Ebook: Noncommutative Dynamics and E-Semigroups

The term Noncommutative Dynamics can be interpreted in several ways. It is used in this book to refer to a set of phenomena associated with the dynamics of quantum systems of the simplest kind that involve rigorous mathematical structures associated with infinitely many degrees of freedom. The dynamics of such a system is represented by a one-parameter group of automorphisms of a noncommutative algebra of observables, and the author focuses primarily on the most concrete case in which that algebra consists of all bounded operators on a Hilbert space.

This subject overlaps with several mathematical areas of current interest, including quantum field theory, the dynamics of open quantum systems, noncommutative geometry, and both classical and noncommutative probability theory. This is the first book to give a systematic presentation of progress during the past fifteen years on the classification of E-semigroups up to cocycle conjugacy. There are many new results that cannot be found in the existing literature, as well as significant reformulations and simplifications of the theory as it exists today.

William Arveson is Professor of Mathematics at the University of California, Berkeley. He has published two previous books with Springer-Verlag, An Invitation to C*-algebras (1976) and A Short Course on Spectral Theory (2001).

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 The term Noncommutative Dynamics can be interpreted in several ways. It is used in this book to refer to a set of phenomena associated with the dynamics of quantum systems of the simplest kind that involve rigorous mathematical structures associated with infinitely many degrees of freedom. The dynamics of such a system is represented by a one-parameter group of automorphisms of a noncommutative algebra of observables, and the author focuses primarily on the most concrete case in which that algebra consists of all bounded operators on a Hilbert space.

This subject overlaps with several mathematical areas of current interest, including quantum field theory, the dynamics of open quantum systems, noncommutative geometry, and both classical and noncommutative probability theory. This is the first book to give a systematic presentation of progress during the past fifteen years on the classification of E-semigroups up to cocycle conjugacy. There are many new results that cannot be found in the existing literature, as well as significant reformulations and simplifications of the theory as it exists today.

William Arveson is Professor of Mathematics at the University of California, Berkeley. He has published two previous books with Springer-Verlag, An Invitation to C*-algebras (1976) and A Short Course on Spectral Theory (2001).

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 The term Noncommutative Dynamics can be interpreted in several ways. It is used in this book to refer to a set of phenomena associated with the dynamics of quantum systems of the simplest kind that involve rigorous mathematical structures associated with infinitely many degrees of freedom. The dynamics of such a system is represented by a one-parameter group of automorphisms of a noncommutative algebra of observables, and the author focuses primarily on the most concrete case in which that algebra consists of all bounded operators on a Hilbert space.

This subject overlaps with several mathematical areas of current interest, including quantum field theory, the dynamics of open quantum systems, noncommutative geometry, and both classical and noncommutative probability theory. This is the first book to give a systematic presentation of progress during the past fifteen years on the classification of E-semigroups up to cocycle conjugacy. There are many new results that cannot be found in the existing literature, as well as significant reformulations and simplifications of the theory as it exists today.

William Arveson is Professor of Mathematics at the University of California, Berkeley. He has published two previous books with Springer-Verlag, An Invitation to C*-algebras (1976) and A Short Course on Spectral Theory (2001).

Content:
Front Matter....Pages i-x
Dynamical Origins....Pages 1-15
Front Matter....Pages 17-17
E-Semigroups....Pages 18-65
Continuous Tensor Products....Pages 66-100
Spectral C*-Algebras....Pages 101-159
Front Matter....Pages 161-161
Path Spaces....Pages 162-198
Decomposable Product Systems....Pages 199-234
Front Matter....Pages 235-235
CP-Semigroups....Pages 236-253
C *-Generators and Dilation Theory....Pages 254-303
Index Theory for CP-Semigroups....Pages 304-323
Bounded Generators....Pages 324-354
Front Matter....Pages 355-355
Pure Perturbations of CAR/CCR Flows....Pages 356-373
Interaction Theory....Pages 374-387
Front Matter....Pages 389-389
Powers’ Examples....Pages 390-411
Tsirelson—Vershik Product Systems....Pages 412-426
Back Matter....Pages 427-434

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 The term Noncommutative Dynamics can be interpreted in several ways. It is used in this book to refer to a set of phenomena associated with the dynamics of quantum systems of the simplest kind that involve rigorous mathematical structures associated with infinitely many degrees of freedom. The dynamics of such a system is represented by a one-parameter group of automorphisms of a noncommutative algebra of observables, and the author focuses primarily on the most concrete case in which that algebra consists of all bounded operators on a Hilbert space.

This subject overlaps with several mathematical areas of current interest, including quantum field theory, the dynamics of open quantum systems, noncommutative geometry, and both classical and noncommutative probability theory. This is the first book to give a systematic presentation of progress during the past fifteen years on the classification of E-semigroups up to cocycle conjugacy. There are many new results that cannot be found in the existing literature, as well as significant reformulations and simplifications of the theory as it exists today.

William Arveson is Professor of Mathematics at the University of California, Berkeley. He has published two previous books with Springer-Verlag, An Invitation to C*-algebras (1976) and A Short Course on Spectral Theory (2001).

Content:
Front Matter....Pages i-x
Dynamical Origins....Pages 1-15
Front Matter....Pages 17-17
E-Semigroups....Pages 18-65
Continuous Tensor Products....Pages 66-100
Spectral C*-Algebras....Pages 101-159
Front Matter....Pages 161-161
Path Spaces....Pages 162-198
Decomposable Product Systems....Pages 199-234
Front Matter....Pages 235-235
CP-Semigroups....Pages 236-253
C *-Generators and Dilation Theory....Pages 254-303
Index Theory for CP-Semigroups....Pages 304-323
Bounded Generators....Pages 324-354
Front Matter....Pages 355-355
Pure Perturbations of CAR/CCR Flows....Pages 356-373
Interaction Theory....Pages 374-387
Front Matter....Pages 389-389
Powers’ Examples....Pages 390-411
Tsirelson—Vershik Product Systems....Pages 412-426
Back Matter....Pages 427-434
....