7 edition of Unitary representations of the Poincaré group and relativistic wave equations found in the catalog.
Originally published in Japanese by Iwanaami Shoten, Publishers, Tokyo, 1976.
|Statement||Y. Ohnuki ; translated by S. Kitakado, T. Sugiyama.|
|The Physical Object|
|Number of Pages||213|
The unitary representations of groups and algebras are of a great interest in physics. We can mention the ubiquitous example of angular momentum or the SU(2) algebra. In this instance, as it is well known, the representations are labeled by . Figure Mechanical representation of the classical wave equation The acceleration of the masses (the second order derivative in time) is given by the force which is exerted by the springs. The force is given by the second order derivative in x, in combination with the strength of the springs given by parameter v2: Classical Wave equation.
For example, in relativistic quantum mechanics, we classify particles as unitary irreducible representations (or ‘irreps’) of a group like this: G × P G \times P Here G G is a compact Lie group depending on the theory of physics we happen to be studying, called the ‘internal symmetry group’. Finally, covariant wave equations are given for each unitary irreducible representation of the Poincaré group with non-negative mass-squared. Tachyonic representations are also examined. All these steps are covered in many details and with examples.
can describe a unitary representation of T by a function d:L∗ → N. This function d deserves a snappy name, so let’s call it the weighting of the representation. We call d(ℓ) the multiplicity of the weight ℓ. More generally, if ρ:K → U(H) is a unitary representation of a compact simply-connected simple Lie group, we can restrict ρ to. The Majorana-Fourier and Majorana-Hankel transforms of Majorana spinor fields are defined and related to the linear and angular momenta of a spin one-half representation of the Poincare group. We show that the Majorana spinor field with finite mass is an unitary irreducible projective representation of the Poincare group on a real Hilbert space.
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This book is devoted to an extensive and systematic study on unitary representations of the Poincaré group. The Poincaré group plays an important role in understanding the relativistic picture of particles in quantum by: An extensive group-theoretical treatment of linear relativistic wave equations on Minkowski spacetime of arbitrary dimension D>2 is presented in these lecture notes.
To start with, the one-to-one correspondence between linear relativistic wave equations and unitary representations of the isometry group is reviewed. In turn, the method of induced representations. Unitary Representations of the Poincare Group and Relativistic Wave Equations.
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Find more information about: ISBN: X The Poincaré 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 Poincaré group are found.
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() No Access. Lorentz Group. Unitary Representations of the Poincaré Group and Relativistic Wave Equations. Metrics. Downloaded 13 times. Life. Poincaré was born on 29 April in Cité Ducale neighborhood, Nancy, Meurthe-et-Moselle, into an influential French family.
His father Léon Poincaré (–) was a professor of medicine at the University of Nancy. His younger sister Aline married the spiritual philosopher Emile r notable member of Henri's family was his cousin, Raymond Poincaré.
In physics, specifically relativistic quantum mechanics (RQM) and its applications to particle physics, relativistic wave equations predict the behavior of particles at high energies and velocities comparable to the speed of the context of quantum field theory (QFT), the equations determine the dynamics of quantum fields.
The solutions to the equations. Abstract. The group of time evolution of relativistic wave equations is contained in nonlinear representations of the Poincaré group.
A general exposition of non linear representations of Lie groups is surveyed in order to exhibit the principal tools concerning the qualitative aspects of the theory. The Dirac operator describes the energy of a particle with spin−1/2 in the presence of external forces in accordance with principles of the special theory of relativity.
The Hilbert space of the Dirac equation supports a unitary representation of the proper orthochronous Poincaré group. The free Dirac equation is invariant under these. REPRESENTATIONS OF THE UNITARY GROUP AND WAVE FUNCTIONS.
Book. Jan ; Hans A. Bethe by which a relativistic wave equation for a few-particle system can be related to a Schrödinger-like. Unitary Representations of the Inhomogeneous Lorentz Group and Their Significance in Quantum Physics. irreducible representations of the inhomogeneous Lorentz group, M.
Fierz, W. Pauli: On the relativistic wave equations for particles of arbitrary spin in an electromagnetic field, Proc. Soc. A We consider the unitary irreducible representations of the group SO(2, 1), belonging to the continuous and the discrete cast them into a form in which the noncompact generator of an O(1, 1) subgroup is examine some properties of the remaining generators in this basis.
Quantum Theory, Groups and Representations: An Introduction Peter Woit Department of Mathematics, Columbia University [email protected] [Show full abstract] group is the archetypical example with the unitary representations defining the Hilbert space of relativistic particle states and the Klein-Gordon, Dirac, Maxwell equations.
APPLICATIONS OF INDUCED REPRESENTATIONS § 1. The Relativistic Position Operator § 2. The Representations of the Heisenberg Commutation Relations. § 3. Comments and Supplements § 4. Exercises CHAPTER 21 GROUP REPRESENTATIONS IN RELATIVISTIC QUANTUM THEORY §1.
Relativistic Wave Equations and Induced Representations. Unitary representations of the Poincaré group. This is the website containing bibliography on the representation theory of the Poincaré group. Its purpose is to collect useful references to aid in the study of this subject.
Notes. These are notes of mine on this and related topics. Some are quite old, some are newer. An extensive group-theoretical treatment of linear relativistic wave equations on Minkowski spacetime of arbitrary dimension D>2 is presented in these lecture notes.
To start with, the one-to-one correspondence between linear relativistic wave equations and unitary representations of the isometry group is reviewed.
Unitary representations of the Poincaré group and relativistic wave equations. By Yoshio Ohnuki. Abstract. This book is devoted to an extensive and systematic study on unitary representations of the Poincaré group.
The Poincaré group plays an important role in understanding the relativistic picture of particles in quantum mechanics.10 Relativistic Wave Equations where!k can be written as in ()!k = c 2ωkV (2α=1 ak,αuk,α, () but with the operators a,a† replaced by numbers a,a∗ since we want to consider A(x,t) as a classical ﬁeld.
If Maxwell’s propagation equation could be regarded as a quantum wave equation, then, according to ordinary quantum mechanics, the.This chapter contains standard preparatory material.
We will present an overview of special relativity, relativistic Klein–Gordon and Dirac wave equations and the convention in this book for Dirac spinors, and a self-contained discussion of representation theory of the rotation and Lorentz groups.