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Symmetry, Volume 2, Issue 4 (December 2010), Pages 1745-1980

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Research

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Open AccessArticle An Application of Symmetry Approach to Finance: Gauge Symmetry in Finance
Symmetry 2010, 2(4), 1763-1775; doi:10.3390/sym2041763
Received: 19 September 2010 / Accepted: 17 October 2010 / Published: 21 October 2010
PDF Full-text (266 KB)
Abstract
The paper presents an application of symmetry approach to finance. This symmetry approach comes from the gauge field theory in Physics. We revise the pricing model of financial derivatives in a financial market in a gauge symmetry view, and rewrite  it as [...] Read more.
The paper presents an application of symmetry approach to finance. This symmetry approach comes from the gauge field theory in Physics. We revise the pricing model of financial derivatives in a financial market in a gauge symmetry view, and rewrite  it as a partial differential equation on a fiber bundle in covariant differential form so as to have invariance in form. The paper shows the form of the pricing equation can keep invariant under all the local num´eraire transformations, this symmetry behind the pricing equation of derivatives is revealed. In addition a  corresponding relationship between the curvature of the fiber bundle and the arbitrage in finance arises. Full article
(This article belongs to the Special Issue Complexity and Symmetry)
Open AccessArticle A Direct Road to Majorana Fields
Symmetry 2010, 2(4), 1776-1809; doi:10.3390/sym2041776
Received: 1 October 2010 / Revised: 18 October 2010 / Accepted: 22 October 2010 / Published: 27 October 2010
Cited by 10 | PDF Full-text (384 KB)
Abstract
A concise discussion of spin-1/2 field equations with a special focus on Majorana spinors is presented. The Majorana formalism which describes massive neutral fermions by the help of two-component or four-component spinors is of fundamental importance for the understanding of mathematical aspects [...] Read more.
A concise discussion of spin-1/2 field equations with a special focus on Majorana spinors is presented. The Majorana formalism which describes massive neutral fermions by the help of two-component or four-component spinors is of fundamental importance for the understanding of mathematical aspects of supersymmetric and other extensions of the Standard Model of particle physics, which may play an increasingly important role at the beginning of the LHC era. The interplay between the two-component and the four-component formalism is highlighted in an introductory way. Majorana particles are predicted both by grand unified theories, in which these particles are neutrinos, and by supersymmetric theories, in which they are photinos, gluinos and other states. Full article
Open AccessArticle Introduction to a Quantum Theory over a Galois Field
Symmetry 2010, 2(4), 1810-1845; doi:10.3390/sym2041810
Received: 18 August 2010 / Revised: 14 September 2010 / Accepted: 8 October 2010 / Published: 1 November 2010
Cited by 2 | PDF Full-text (286 KB)
Abstract
We consider a quantum theory based on a Galois field. In this approach infinities cannot exist, the cosmological constant problem does not arise, and one irreducible representation (IR) of the symmetry algebra splits into independent IRs describing a particle an its antiparticle [...] Read more.
We consider a quantum theory based on a Galois field. In this approach infinities cannot exist, the cosmological constant problem does not arise, and one irreducible representation (IR) of the symmetry algebra splits into independent IRs describing a particle an its antiparticle only in the approximation when de Sitter energies are much less than the characteristic of the field. As a consequence, the very notions of particles and antiparticles are only approximate and such additive quantum numbers as the electric, baryon and lepton charges are conserved only in this approximation. There can be no neutral elementary particles and the spin-statistics theorem can be treated simply as a requirement that standard quantum theory should be based on complex numbers. Full article
(This article belongs to the Special Issue Quantum Symmetry)
Open AccessArticle Structures of Annulenes and Model Annulene Systems in the Ground and Lowest Excited States
Symmetry 2010, 2(4), 1846-1924; doi:10.3390/sym2041846
Received: 23 September 2010 / Revised: 6 October 2010 / Accepted: 19 October 2010 / Published: 5 November 2010
Cited by 7 | PDF Full-text (1887 KB)
Abstract
The paper introduces general considerations on structural properties of aromatic, antiaromatic and non-aromatic conjugated systems in terms of potential energy along bond length alternation and distortion coordinates, taking as examples benzene, cyclobutadiene and cyclooctatetraene. Pentalene, formally derived from cyclooctatetraene by cross linking, [...] Read more.
The paper introduces general considerations on structural properties of aromatic, antiaromatic and non-aromatic conjugated systems in terms of potential energy along bond length alternation and distortion coordinates, taking as examples benzene, cyclobutadiene and cyclooctatetraene. Pentalene, formally derived from cyclooctatetraene by cross linking, is also considered as a typical antiaromatic system. The main interest is concerned with [n]annulenes and model [n]annulene molecular systems, n ranging from 10 to 18. The rich variety of conformational and  configurational isomers and of dynamical processes among them is described. Specific attention is devoted to bridged [10]- and [14]annulenes in the ground and lowest excited states as well as to s-indacene and biphenylene. Experimental data obtained from vibrational and electronic spectroscopies are discussed and compared with ab initio calculation results. Finally, porphyrin, tetraoxaporphyrin dication and diprotonated porphyrin are presented as annulene structures adopting planar/non-planar geometries depending on the steric hindrance in the inner macrocycle ring. Radiative and non-radiative relaxation processes from excited state levels have been observed by means of time-resolved fluorescence and femtosecond transient absorption spectroscopy. A short account is also given of porphycene, the structural isomer of porphyrin, and of porphycene properties. Full article
(This article belongs to the Special Issue Aromaticity and Molecular Symmetry)
Open AccessArticle Three-Dimensional Facial Asymmetry in Attractive and Normal People from Childhood to Young Adulthood
Symmetry 2010, 2(4), 1925-1944; doi:10.3390/sym2041925
Received: 1 October 2010 / Accepted: 19 October 2010 / Published: 9 November 2010
Cited by 8 | PDF Full-text (161 KB)
Abstract
We are currently investigating measurable esthetic characteristics in persons considered “attractive” by the media. Three-dimensional soft-tissue facial asymmetry was quantified in 380 attractive (148 males, 232 females) and 669 control (397 males, 272 females) healthy persons aged 4–30 years. The coordinates of [...] Read more.
We are currently investigating measurable esthetic characteristics in persons considered “attractive” by the media. Three-dimensional soft-tissue facial asymmetry was quantified in 380 attractive (148 males, 232 females) and 669 control (397 males, 272 females) healthy persons aged 4–30 years. The coordinates of 50 facial landmarks were collected by a computerized digitizer, and asymmetry computed. Soft-tissue facial asymmetries reduced as a function of age in all cases. Attractive children were more symmetric than control children, but the reverse was true for young adults. The effect of symmetry on attractiveness seems to change as a function of age. Full article
(This article belongs to the Special Issue Symmetry and Beauty)
Figures

