Artículos de revistas: "Right/left symmetry"

1

Gu, Pei-Hong. "Mirror left–right symmetry". Physics Letters B 713, n.º 4-5 (julio de 2012): 485–89. http://dx.doi.org/10.1016/j.physletb.2012.06.042.

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2

Rosen, S. P. "OnZ4horizontal symmetry and left-right-symmetric theories". Physical Review D 31, n.º 11 (1 de junio de 1985): 2952–57. http://dx.doi.org/10.1103/physrevd.31.2952.

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3

Ferdiyan, Akmal, Apriadi Salim Adam y Mirza Satriawan. "The Left-Right Symmetry Breaking Mechanism for the New Left-Right Symmetry Model". JPSE (Journal of Physical Science and Engineering) 5, n.º 1 (27 de agosto de 2020): 1–5. http://dx.doi.org/10.17977/um024v5i12020p001.

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4

Shafaq, Saba y Mariam Saleh Khan. "Left right symmetric model with additional family symmetry". Physics Essays 30, n.º 2 (13 de junio de 2017): 161–67. http://dx.doi.org/10.4006/0836-1398-30.2.161.

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5

Akhmedov, Eugeni, Manfred Lindner, Erhard Schnapka y Jose W. F. Valle. "Dynamical left-right symmetry breaking". Physical Review D 53, n.º 5 (1 de marzo de 1996): 2752–80. http://dx.doi.org/10.1103/physrevd.53.2752.

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6

MATUTE, ERNESTO A. "RESTORATION OF PARITY SYMMETRY THROUGH PRESYMMETRY". Modern Physics Letters A 26, n.º 34 (10 de noviembre de 2011): 2579–85. http://dx.doi.org/10.1142/s0217732311036917.

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Presymmetry, the hidden symmetry underlying the charge and generational patterns of quarks and leptons, is utilized for repairing the left–right asymmetry of the standard model with Dirac neutrinos. It is shown that the restoration of parity is consequent with an indispensable left–right symmetric residual presymmetry. Thus, presymmetry substantiates left–right symmetry and the experimental search for the latter is the test of the former, with the nature of neutrinos as a crucial feature that can distinguish the left–right symmetry alone and its combination with presymmetry. This phenomenological implication is in accordance with the fact that Majorana neutrinos are usually demanded in the first case, but forbidden in the second.

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7

Shinohara, Kyosuke y Hiroshi Hamada. "Cilia in Left–Right Symmetry Breaking". Cold Spring Harbor Perspectives in Biology 9, n.º 10 (17 de febrero de 2017): a028282. http://dx.doi.org/10.1101/cshperspect.a028282.

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8

Ma, Ernest. "Left-right symmetry and supersymmetric unification". Physical Review D 51, n.º 1 (1 de enero de 1995): 236–39. http://dx.doi.org/10.1103/physrevd.51.236.

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9

Akhmedov, Eugeni Kh, Anjan S. Joshipura, Stefano Ranfone y José W.F. Valle. "Left-right symmetry and neutrino stability". Nuclear Physics B 441, n.º 1-2 (mayo de 1995): 61–75. http://dx.doi.org/10.1016/0550-3213(95)00072-z.

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10

Senjanović, Goran. "Is left–right symmetry the key?" Modern Physics Letters A 32, n.º 04 (24 de enero de 2017): 1730004. http://dx.doi.org/10.1142/s021773231730004x.

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In collaboration with Jogesh Pati, Abdus Salam challenged the chiral gauge nature of the Standard Model by paving the road towards the left-right symmetric electro-weak theory. I describe here the logical and historical construction of this theory, by emphasising the pioneering and key role it played for neutrino mass. I show that it is a self-contained and predictive model with the Higgs origin of Majorana neutrino mass, in complete analogy with the SM situation regarding charged fermions.

