Principle of symmetry

Harter W G 1993 Principles of Symmetry, Dynamics, and Spectroscopy (New York Wiley)... 

H.F. Franzen, Physical Chemistry of Solids. Basic Principles of Symmetry and Stability of Crystalline Solids. World Scientific, 1994. 

In addition to the needs following from the stoichiometry the VEP also takes those requirements of structural geometry into consideration which coincide with the principles of symmetry and connection. The space principle is also discussed here, however, with the difference that we do not start from a model of rigid mutually contacting spheres but also plastical or soft contacts between atoms and ions are admitted. Let us try and delimit the physical meaning of the VEP by the following consideration ... 

E.V. Babaev, In Principles of Symmetry and Systemic Approach in Chemistry, Nauka, Moscow, 1987, 30-54 (Russian). 

Another important relationship between the kinetic coefficients is the so-called principle of symmetry , as formulated by P. Curie and introduced to nonlinear thermodynamics by Kondepudi and Prigogine [37]. As applied to thermodynamics, this postulates that a scalar quantity could not evoke a vector effect. For example, a scalar thermodynamic force - chemical affinity (driving the process of chemical reaction) that has very high isotropy symmetry - could not cause heat flow, which has a particular direction and is therefore anisotropic. Taking into account the reciprocal relationships, this can be formulated as... 

The principles of symmetry and group theory used in the area of quantum chemistry ... 

Principles of symmetry and group theory find applications in several areas of quantum chemistry like chemical bonding, molecular spectroscopy, ligand field theory, crystal field theory etc. The procedure in all these cases involves—... 

It is possible for more than two forces to couple. There exists a criterion which allows one to deduce a priori the number of effective couplings. This is Curie s principle of symmetry. The principle states that a macroscopic phenomenon in the system never has more elements of symmetry than the cause that produces it. For example, the chemical affinity (which is a scalar quantity) can never cause a vectorial heat flux and the corresponding coupling coefficient disappears. A coupling is possible only between phenomenon which have the same tensor symmetry. Thus Onsager reciprocity relation is not valid for a situation when the fluxes have different tensorial character. 

All the particles mentioned have their anti-particles (designated by a bar above the particle symbol), except the photon and the mesons, who are their own antiparticles. We may think about antimatter as consisting of antiprotons and antineutrons in an antinucleus surrounded by antielectrons (i.e. positrons). Superficially, there would be no way to distinguish such antimatter from our matter (sometimes called koino matter). It has been proposed that the universe is made up of matter and antimatter as a requirement of the principle of symmetry. In that case some galaxies, which perhaps can be observed, should be made up of antimatter. When such antimatter galaxies (or material expelled fi-om them) collide with koino matter galaxies, both types of matter are annihilated and tremendous amounts of energy released. 

In the theoretical world of Vernadsky the principle of symmetry is refracted not only by the prism of dissymmetry, but also by the character of symmetry in living matter. It manifests itself, first of all, in the fact that the kinds of symmetry in inert matter is restricted. In the living world one can observe bioobjects with axes of symmetry of 5, 7, 8, 9 etc. orders not observed among the crystals. Already first crystaBographers... 

Different states of space can be more or less separated, but also close to each other (Vernadsky, 1965, p. 169). S5nnmetry is a criteria of a state of space Symmetry characterises the different states of the Earth space (Vernadsky, 1965, p. 169). The state of space of any natwal body can be determined by the basic principle of symmetry. This principle deckoes that the state of space of a natural body is determined by the minimum s)munetry of its properties (Vemadsky, 1988, p. 379). 

Thus the dissymmetry of Pasteur corresponds to a special case of symmetry-breaking because it is completely outside of the traditional laws of symmetry of the non-living natural world. Using the terms state of space , the basic principle of symmetry , and the characteristics of dissjmimetiy, we can perceive that the state of space of a living natural body will be characterised as dissymmetric, although some elements of its structure can be symmetric or asymmetric in a non-dissymmetric way. 

