Massless Representations of the Poincaré Group PDF Download

Author: R. Mirman
Publisher: iUniverse
ISBN: 0595341241
Category : Elektromanyetizma
Languages : en
Pages : 233

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Book Description
Preface 1 The Physical Meaning of Poincare Massless Representations 1 2 Massless Representations 12 3 Massless Fields are Different 32 4 How to Couple Massless and Massive Matter 56 5 The Behavior of Matter in Fields 73 6 Geometrical Reasons for the Poincare Group 95 7 Description of the Electromagnetic Field 123 8 The Equations Governing Free Gravitation 135 9 How Matter Determines Gravitational Fields 150 10 Nonlinearity and Geometry 165 11 Quantum Gravity 183 References 201 Index 207.

Author: Yoshio Ohnuki
Publisher: World Scientific
ISBN: 9789971502508
Category : Science
Languages : en
Pages : 234

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Book Description
This book is devoted to an extensive and systematic study on unitary representations of the Poincar‚ group. The Poincar‚ group plays an important role in understanding the relativistic picture of particles in quantum mechanics. Complete knowledge of every free particle states and their behaviour can be obtained once all the unitary irreducible representations of the Poincar‚ group are found. It is a surprising fact that a simple framework such as the Poincar‚ group, when unified with quantum theory, fixes our possible picture of particles severely and without exception. In this connection, the theory of unitary representations of the Poincar‚ group provides a fundamental concept of relativistic quantum mechanics and field theory.

Author: Young Suh Kim
Publisher: Springer Science & Business Media
ISBN: 9400945582
Category : Science
Languages : en
Pages : 346

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Book Description
Special relativity and quantum mechanics, formulated early in the twentieth century, are the two most important scientific languages and are likely to remain so for many years to come. In the 1920's, when quantum mechanics was developed, the most pressing theoretical problem was how to make it consistent with special relativity. In the 1980's, this is still the most pressing problem. The only difference is that the situation is more urgent now than before, because of the significant quantity of experimental data which need to be explained in terms of both quantum mechanics and special relativity. In unifying the concepts and algorithms of quantum mechanics and special relativity, it is important to realize that the underlying scientific language for both disciplines is that of group theory. The role of group theory in quantum mechanics is well known. The same is true for special relativity. Therefore, the most effective approach to the problem of unifying these two important theories is to develop a group theory which can accommodate both special relativity and quantum mechanics. As is well known, Eugene P. Wigner is one of the pioneers in developing group theoretical approaches to relativistic quantum mechanics. His 1939 paper on the inhomogeneous Lorentz group laid the foundation for this important research line. It is generally agreed that this paper was somewhat ahead of its time in 1939, and that contemporary physicists must continue to make real efforts to appreciate fully the content of this classic work.

Author: Sibel Baskal
Publisher: Morgan & Claypool Publishers
ISBN: 1681740621
Category : Science
Languages : en
Pages : 173

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Book Description
This book explains the Lorentz mathematical group in a language familiar to physicists. While the three-dimensional rotation group is one of the standard mathematical tools in physics, the Lorentz group of the four-dimensional Minkowski space is still very strange to most present-day physicists. It plays an essential role in understanding particles moving at close to light speed and is becoming the essential language for quantum optics, classical optics, and information science. The book is based on papers and books published by the authors on the representations of the Lorentz group based on harmonic oscillators and their applications to high-energy physics and to Wigner functions applicable to quantum optics. It also covers the two-by-two representations of the Lorentz group applicable to ray optics, including cavity, multilayer and lens optics, as well as representations of the Lorentz group applicable to Stokes parameters and the Poincaré sphere on polarization optics.

Author: Bruce W. Shore
Publisher: Oxford University Press, USA
ISBN: 0198862857
Category : Photons
Languages : en
Pages : 506

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Book Description
Our Changing Views of Photons: A Tutorial Memoir presents those general topics as a memoir of the author's involvement with physics and the photons of theoretical Quantum Optics, written conversationally for readers with no assumed prior exposure to science. .

