Results 221 to 230 of about 12,509 (248)

Position Operators as ``Internal'' Symmetries

Journal of Mathematical Physics, 1972
Space-time variables are generated as representation labels of an underlying group, the group itself being combined with the Poincaré group in a manner reminiscent of the way in which internal symmetries are combined with the Poincaré group. After representations of the group are found, a transform is introduced which allows one to pass from spinor to ...
Warren, Russell E., Klink, William H.
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Symmetry elements and symmetry operations

1991
The idea of ‘symmetry’ has been understood for a very long time, and the relationship of the symmetry of an object to its aesthetic appeal has been appreciated from the earliest ages. Our aim here is to make the idea of symmetry quantitative, so that we can use the symmetry properties of a molecule to simplify many of the problems concerning the ...
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Representation of Discrete Symmetry Operators

Journal of Mathematical Physics, 1966
Representations of discrete symmetry operators (DSO's) connected with space (𝒫), time (T), and generalized charge (𝒞) are considered. It is shown that if one writes a DSO as exp (iπΩ) × a phase transformation, then (under certain conditions on Ωs) to each DSO there corresponds a set of Ωs which is closed with respect a Lie algebra, which is isomorphic ...
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Crystallographic Symmetry Operations

1986
In this chapter We investigate the restrictions imposed by a lattice on the symmetry operations acting on a regular point system X C En.
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Symmetry operators for Riemann’s method

Journal of Mathematical Physics, 2004
Riemann’s method is one of the definitive ways of solving Cauchy’s problem for a second order linear hyperbolic partial differential equation in 2 variables. Chaundy’s equation, with 4 parameters, is the most general self-adjoint equation for which the Riemann function is known.
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Representations of symmetry operators

Il Nuovo Cimento, 1958
Explicit representations in terms of the field variables are given for the charge conjugation, space inversion, and time reversal operators, for the case of free fields. These expressions are generalized to the case of coupled fields.
Federbush, P. G., Grisaru, M. T.
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Symmetries and Symmetry Operations. A Systematic Approach

1995
This chapter provides a systematic approach to the application of group theory for the determination of molecular wavefunctions. We treat molecular point groups, the effect of symmetry operators on wavefunctions, and then the basic concepts of the theory of group representations. The method is demonstrated using the explicit example of the H2O molecule.
Hermann Haken, Hans Christoph Wolf
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Symmetries and Symmetry Operations: A First Overview

1995
In this chapter, we cover the fundamentals and theoretical approaches which we will need for — among other things — determining the wavefunctions and the energies of the π-electrons in benzene. A second example will be the ethene molecule.
Hermann Haken, Hans Christoph Wolf
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Factored irreducible symmetry operators

Journal of Mathematical Physics, 1977
Irreducible symmetry operators (ISO’s) are defined and their properties are displayed. A method for the systematic construction of ISO’s in the form of products of interchangeable factors is described. The key to the method is a set of conditions for directly testing for the irreducibility of induced symmetry operators formulated in terms of the ...
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Symmetry and Symmetry Operations

2021
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