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11

Hung, P. Q. y Subir Mohan. "Left-right symmetry and nonperturbative unification". Physical Review D 41, n.º 1 (1 de enero de 1990): 253–63. http://dx.doi.org/10.1103/physrevd.41.253.

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12

Adam, Apriadi Salim, Akmal Ferdiyan y Mirza Satriawan. "A New Left-Right Symmetry Model". Advances in High Energy Physics 2020 (16 de enero de 2020): 1–8. http://dx.doi.org/10.1155/2020/3090783.

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We propose a new L-R symmetry model where the L-R symmetry transformation reverses both the L-R chirality and the local quantum number. We add to the model a global quantum number F whose value is one for fermions (minus one for antifermion) and vanishes for bosons. For each standard model (SM) particle, we have the corresponding L-R dual particle whose mass is very large and which should have decayed at the current low energy level. Due to the global quantum number F, there is no Majorana neutrino in the model but a Dirac seesaw mechanism can still occur and the usual three active neutrino oscillation can still be realized. We add two leptoquarks and their L-R duals, for generating the baryon number asymmetry and for facilitating the decay of the L-R dual particles. The decay of the L-R dual particles will produce a large entropy to the SM sector and give a mechanism for avoiding the big bang nucleosynthesis constraint.

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13

Ecker, G. y W. Grimus. "CP violation and left-right symmetry". Nuclear Physics B 258 (enero de 1985): 328–60. http://dx.doi.org/10.1016/0550-3213(85)90616-9.

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14

Huitu, Katri. "A minimal supersymmetric left-right model, dark matter and signals at the LHC". European Physical Journal Special Topics 229, n.º 21 (diciembre de 2020): 3187–203. http://dx.doi.org/10.1140/epjst/e2020-000039-9.

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AbstractThe left-right symmetric models extend the gauge group of the Standard Model enabling treatment of the left- and right-handed fermions in the same footing. The left-right symmetry requires the existence of right-handed neutrinos, leading naturally to non-zero masses for neutrinos. Here some aspects of a supersymmetric version of the left-right symmetric models are reviewed. Such models have many virtues, including possibility for dark matter without any new additional symmetry needed in order to have a stable lightest supersymmetric particle. In the model the lightest sneutrino or the lightest neutralino can form dark matter of the universe, at the same time fulfilling all the experimental constraints. The dark matter particle in the model can be very different from the dark matter typical in the minimal supersymmetric standard model. Specific signals for this kind of models at the LHC are also discussed.

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15

SENJANOVIĆ, GORAN. "SEESAW AT LHC THROUGH LEFT–RIGHT SYMMETRY". International Journal of Modern Physics A 26, n.º 09 (10 de abril de 2011): 1469–91. http://dx.doi.org/10.1142/s0217751x1105302x.

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I argue that LHC may shed light on the nature of neutrino mass through the probe of the seesaw mechanism. The smoking gun signature is lepton number violation through the production of same sign lepton pairs, a collider analogy of the neutrinoless double beta decay. I discuss this in the context of left–right symmetric theories, which led originally to neutrino mass and the seesaw mechanism. A WR gauge boson with a mass in a few TeV region could easily dominate neutrinoless double beta decay, and its discovery at LHC would have spectacular signatures of parity restoration and lepton number violation. Moreover, LHC can measure the masses of the right-handed neutrinos and the right-handed leptonic mixing matrix, which could in turn be used to predict the rates for neutrinoless double decay and lepton flavor violating violating processes. The LR scale at the LHC energies offers great hope of observing these low energy processes in the present and upcoming experiments.

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16

Pérez, Pavel Fileviez. "Type III seesaw and left-right symmetry". Journal of High Energy Physics 2009, n.º 03 (30 de marzo de 2009): 142. http://dx.doi.org/10.1088/1126-6708/2009/03/142.

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17

Dupont, C., K. Agladze y V. Krinsky. "Excitable medium with left–right symmetry breaking". Physica A: Statistical Mechanics and its Applications 249, n.º 1-4 (enero de 1998): 47–52. http://dx.doi.org/10.1016/s0378-4371(97)00430-5.

