Carmeli M., Malin S. - Theory of spinors._An introduction
Theory of spinors: An introduction Carmeli M., Malin S.
Language: English
Page: 228
Format: djvu
ISBN: 9810242611, 9789810242619
Publisher: WS
Preface
This is a textbook intended for advanced undergraduate and graduate
students in physics and mathematics, as well as a reference for researchers.
The book is based on lectures given during the years at the Ben Gurion
University, Israel. Spinors are used extensively in physics; it is widely,
accepted that they are more fundamental than tensors and the easy way to
see this fact is the results obtained in general relativity theory by using
spinors, results that could not have been obtained by using tensor methods
only. The book is written for the general physicist and not only to the
workers in general relativity, even though the latter will find it most useful
since it includes all what is needed in that theory.
But the foundations of the concept of spinors are groups; spinors appear
as representations of groups. In this text we give a wide exposition to the
relationship between the spinors and the representations of the groups. As
is well known, both the spinors and the representations are widely used in
the theory of elementary particles.
After presenting the origin of spinors from representation theory we,
nevertheless, apply the theory of spinors to general relativity theory, and a
part of the book is devoted to curved spacetime applications.
In the first four chapters we present the group-theoretical foundations
of the concept of two-component spinors. Chapter 1 starts with an
introduction to group theory emphasizing the rotation group. This followed
by discussing representation theory in Chapter 2, including a brief
outline of the infinite-dimensional case. Chapters 3 and 4 discuss in detail
the Lorentz and the SL(2,C) groups. Here we give an extensive discussion
on how two-component spinors emerge from the finite-dimensional
representations of the group SL(2,C). Chapter 4 also includes the derivation
of infinite-dimensional spinors as a generalization to the two-component
spinors.
In Chapters 5 and 6 we apply the two-component spinors to a variety of
problems in curved spacetime. In Chapter 5 we discuss the Maxwell, Dirac
and Pauli spinors. Also given in this chapter the passage to the curved
spacetime of spinors. The gravitational field spinors are subsequently
discussed in detail in Chapter 6. Here we derive the curvature spinor and give
the spinors equivalent to the Riemann, Weyl, Ricci and Einstein tensors.
In Chapter 7 we present the gauge field spinors and discuss their
geometrical properties. As is well known, gauge fields are extremely important
nowadays. The Euclidean gauge field spinors are finally discussed in
Chapter 8.
All chapters of the book start with the ordinary physical material before
introducing the spinors of that subject. Thus, for instance, the chapters
dealing with the Lorentz group and gravitation start with detailed
discussion of the theories of special relativity and general relativity.
It is a pleasure to thank our wifes Elisheva and Tova for creating the
necessary atmosphere and for their patience while writing this book. We are
grateful to the many students who attended the courses in spinors during
the years for their suggestions which led to a better presentation of the
material in the book. We also want to thank Silvia Behar for her help with
the Index of the book. Finally, we want to thank Julia Goldbaum for the
excellent job of typing the book, prepairing the Index, and for the many
suggestions for improvements.
Theory of spinors: An introduction Carmeli M., Malin S.
Language: English
Page: 228
Format: djvu
ISBN: 9810242611, 9789810242619
Publisher: WS
Preface
This is a textbook intended for advanced undergraduate and graduate
students in physics and mathematics, as well as a reference for researchers.
The book is based on lectures given during the years at the Ben Gurion
University, Israel. Spinors are used extensively in physics; it is widely,
accepted that they are more fundamental than tensors and the easy way to
see this fact is the results obtained in general relativity theory by using
spinors, results that could not have been obtained by using tensor methods
only. The book is written for the general physicist and not only to the
workers in general relativity, even though the latter will find it most useful
since it includes all what is needed in that theory.
But the foundations of the concept of spinors are groups; spinors appear
as representations of groups. In this text we give a wide exposition to the
relationship between the spinors and the representations of the groups. As
is well known, both the spinors and the representations are widely used in
the theory of elementary particles.
After presenting the origin of spinors from representation theory we,
nevertheless, apply the theory of spinors to general relativity theory, and a
part of the book is devoted to curved spacetime applications.
In the first four chapters we present the group-theoretical foundations
of the concept of two-component spinors. Chapter 1 starts with an
introduction to group theory emphasizing the rotation group. This followed
by discussing representation theory in Chapter 2, including a brief
outline of the infinite-dimensional case. Chapters 3 and 4 discuss in detail
the Lorentz and the SL(2,C) groups. Here we give an extensive discussion
on how two-component spinors emerge from the finite-dimensional
representations of the group SL(2,C). Chapter 4 also includes the derivation
of infinite-dimensional spinors as a generalization to the two-component
spinors.
In Chapters 5 and 6 we apply the two-component spinors to a variety of
problems in curved spacetime. In Chapter 5 we discuss the Maxwell, Dirac
and Pauli spinors. Also given in this chapter the passage to the curved
spacetime of spinors. The gravitational field spinors are subsequently
discussed in detail in Chapter 6. Here we derive the curvature spinor and give
the spinors equivalent to the Riemann, Weyl, Ricci and Einstein tensors.
In Chapter 7 we present the gauge field spinors and discuss their
geometrical properties. As is well known, gauge fields are extremely important
nowadays. The Euclidean gauge field spinors are finally discussed in
Chapter 8.
All chapters of the book start with the ordinary physical material before
introducing the spinors of that subject. Thus, for instance, the chapters
dealing with the Lorentz group and gravitation start with detailed
discussion of the theories of special relativity and general relativity.
It is a pleasure to thank our wifes Elisheva and Tova for creating the
necessary atmosphere and for their patience while writing this book. We are
grateful to the many students who attended the courses in spinors during
the years for their suggestions which led to a better presentation of the
material in the book. We also want to thank Silvia Behar for her help with
the Index of the book. Finally, we want to thank Julia Goldbaum for the
excellent job of typing the book, prepairing the Index, and for the many
suggestions for improvements.
