By Syed Twareque Ali,Jean-Pierre Antoine,Jean-Pierre Gazeau

This moment version is totally up-to-date, overlaying specifically new forms of coherent states (the so-called Gazeau-Klauder coherent states, nonlinear coherent states, squeezed states, as used now usually in quantum optics) and diverse generalizations of wavelets (wavelets on manifolds, curvelets, shearlets, etc.). furthermore, it features a new bankruptcy on coherent nation quantization and the similar probabilistic elements. As a survey of the idea of coherent states, wavelets, and a few in their generalizations, it emphasizes mathematical ideas, subsuming the theories of either wavelets and coherent states right into a unmarried analytic constitution. The technique permits the consumer to take a classical-like view of quantum states in physics.

Starting from the traditional conception of coherent states over Lie teams, the authors generalize the formalism by means of associating coherent states to staff representations which are sq. integrable over a homogeneous area; yet another step permits one to dispense with the crowd context altogether. during this context, wavelets may be generated from coherent states of the affine staff of the true line, and higher-dimensional wavelets come up from coherent states of different teams. The unified historical past makes obvious a whole variety of houses of wavelets and coherent states. Many concrete examples, reminiscent of coherent states from semisimple Lie teams, Gazeau-Klauder coherent states, coherent states for the relativity teams, and several other varieties of wavelets, are mentioned intimately. The publication concludes with a palette of potential applications, from the quantum bodily oriented, like the quantum-classical transition or the development of enough states in quantum info, to the main cutting edge concepts for use in info processing.

Intended as an advent to present learn for graduate scholars and others getting into the sector, the mathematical dialogue is self-contained. With its vast references to the study literature, the 1st version of the booklet is already a confirmed compendium for physicists and mathematicians lively within the box, and with complete insurance of the newest conception and effects the revised moment version is much more valuable.

**Read or Download Coherent States, Wavelets, and Their Generalizations (Theoretical and Mathematical Physics) PDF**

**Similar quantum theory books**

**Field Theory of Non-Equilibrium Systems**

The physics of non-equilibrium many-body platforms is among the such a lot quickly increasing components of theoretical physics. routinely utilized in the examine of laser physics and superconducting kinetics, those innovations have extra lately came upon purposes within the learn of dynamics of chilly atomic gases, mesoscopic and nano-mechanical platforms.

Quantum physics has, at the one hand, greatly replaced our theoretical description of the actual global and has, nevertheless, revolutionized lifestyle, by means of permitting us to construct lasers, atomic clocks utilized in GPS, and semiconductor-based units reminiscent of computing device desktops and smartphones. the thing of this ebook is to offer a self-contained creation to either points.

The 1st quantity (General concept) differs from such a lot textbooks because it emphasizes the mathematical constitution and mathematical rigor, whereas being tailored to the educating the 1st semester of a complicated path in Quantum Mechanics (the content material of the publication are the lectures of classes truly introduced.

**Introduction to Quantum Theory**

Given that its emergence within the early 20th century, quantum conception has turn into the elemental actual paradigm, and is vital to our knowing of the area. supplying a deeper figuring out of the microscopic international via quantum concept, this supplementary textual content reports a much wider variety of themes than traditional textbooks.

- Theoretical Frontiers in Black Holes and Cosmology: Theoretical Perspective in High Energy Physics (Springer Proceedings in Physics)
- Quantum Mechanics for Pedestrians 1: Fundamentals (Undergraduate Lecture Notes in Physics)
- The Innermost Kernel: Depth Psychology and Quantum Physics. Wolfgang Pauli's Dialogue with C.G. Jung
- Renormalization Methods: A Guide For Beginners
- The Emerging Quantum: The Physics Behind Quantum Mechanics

**Additional resources for Coherent States, Wavelets, and Their Generalizations (Theoretical and Mathematical Physics)**

**Example text**