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18

Freedman, Douglas M., George S. Edwards, Matthew J. Willems y Roy A. Meals. "Right Versus Left Symmetry of Ulnar Variance". Clinical Orthopaedics and Related Research 354 (septiembre de 1998): 153–58. http://dx.doi.org/10.1097/00003086-199809000-00018.

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19

Mimura, Yukihiro y S. Nandi. "Orbifold breaking of left–right gauge symmetry". Physics Letters B 538, n.º 3-4 (julio de 2002): 406–14. http://dx.doi.org/10.1016/s0370-2693(02)02000-2.

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20

Akhmedov, Eugeni, Manfred Lindner, Erhard Schnapka y JoséW F. Valle. "Left-right symmetry breaking in NJL approach". Physics Letters B 368, n.º 4 (febrero de 1996): 270–80. http://dx.doi.org/10.1016/0370-2693(95)01504-3.

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21

Jain, S. K., Husain S. Al-Hazmi y Adel N. Alahmadi. "Right-Left Symmetry of Right Nonsingular Right Max-Min CS Prime Rings". Communications in Algebra 34, n.º 11 (noviembre de 2006): 3883–89. http://dx.doi.org/10.1080/00927870600862714.

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22

SABRA, W. A. "SPACETIME DUALITY AND $\frac{{{\rm{SU}}\left( {n,\,1} \right)}}{{{\rm{SU}}\left( n \right) \otimes {\rm{U}}\left( 1 \right)}}$ COSETS OF ORBIFOLD COMPACTIFICATION". Modern Physics Letters A 11, n.º 18 (14 de junio de 1996): 1497–507. http://dx.doi.org/10.1142/s0217732396001491.

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The duality symmetry group of the cosets [Formula: see text] which describe the moduli space of a two-dimensional subspace of an orbifold model with (n – 1) complex Wilson lines moduli, is discussed. The full duality group and its explicit action on the moduli fields are derived.

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23

Phung, Dong Van y Huong Thi Do. "Left-right model for dark matter". Communications in Physics 28, n.º 1 (26 de marzo de 2018): 21. http://dx.doi.org/10.15625/0868-3166/28/1/11081.

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We argue that dark matter can automatically arise from a gauge theory that possesses a non-minimal left-right gauge symmetry, SU(3)_C \otimes SU(M)_L \otimes SU(N)_R \otimes U(1)_X, for (M,N)=(2,3), (3,2), (3,3), \cdots, and (5,5).

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24

Chacko, Zackaria, Hock-Seng Goh y Roni Harnik. "A twin Higgs model from left-right symmetry". Journal of High Energy Physics 2006, n.º 01 (23 de enero de 2006): 108. http://dx.doi.org/10.1088/1126-6708/2006/01/108.

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25

Ewing, T. "Genetic 'master switch' for left-right symmetry found". Science 260, n.º 5108 (30 de abril de 1993): 624–25. http://dx.doi.org/10.1126/science.8480173.

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26

Czakon, M., J. Gluza y M. Zrałek. "Left–right symmetry and heavy particle quantum effects". Nuclear Physics B 573, n.º 1-2 (mayo de 2000): 57–74. http://dx.doi.org/10.1016/s0550-3213(99)00717-8.

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27

Fileviez Pérez, Pavel y Sogee Spinner. "Spontaneous R-parity breaking and left–right symmetry". Physics Letters B 673, n.º 4-5 (marzo de 2009): 251–54. http://dx.doi.org/10.1016/j.physletb.2009.02.047.

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28

Hamada, Hiroshi. "Left-right symmetry breaking in the mouse embryo". Mechanisms of Development 145 (julio de 2017): S1. http://dx.doi.org/10.1016/j.mod.2017.04.515.

