| Hardcover ISBN: | 978-0-8218-4319-2 |
| Product Code: | AMSIP/40 |
| List Price: | $73.00 |
| MAA Member Price: | $65.70 |
| AMS Member Price: | $58.40 |
| eBook ISBN: | 978-1-4704-3829-6 |
| Product Code: | AMSIP/40.E |
| List Price: | $69.00 |
| MAA Member Price: | $62.10 |
| AMS Member Price: | $55.20 |
| Hardcover ISBN: | 978-0-8218-4319-2 |
| eBook: ISBN: | 978-1-4704-3829-6 |
| Product Code: | AMSIP/40.B |
| List Price: | $142.00 $107.50 |
| MAA Member Price: | $127.80 $96.75 |
| AMS Member Price: | $113.60 $86.00 |
| Hardcover ISBN: | 978-0-8218-4319-2 |
| Product Code: | AMSIP/40 |
| List Price: | $73.00 |
| MAA Member Price: | $65.70 |
| AMS Member Price: | $58.40 |
| eBook ISBN: | 978-1-4704-3829-6 |
| Product Code: | AMSIP/40.E |
| List Price: | $69.00 |
| MAA Member Price: | $62.10 |
| AMS Member Price: | $55.20 |
| Hardcover ISBN: | 978-0-8218-4319-2 |
| eBook ISBN: | 978-1-4704-3829-6 |
| Product Code: | AMSIP/40.B |
| List Price: | $142.00 $107.50 |
| MAA Member Price: | $127.80 $96.75 |
| AMS Member Price: | $113.60 $86.00 |
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Book DetailsAMS/IP Studies in Advanced MathematicsVolume: 40; 2007; 244 ppMSC: Primary 53; 35; Secondary 46; 20
The theory of subRiemannian manifolds is closely related to Hamiltonian mechanics. In this book, the authors examine the properties and applications of subRiemannian manifolds that automatically satisfy the Heisenberg principle, which may be useful in quantum mechanics. In particular, the behavior of geodesics in this setting plays an important role in finding heat kernels and propagators for Schrödinger's equation. One of the novelties of this book is the introduction of techniques from complex Hamiltonian mechanics.
Titles in this series are co-published with International Press of Boston, Inc., Cambridge, MA.
ReadershipGraduate students and research mathematicians interested in subRiemannian geometry and connections to quantum mechanics.
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Table of Contents
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Chapters
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Geometric mechanics on the Heisenberg group
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Geometric analysis of step 4 case
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The geometric analysis of step $2(k+1)$ case
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Geometry on higher dimensional Heisenberg groups
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Complex Hamiltonian mechanics
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Quantum mechanics on the Heisenberg group
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Additional Material
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Reviews
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...a resource for pure and applied mathematicians and theoretical physics working in quantum mechanics. One of the authors' most interesting innovations is introducing the complex Hamiltonian mechanics techniques and use them to describe the fundamental solutions and heat propagators in quantum mechanics. ...result is fresh and livelywhile also being thorough. The authors provide exercises for each chapter.
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RequestsReview Copy – for publishers of book reviewsAccessibility – to request an alternate format of an AMS title
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The theory of subRiemannian manifolds is closely related to Hamiltonian mechanics. In this book, the authors examine the properties and applications of subRiemannian manifolds that automatically satisfy the Heisenberg principle, which may be useful in quantum mechanics. In particular, the behavior of geodesics in this setting plays an important role in finding heat kernels and propagators for Schrödinger's equation. One of the novelties of this book is the introduction of techniques from complex Hamiltonian mechanics.
Titles in this series are co-published with International Press of Boston, Inc., Cambridge, MA.
Graduate students and research mathematicians interested in subRiemannian geometry and connections to quantum mechanics.
-
Chapters
-
Geometric mechanics on the Heisenberg group
-
Geometric analysis of step 4 case
-
The geometric analysis of step $2(k+1)$ case
-
Geometry on higher dimensional Heisenberg groups
-
Complex Hamiltonian mechanics
-
Quantum mechanics on the Heisenberg group
-
...a resource for pure and applied mathematicians and theoretical physics working in quantum mechanics. One of the authors' most interesting innovations is introducing the complex Hamiltonian mechanics techniques and use them to describe the fundamental solutions and heat propagators in quantum mechanics. ...result is fresh and livelywhile also being thorough. The authors provide exercises for each chapter.
SciTech Book News