Author: E. R. Pike
Publisher: Clarendon Press
ISBN: 0191590053
Category : Science
Languages : en
Pages : 358

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Book Description
This book is unique in covering phenomena in photon- matter interactions in a unified way over a range of many orders in energy. The quantum field theoretic approach to the fully relativistic theory of quantum electrodynamics (QED) is presented together with the non- relativistic theory in both confined and unconfined geometries. The predictions of QED have been verified to a greater accuracy than any other physical theory. Moreover QED is a paradigm for other gauge theories and is presented in such a way that the generalisation to other gauge theories is natural. Gauge and Poincare symmetry properties and the non-existence of a photon wave function are thoroughly discussed. Starting from the Dirac equation the non-relativistic interaction of the electron with the electromagnetic field is derived as an effective Hamiltonian of multipole expansions. Much of quantum optics is based on the lowest order dipole approximation. From this point on the treatment of fully relativistic QED and quantum optics is done in parallel. Applications of perturbation theory such as Compton and Moller scattering and the theory photdetection are given. After the impressive successes of QED, the limitation of the theory and the necessity of electroweak theory and quantumchromodynamics are discussed. The remaining chapters are devoted to quantum optics inside cavaties. Various approaches to open systems such as master equations are discussed within the context of active systems (e.g. the laser) and passive systems. Semi- classical approximarions are shown to imply a rich non- linear dynamics including chaos for certain parameter regimes. The effect of fluctuations on such non-linear dynamics is also studied. The final chapter is devoted to highly non- classical states of the light field such as photon number, squeezed and two photon entangled states. The latter are studied for the important system of parametric down conversion and the localisation properties of photons are characterised in terms of asympotic tails in photodetection probabilities as a function of time delay. The range of the book has wider benefits. Workers in quantum optics will gain a deeper understanding of the foundations of their subject and field theorists will see concrete examples of open systems, which are beginning to impinge on fundamental theories.

Author: Andrew E. Chubykalo
Publisher: World Scientific
ISBN: 9789810240622
Category : Science
Languages : en
Pages : 492

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Book Description
The topics in this volume range from mathematical aspects of the theory of the Poincar‚ group, Clifford algebras and the CPT theorem, through new theoretical physical constructions and concepts (such as the physical significance of the 4-potential, the interplay between quantum mechanics and gravity, Majorana-like models, the photon as a composite particle, action-at-a-distance and superluminal phenomena), to experiments in neutrino physics. The book will be of interest to graduate students and researchers working in fundamental physics and phenomenology, and also to experimentalists.

Author: R Campoamor Strursberg
Publisher: World Scientific
ISBN: 9813273623
Category : Science
Languages : en
Pages : 759

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Book Description
'The book contains a lot of examples, a lot of non-standard material which is not included in many other books. At the same time the authors manage to avoid numerous cumbersome calculations … It is a great achievement that the authors found a balance.'zbMATHThis book presents the study of symmetry groups in Physics from a practical perspective, i.e. emphasising the explicit methods and algorithms useful for the practitioner and profusely illustrating by examples.The first half reviews the algebraic, geometrical and topological notions underlying the theory of Lie groups, with a review of the representation theory of finite groups. The topic of Lie algebras is revisited from the perspective of realizations, useful for explicit computations within these groups. The second half is devoted to applications in physics, divided into three main parts — the first deals with space-time symmetries, the Wigner method for representations and applications to relativistic wave equations. The study of kinematical algebras and groups illustrates the properties and capabilities of the notions of contractions, central extensions and projective representations. Gauge symmetries and symmetries in Particle Physics are studied in the context of the Standard Model, finishing with a discussion on Grand-Unified Theories.

Author: Trilochan Pradhan
Publisher: Nova Publishers
ISBN: 9781560729280
Category : Science
Languages : en
Pages : 146

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Book Description
This book is about Maxwell's electromagnetic theory of light. First, it is a fully relativistic theory without having a non-relativistic limit. There arise many difficulties in quantising the electromagnetic field and in the physical interpretation of the wavefunction of its quanta. Further, the first quantisation of the Maxwell equations similar to quantisation of classical mechanics by the Schrodinger method, has not been discussed in most books on quantum mechanics. Second, the Maxwell field is the simplest gauge field possessing symmetry with respect to Poincare group of transformations in addition to scale, duality and special conformal transformations whose local versions give rise to new interaction of photons through new gauge fields. One of these gauge fields couples to the spin density of the photon and other particles and can bind fermion-antifermion pairs to give transverse photons. Another interesting aspect of the electromagnetic field is its coherence properties and their interpretation in terms of quantised theory.

Author: Young Suh Kim
Publisher: World Scientific
ISBN: 9814506672
Category : Science
Languages : en
Pages : 352

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Book Description
This book covers the theory and applications of the Wigner phase space distribution function and its symmetry properties. The book explains why the phase space picture of quantum mechanics is needed, in addition to the conventional Schrödinger or Heisenberg picture. It is shown that the uncertainty relation can be represented more accurately in this picture. In addition, the phase space picture is shown to be the natural representation of quantum mechanics for modern optics and relativistic quantum mechanics of extended objects.