Science Mathematics

Symmetry of equations of quantum mechanics by Vilgelm Ilich Fushchich, A. G. Nikitin, W. I. Fushchich

By Vilgelm Ilich Fushchich, A. G. Nikitin, W. I. Fushchich

This publication is dedicated to the research of outdated (classical) and new (non-Lie) symmetries of the basic equations of quantum mechanics and classical box conception, and to the class and algebraic-theoretical deduction of equations of movement of arbitrary spin debris in either Poincaré invariant method. The authors current targeted information regarding the representations of the Galilei and Poincaré teams and their attainable generalizations, and expound a brand new method for investigating symmetries of partial differential equations; this results in discovering formerly unknown algebras and teams of invariance of the Dirac, Maxwell and different equations.

Show description

Read Online or Download Symmetry of equations of quantum mechanics PDF

Similar science & mathematics books

Symmetry of equations of quantum mechanics

This ebook is dedicated to the research of outdated (classical) and new (non-Lie) symmetries of the elemental equations of quantum mechanics and classical box concept, and to the class and algebraic-theoretical deduction of equations of movement of arbitrary spin debris in either Poincaré invariant process.

Topics in complex function theory. Abelian and modular functions of several variables

Develops the better components of functionality conception in a unified presentation. begins with elliptic integrals and services and uniformization conception, keeps with automorphic services and the speculation of abelian integrals and ends with the idea of abelian capabilities and modular services in different variables.

The Mathematical Writings of Évariste Galois (Heritage of European Mathematics)

Earlier than he died on the age of twenty, shot in a mysterious early-morning duel on the finish of could 1832, Évariste Galois created arithmetic that modified the path of algebra. This ebook comprises English translations of just about all of the Galois fabric. The translations are offered along a brand new transcription of the unique French and are better via 3 degrees of observation.

Future energy : opportunities and challenges

The US and the area face daunting questions about how we produce strength and the way we use it. Conservation and enhanced strength potency may also help in lowering power specifications, yet can't halt the regular elevate in power intake. expanding international inhabitants and lengthening power appetites in rising economies will create pageant for strength assets for all countries.

Additional resources for Symmetry of equations of quantum mechanics

Example text

1. Introduction Maxwell’s equations are one of the main foundations of modern physics. Describing a very extensive branch of physical phenomena, these equations are distinguished by their extremely simple and elegant form. But the source of this simplicity and elegance lies in the remarkably rich symmetry of Maxwell’s equations. The investigation of the symmetry of Maxwell’s equations has a long and glorious history. In 1893, having written these equations in the vector notations, Heaviside [219] pointed out that they are invariant under the change E→H, H→ E, 28 Chapter 1.

G. for the construction of nonlinear generalizations of Maxwell’s equations, being invariant under the conformal group. 6. Symmetry Under the P-, T- and C-Transformations Invariance under the transformations considered above does not exhaust all symmetry properties of Maxwell’s equations. We will see later that these equations are invariant also with respect to nonlocal transformations not connected with geometrical space-time symmetries. But there exist discrete symmetry transformations of dependent and independent variables which we not considered in the previous subsection.

In conclusion we notice that the algebra AC(1,3) is isomorphic to the Lie algebra of the group O(2,4) (the group of pseudoorthogonal matrices conserving the vector length in the (2+4) Minkowski space. 49) g44 g55 0, gmn 0, m≠ n. The existence of this isomorphism means that the problem of the description of the representations of the algebra AC(1,3) reduces to the description of the representations of the algebra AO(2,4). 8. 22) inasmuch as such representations are used for description of actual physical fields.

Download PDF sample

Rated 4.17 of 5 – based on 32 votes