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29

Aulakh, Charanjit S., Karim Benakli y Goran Senjanović. "Reconciling High-Scale Left-Right Symmetry with Supersymmetry". Physical Review Letters 79, n.º 12 (22 de septiembre de 1997): 2188–91. http://dx.doi.org/10.1103/physrevlett.79.2188.

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30

Bertolini, S. y J. Liu. "Small Dirac neutrino mass and left-right symmetry". Nuclear Physics B 297, n.º 2 (febrero de 1988): 401–11. http://dx.doi.org/10.1016/0550-3213(88)90026-0.

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31

Grimes, Daniel T. y Rebecca D. Burdine. "Left–Right Patterning: Breaking Symmetry to Asymmetric Morphogenesis". Trends in Genetics 33, n.º 9 (septiembre de 2017): 616–28. http://dx.doi.org/10.1016/j.tig.2017.06.004.

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32

Reig, Mario, José W. F. Valle y C. A. Vaquera-Araujo. "Unifying left–right symmetry and 331 electroweak theories". Physics Letters B 766 (marzo de 2017): 35–40. http://dx.doi.org/10.1016/j.physletb.2016.12.049.

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33

Czyż, H. y M. Zrałek. "Left-right symmetry and the top quark mass". Physics Letters B 308, n.º 3-4 (julio de 1993): 360–64. http://dx.doi.org/10.1016/0370-2693(93)91298-2.

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34

Gronau, M. y R. N. Mohapatra. "Maximal spontaneous CP-violation and left-right symmetry". Physics Letters B 168, n.º 3 (marzo de 1986): 248–52. http://dx.doi.org/10.1016/0370-2693(86)90973-1.

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35

Hamada, Hiroshi y Patrick Tam. "Diversity of left-right symmetry breaking strategy in animals". F1000Research 9 (19 de febrero de 2020): 123. http://dx.doi.org/10.12688/f1000research.21670.1.

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Left-right (L-R) asymmetry of visceral organs in animals is established during embryonic development via a stepwise process. While some steps are conserved, different strategies are employed among animals for initiating the breaking of body symmetry. In zebrafish (teleost), Xenopus (amphibian), and mice (mammal), symmetry breaking is elicited by directional fluid flow at the L-R organizer, which is generated by motile cilia and sensed by mechanoresponsive cells. In contrast, birds and reptiles do not rely on the cilia-driven fluid flow. Invertebrates such as Drosophila and snails employ another distinct mechanism, where the symmetry breaking process is underpinned by cellular chirality acquired downstream of the molecular interaction of myosin and actin. Here, we highlight the convergent entry point of actomyosin interaction and planar cell polarity to the diverse L-R symmetry breaking mechanisms among animals.

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36

Dev, P. S. Bhupal, Rabindra N. Mohapatra y Yongchao Zhang. "Heavy right-handed neutrino dark matter in left–right models". Modern Physics Letters A 32, n.º 15 (6 de abril de 2017): 1740007. http://dx.doi.org/10.1142/s0217732317400077.

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We show that in a class of non-supersymmetric left–right extensions of the Standard Model (SM), the lightest right-handed neutrino (RHN) can play the role of thermal Dark Matter (DM) in the Universe for a wide mass range from TeV to PeV. Our model is based on the gauge group [Formula: see text] in which a heavy copy of the SM fermions is introduced and the stability of the RHN DM is guaranteed by an automatic [Formula: see text] symmetry present in the leptonic sector. In such models, the active neutrino masses are obtained via the type-II seesaw mechanism. We find a lower bound on the RHN DM mass of order TeV from relic density constraints, as well as a unitarity upper bound in the multi-TeV to PeV scale, depending on the entropy dilution factor. The RHN DM could be made long-lived by soft-breaking of the [Formula: see text] symmetry and provides a concrete example of decaying DM interpretation of the PeV neutrinos observed at IceCube.