The state of space of a natural body is indicated by the investigation of its symmetry. The principle of symmetry is for Vernadsky one of the ntost fundamental principles of nature (Vernadsky, 1994, p. 297 1988, p. 220). It can be sad that the principle of symmetry is for him a corner-stone of the problems to be discussed. 

Man appears to have an innate appreciation of the principles of symmetry. Every civilization, from ancient Egypt to classical Greece, from the Arabian empires to the American Indians, has produced symmetrical ornaments and friezes, and has intuitively discovered the mathematical principles underlying the construction of periodic patterns. It was not until the 19th and 20th centuries that group theory was rigorously formulated by mathematicians. Today, the fundamental importance of symmetry to the exact sciences is fully appreciated. 

In more complicated material models we modify oruse further constitutive principles determinism is enlarged for densities (mass concentrations) in mixtures (cf. Sects. 2.4,3.5,4.5), and the definition of fluid used in this principle is in fact the result of constitutive principle of symmetry (see Rem. 30 in Chap. 3). Another constitutive principle is the objectivity (frame indifference) principle. Here it is trivially satisfied because motion is neglected and all quantities are objective (see Sects. 3.2,3.5). In nonuniform systems the influence of neighborhood is described in the principle of local action (cf. Sect. 3.5). In mixtures, the property of mixture invariance [32] may also be used as a constitutive principle [33]. 

How the principle of symmetry works we outline on simple material (3.123) (see [6, 7, 10, 14, 41, 63, 69] for details) for nonsimple fluid the similar procedure is more complicated, see [14, 70, 71]. Assume for simplicity a unique reference with reference density po in the whole body (everywhere is uniform material without dislocations, see Rem. 27) and all responses behave equally (their symmetries are the same). The material symmetry may be expressed by (referential) tensor H (in components H ) which, changing deformation F to FH in constitutive relation (3.123), gives the same response... 

Results for thermoelastic fluid might be also obtained by the constitutive principle of symmetry but we get them directly from the following fluid model, cf. (3.182) and the end of this section. 

By the constitutive principle of symmetry, we confine in this treatise to fluids mixtures only in which the independent variables of constitutive equations for (all) responses (4.120) reduce to ... 

Further information in F. M. Jaeger, Lectures on the Principle of Symmetry and its Applications in all Natural Sciencesy Amsterdam, 1917 T. M. Lowry, Optical Rotatory Power. 193 Partington, (3), iv, 290 f. 

Abstract The time has come to see how the concept of irreducible representations ties in with quantum chemistry. After a brief introduction to the prequantum principles of symmetry, we will show that eigenfunctions of the Hamiltonian are also eigenfunctions of the symmetry operators that commute with the Hamiltonian. We further analyze the concept of a degeneracy and show how the degenerate components can be characterized by canonical symmetry relationships. The final section will then provide a detailed account of the symmetry operations that leave the Hamiltonian invariant. 

Katzir, S. The emergence of the principle of symmetry in physics. Historical Studies in the... 

S. Tratch and N. Zefirov. Combinatorial models and algorithms in chemistry. The ladder of combinatorial objects and its application to the formalization of structural problems of organic chemistry, in N. Stepanov, editor. Principles of Symmetry and Systemology in Chemistry, pages 54-86. Moscow State University Publishers, Moscow, 1987. 

It can be said that there are three stages of the cognition of our world. At the lowest stage is the phenomena, at the second upper, the laws of nature and lastly at the top third stage symmetry principles. The laws of nature govern phenomena, and the principle of symmetry governs the laws of nature. If the natural laws enable the phenomena to be predicted, then the symmetry principle enables the laws of nature to be dictated. There are also the laws and the concept of compensation of symmetry once the symmetry is lowered at one... 

Tratch SS, Zefirov NS (1987) In Stepanov NF (ed) Principles of symmetry and systemology in chemistry (in Russian),... 

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