Open AccessArticle Positive Cosmological Constant and Quantum Theory
Symmetry 2010, 2(4), 1945-1980; doi:10.3390/sym2041945
Received: 20 September 2010 / Revised: 26 October 2010 / Accepted: 11 November 2010 / Published: 19 November 2010
Cited by 2 | PDF Full-text (418 KB)
Abstract
We argue that quantum theory should proceed not from a spacetime background but from a Lie algebra, which is treated as a symmetry algebra. Then the fact that the cosmological constant is positive means not that the spacetime background is curved but [...] Read more.
We argue that quantum theory should proceed not from a spacetime background but from a Lie algebra, which is treated as a symmetry algebra. Then the fact that the cosmological constant is positive means not that the spacetime background is curved but that the de Sitter (dS) algebra as the symmetry algebra is more relevant than the Poincare or anti de Sitter ones. The physical interpretation of irreducible representations (IRs) of the dS algebra is considerably different from that for the other two algebras. One IR of the dS algebra splits into independent IRs for a particle and its antiparticle only when Poincare approximation works with a high accuracy. Only in this case additive quantum numbers such as electric, baryon and lepton charges are conserved, while at early stages of the Universe they could not be conserved. Another property of IRs of the dS algebra is that only fermions can be elementary and there can be no neutral elementary particles. The cosmological repulsion is a simple kinematical consequence of dS symmetry on quantum level when quasiclassical approximation is valid. Therefore the cosmological constant problem does not exist and there is no need to involve dark energy or other fields for explaining this phenomenon (in agreement with a similar conclusion by Bianchi and Rovelli). Full article
(This article belongs to the Special Issue Quantum Symmetry)

Review

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Open AccessReview Polyanionic Hexagons: X6n(X = Si, Ge)
Symmetry 2010, 2(4), 1745-1762; doi:10.3390/sym2041745
Received: 16 August 2010 / Revised: 7 September 2010 / Accepted: 27 September 2010 / Published: 30 September 2010
Cited by 2 | PDF Full-text (293 KB)
Abstract
The paper reviews the polyanionic hexagons of silicon and germanium, focusing on aromaticity. The chair-like structures of hexasila- and hexagermabenzene are similar to a nonaromatic cyclohexane (CH2)6 and dissimilar to aromatic D6h-symmetric benzene (CH)6, although [...] Read more.
The paper reviews the polyanionic hexagons of silicon and germanium, focusing on aromaticity. The chair-like structures of hexasila- and hexagermabenzene are similar to a nonaromatic cyclohexane (CH2)6 and dissimilar to aromatic D6h-symmetric benzene (CH)6, although silicon and germanium are in the same group of the periodic table as carbon. Recently, six-membered silicon and germanium rings with extra electrons instead of conventional substituents, such as alkyl, aryl, etc., were calculated by us to have D6h symmetry and to be aromatic. We summarize here our main findings and the background needed to reach them, and propose a synthetically accessible molecule. Full article
(This article belongs to the Special Issue Aromaticity and Molecular Symmetry)

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