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37

Isnawati, Nurul Embun, Istikomah Istikomah y Muhammad Ardhi Khalif. "Fermion mass formulation in the Modified Left-Right Symmetry Model". Journal of Natural Sciences and Mathematics Research 8, n.º 2 (31 de diciembre de 2022): 66–74. http://dx.doi.org/10.21580/jnsmr.2022.8.2.13633.

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The Modified Left Right Symmetry Model is an extension of the Standard Model. This model introduces left-handed neutrinos to the right sector and a doublet scalar field to the left sector. This model cannot yet explain the mass generation of fermions and neutrinos. This study is theoretical research using the literature review method. Generating the masses of fermions (quark up-down) and electrons through spontaneous symmetry breaking in Yukawa's Lagrangian term produces a particle mass in the left sector, the same as the calculations in the Standard Model. The masses of fermions (up-down quarks) and electrons for the right sector produced in this study are much more massive than those of fermions (up-down quarks) and the left sector. The neutrino masses produced in this study are by following the Seesaw Mechanism. That is, if one neutrino mass is massive, then the other neutrino masses will be light.©2022 JNSMR UIN Walisongo. All rights reserved.

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38

BORAH, DEBASISH. "SUPERSYMMETRIC LEFT–RIGHT MODELS WITH B-L ODD HIGGS DOUBLETS". International Journal of Modern Physics A 26, n.º 07n08 (30 de marzo de 2011): 1305–26. http://dx.doi.org/10.1142/s0217751x11052876.

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We study various possible Supersymmetric Left–Right (SUSYLR) models with Higgs doublets carrying B-L charge ±1: with single step symmetry breaking down to the Minimal Supersymmetric Standard Model (MSSM) as well as multistep symmetry breaking. Single step symmetry breaking can be achieved with the minimal field content of just Higgs doublet and bidoublets whereas multistep symmetry breaking can be realized only at the cost of including additional Higgs superfields. However, going beyond the minimal field content comes up with the exciting possibility of TeV scale intermediate symmetry which can have important implications in the ongoing collider experiments. We show that spontaneous parity violation can be achieved naturally in all these models and R-parity is spontaneously broken by the vacuum expectation value of B-L odd Higgs doublets. The tiny neutrino mass can arise from a double seesaw mechanism in the presence of additional singlet or triplet fermions. We show that gauge coupling unification can be achieved in these models with the possibility of TeV scale intermediate symmetry in some specific nonminimal versions.

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39

Zhang Feng, Zhang Chun-Xu y Huang Ming-Qiu. "Neutrino masses in the left-right symmetry model with a family symmetry". Acta Physica Sinica 59, n.º 5 (2010): 3130. http://dx.doi.org/10.7498/aps.59.3130.

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40

Yang, Wei-Min y Hong-Huan Liu. "The new extended left–right symmetric grand unified model with family symmetry". Nuclear Physics B 820, n.º 1-2 (octubre de 2009): 364–84. http://dx.doi.org/10.1016/j.nuclphysb.2009.05.028.

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41

Siringo, F. "Symmetry breaking of the symmetric left-right model without a scalar bidoublet". European Physical Journal C 32, n.º 4 (febrero de 2004): 555–59. http://dx.doi.org/10.1140/epjc/s2003-01442-7.

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42

JANG, IK GYU, KYOUNG WON NAM, HONG SEONG PARK, YUNG HO JO, HYUN GUY KANG, JEONG YUN PARK y KWANG GI KIM. "GAIT SYMMETRY ANALYSIS PROTOCOL FOR WHOLE LEG MOVEMENT SYMMETRY EVALUATION". Journal of Mechanics in Medicine and Biology 12, n.º 04 (septiembre de 2012): 1250073. http://dx.doi.org/10.1142/s0219519412005010.

