1988 |

The Physical Object | |

Pagination | x, 248 p. : |

Number of Pages | 248 |

ID Numbers | |

Open Library | OL2185464M |

ISBN 10 | 0444873597 |

LC Control Number | 89003414 |

The main result of this synthesis is Secondary Calculus on diffieties, new geometrical objects which are analogs of algebraic varieties in the context of (nonlinear) PDE's. Secondary Calculus surprisingly reveals a deep cohomological nature of the general theory of PDE's and indicates new directions of its further progress. A diffiety is a geometrical object that properly formalizes the concept of the solution space of a given system of (nonlinear) PDEs, much as an algebraic variety does with respect to solutions of.

This book is dedicated to fundamentals of a new theory, which is an analog of affine algebraic geometry for (nonlinear) partial differential equations. This theory grew up from the classical geometry of PDE's originated by S. Lie and his followers by incorporating some nonclassical ideas from the theory of integrable systems, the formal theory of PDE's in its modern cohomological form. This includes not only the traditional area of general relativity but also the theory of Yang-Mills fields, nonlinear sigma models and other types of nonlinear field systems that feature in modern quantum field volume is divided into four parts: (i) introduction to general topology; (ii) introductory coordinate-free differential.

Commutative Algebra, Algebraic Geometry, Number theory, Field Theory, Galois Theory by Sudhir R. Ghorpade Fundamental Problems in Algorithmic Algebra by Chee Yap Braid groups and Galois theory by Author: Kevin de Asis. FIELD THEORY 3 About these notes The purpose of these notes is to give a treatment of the theory of elds. Some as-pects of eld theory are popular in algebra courses at the undergraduate or graduate levels, especially the theory of nite eld extensions and Galois theory. However, aFile Size: KB.

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Geometrical and Algebraic Aspects of Nonlinear Field Theory A volume in North-Holland Delta Series. Book • (ordering of operators in quantum theory) The main emphasis is on the geometrical and algebraic methods used in solving a wide range of problems.

Purchase Geometrical and Algebraic Aspects of Nonlinear Field Theory - 1st Edition. Print Book & E-Book. ISBNBook Edition: 1. Get this from a library. Geometrical and Algebraic Aspects of Nonlinear Field Theory. [S De Filippo; M Marinaro; G Marmo; G Vilasi] -- Experts in general relativity, particle physics and mathematical physics discuss aspects of their recent research.

The main emphasis is on the geometrical and algebraic methods used in solving a wide. Get this from a library. Geometrical and algebraic aspects of nonlinear field theory: proceedings of the meeting on geometrical and algebraic aspects of nonlinear field theory, Amalfi, Italy, May[S De Filippo; Università degli studi di Salerno.;].

The book The Nonlinear Quantum Field Theory as a Generalization of Standard Model (Geometrical Approach), by Alexander G.

Kyriakos is dedicated to a nonlinear generalization of the Standard Model theory - the contemporary theory of elementary particles and their interactions. The Standard Model is a very successful : Alexander G Kyriakos.

Geometrical and algebraic aspects of nonlinear field theory book This book discusses the deep connection between gravitation and the nonlinear sigma model coupled to gauge fields in a new perspective. Interesting developments emerge. Some other new aspects are provided such as the constant use of infinite dimensional differential geometry, a powerful tool not only for making the theory more rigorous but also.

In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined and behave as the corresponding operations on rational and real numbers do. A field is thus a fundamental algebraic structure which is widely used in algebra, number theory, and many other areas of mathematics.

The best known fields are the field of rational numbers, the field of real. Geometric phases, recognized as a universal phenomenon 35 years ago by Michael Berry [1, 2], play a fundamental role in the interference of vector waves, especially monochromatic optical fields [3–8].They are therefore ubiquitous in several areas of modern optics including polarization manipulations [4, 9–11], singular optics [12–14], and the angular momentum (AM) of light [15–19].Cited by: 5.

Suitable for specialists as well as graduate students working in the field of quantum geometry and its applications; Includes a new chapter on the geometry of dilatonic non-linear sigma model and its subtle and many-faceted connection with Ricci flow theory; see more benefits.

Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical problems about these sets of zeros.

The fundamental objects of study in algebraic geometry are algebraic varieties, which are geometric manifestations of. In Quantum Field Theory, elementary particles come up as field quanta. Their quantum numbers, such as mass and helicity, are fixed by the corresponding free fields.

This means that, to be related to a particle, a field must exist in free state, or to be well defined far. Non-Linear Field Theories of Mechanics has become a classic treatise in the field of continuum mechanics. Originally published nearly forty years ago, it probably has influenced practically all subsequent monographs on the subject.

Its main parts are: The General Theory of Material Behavior - Elasticity - FluidityCited by: This includes not only the traditional area of general relativity but also the theory of Yang-Mills fields, nonlinear sigma models and other types of nonlinear field systems that feature in modern quantum field volume is divided into four parts: (i) introduction to general topology; (ii) introductory coordinate-free differential 3/5(2).

B.6 Algebraic quantum ﬁeld theory Bibliography Index However, the book in hand is a good ﬁrst step for the mathematicians. The method of the text is to explain the meaning of a large number of - Mathematical Aspects of Quantum Field Theory. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non trivially) in regional and theoretical economics; algebraic geometry interacts with physics; ihe Minkowsky lemma, coding theory and the structure of water meet one another in packing and.

Here we review current progress in understanding these sequences from algebraic, geometric and arithmetic viewpoints.

Christian Klein: Numerical study of $2+1$ dimensional nonlinear dispersive PDEs. We present several numerical studies of solutions to PDEs from the family of nonlinear Schrödinger and Korteweg-de Vries equations. When a field itself admits a notion of addition, the theory can still fail to be linear when the equations of motions are nonlinear.

This is, for example, the case for ¨nonlinear Klein-Gordon equations¨. A geometrical approach to the nonlinear solvable equations, based on the study of the “groups of motion” of special infinite-dimensional manifolds called “symplectic Kahler manifolds”, is suggested.

This approach is constructive, tensorial and simple in its by: GEOMETRIC ASPECTS OF THE THEORY OF FULLY NON LINEAR ELLIPTIC EQUATIONS JOEL SPRUCK Lecture 1: Introduction In these lectures, we will talk about various aspects of the theory of fully nonlinear elliptic equations as they pertain to Global Di erential Geometry.

Advances in this theory in the last twenty years have opened the possibility of File Size: KB. The book is a collection of solved problems in linear algebra, this fourth volume covers quadratic equations in two or three variables. All examples are solved, and the solutions usually consist of step-by-step instructions.

( views) Linear Algebra C Geometrical Vectors, Vector Spaces and Linear Maps by Leif Mejlbro - BookBoon. An overview of Lie's line-sphere correspondence by R. Milson Application of Lie group analysis to a mathematical model which describes HIV transmission by V.

Torrisi and M. C. Nucci Geometry and PDE on the Heisenberg group: A case study by R. Beals Invariant evolutions of curves and surfaces and completely integrable Hamiltonian systems by G. Mari Beffa On the fixed points of .We prove the main theorem of Class Field Theory, study the reciprocity map and some cohomological aspects.

Contents of the course Part I: Introduction to the theory of algebraic curves 1. Basics of algebraic curves following Chapter 4 of Hartshorne 2. More in depth study of the theory of algebraic curves following Chapters IV and V of Serre’s.The book, "algebraic geometry and statistical learning theory", proves these theorems.

A new mathematical base is established, on which statistical learning theory is studied. Algebraic geometry is explained for non-specialists and non-mathematicians. Special Remark Please see the true likelihood function or the posterior distribution.