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Objective and accurate evaluation of patients who underwent lower limb operation is important in determining a proper rehabilitation process according to the patient's recovery status. Gait symmetry analysis is a common protocol that is used to evaluate lower limb function; however, most studies have focused only on the terminal symmetry of lower limb during gait motion and were unable to provide information about detailed motions of the whole leg. To more accurately analyze mutual symmetry of the left and right leg during gait motion, measurement of motions of the whole left and right leg including the pelvis, hip, knee, and ankle is required. Eight patients (mean [standard deviation]: age = 22.87 [6.05] years; height = 167.81 [5.86] cm; weight = 629.52 [133.63] Newtons) who underwent limbsalvage surgery and eight normal volunteers (age = 28.87 [3.79] years; height = 167 [8.36] cm; weight = 657.46 [157.02] Newtons) participated in this study. Using motion capture cameras arranged around each subject, real-time gait motion of each participant was recorded and moving trajectories of 12 submotion elements were extracted. Mutual symmetry of the motion between the left and right leg was then calculated using a Pearson correlation method, while a nonparametric Mann-Whitney test was performed for group comparison. Experimental results showed that the moving trajectories of the left and right leg were similar in the normal group (r = 0.8114[0.22]) but were critically different in the patient group (r = 0.624286[0.15]). In addition, there was statistically significant difference (p = 0.0162) in gait symmetry between the normal group and the patient group (95% confidence level). We conclude that the proposed protocol can provide a useful evaluation tool for patient recovery condition and that it could be helpful in establishing an effective postoperative treatment protocol for lower limb patients.

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43

Knox, Ethan y P. T. Leung. "Constraints on the reciprocal propagation of a quantum particle through a one-dimensional localized complex potential". Canadian Journal of Physics 91, n.º 3 (marzo de 2013): 246–50. http://dx.doi.org/10.1139/cjp-2012-0459.

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In the propagation of an electron through a one-dimensional asymmetric complex potential, it is known that while the conventional Green function reciprocity symmetry will ensure transmission to be symmetric between a “left-incident” and a “right-incident” beam, no such symmetry exists for the case of reflection. Here we derive generalized reciprocity relations for both the amplitude and phase of the reflected waves as constraints on the left- and right-incident beams, in complete analogy to what was established in optics. We further provide illustrations of these relations via direct analytical calculations in the case of a real potential, and via numerical studies in the case of a complex potential.

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44

ASATRIAN, H. M. y A. N. IOANNISSIAN. "RARE B-MESON DECAYS IN SU(2)L × SU(2)R × U(1) MODEL". Modern Physics Letters A 05, n.º 14 (10 de junio de 1990): 1089–96. http://dx.doi.org/10.1142/s0217732390001219.

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Rare B-meson decays are investigated in the left–right symmetric models. The scalar particle contribution to the amplitude of the b → sγ decay is calculated. It is shown that this contribution can be essential even for scalar particle masses of about several TeV. The effects due to the left–right symmetry and scalar particles can be detected by measuring photon polarization in the decay B → K*γ.

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45

Chen, J. N., F. J. van Eeden, K. S. Warren, A. Chin, C. Nusslein-Volhard, P. Haffter y M. C. Fishman. "Left-right pattern of cardiac BMP4 may drive asymmetry of the heart in zebrafish". Development 124, n.º 21 (1 de noviembre de 1997): 4373–82. http://dx.doi.org/10.1242/dev.124.21.4373.

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The first evident break in left-right symmetry of the primitive zebrafish heart tube is the shift in pattern of BMP4 expression from radially symmetric to left-predominant. The midline heart tube then ‘jogs’ to the left and subsequently loops to the right. We examined 279 mutations, affecting more than 200 genes, and found 21 mutations that perturb this process. Some cause BMP4 to remain radially symmetric. Others randomize the asymmetric BMP4 pattern. Retention of BMP4 symmetry is associated with failure to jog: right-predominance of the BMP4 pattern is associated with reversal of the direction of jogging and looping. Raising BMP4 diffusely throughout the heart, via sonic hedgehog injection, or the blocking of its action by injection of a dominant negative BMP4 receptor, prevent directional jogging or looping. The genes crucial to directing cardiac asymmetry include a subset of those needed for patterning the dorsoventral axis and for notochord and ventral spinal cord development. Thus, the pattern of cardiac BMP4 appears to be in the pathway by which the heart interprets lateralizing signals from the midline.

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46

Liu, Xiang-Shu, Han-Xiang Xu, Yan-Hong Qin y Liang Duan. "Excitation of mirror symmetry higher-order rational soliton in modulation stability regimes on continuous wave background". Chaos: An Interdisciplinary Journal of Nonlinear Science 32, n.º 12 (diciembre de 2022): 123105. http://dx.doi.org/10.1063/5.0106915.

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We study the relationship between the structures of the nonlinear localized waves and the distribution characteristics of the modulation stability regime in a nonlinear fiber with both third-order and fourth-order effects. On the background frequency and background amplitude plane, the modulation stability region consists of two symmetric curves on the left and right and a point on the symmetry axis. We find that the higher-order excitation characteristics are obviously different at different positions in the modulation stability region. Their excitation characteristics are closely related to the modulation instability distribution characteristics of the system. It is shown that asymmetric high-order rational solitons are excited at the left and right stable curves, and the symmetric one is excited at the stable points. Interestingly, the asymmetric higher-order rational solitons on the left and right sides are mirror-symmetrical to each other, which coincides with the symmetry of the modulation instability distribution. These results can deepen our understanding of the relationship between nonlinear excitation and modulation instability and enrich our knowledge about higher-order nonlinear excitations.

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47

McMANUS, I. C. "Symmetry and asymmetry in aesthetics and the arts". European Review 13, S2 (22 de agosto de 2005): 157–80. http://dx.doi.org/10.1017/s1062798705000736.

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Symmetry and beauty are often claimed to be linked, particularly by mathematicians and scientists. However philosophers and art historians seem generally agreed that although symmetry is indeed attractive, there is also a somewhat sterile rigidity about it, which can make it less attractive than the more dynamic, less predictable beauty associated with asymmetry. Although a little asymmetry can be beautiful, an excess merely results in chaos. As Adorno suggested, asymmetry probably results most effectively in beauty when the underlying symmetry upon which it is built is still apparent. This paper examines the ways in which asymmetries, particularly left-right asymmetries, were used by painters in the Italian Renaissance. Polyptychs often show occasional asymmetries, which are more likely to involve the substitution of a left cheek for a right cheek, than vice-versa. A hypothesis is developed that the left and right cheeks have symbolic meanings, with the right cheek meaning ‘like self’ and the left cheek meaning ‘unlike self’. This principle is evaluated in pictures such as the Crucifixion, the Annunciation and, the Madonna and Child. The latter is particularly useful because the theological status of the Madonna changed during the Renaissance, and her left–right portrayal also changed at the same time in a comprehensible way. Some brief experimental tests of the hypothesis are also described. Finally the paper ends by considering why it is that the left rather than the right cheek is associated with ‘unlike self’, and puts that result in the context of the universal ‘dual symbolic classification’ of right and left, which was first described by the anthropologist Robert Hertz.

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48

CRIVEI, SEPTIMIU y MIODRAG CRISTIAN IOVANOV. "SYMMETRY FOR COMODULE CATEGORIES". Journal of Algebra and Its Applications 11, n.º 01 (febrero de 2012): 1250009. http://dx.doi.org/10.1142/s0219498811005324.

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For coalgebras C over a field, we study when the categories [Formula: see text] of left C-comodules and [Formula: see text] of right C-comodules are symmetric categories, in the sense that there is a duality between the categories of finitely presented unitary left R-modules and finitely presented unitary left L-modules, where R and L are the functor rings associated to the finitely accessible categories [Formula: see text] and [Formula: see text].

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49

Maclean, K. y SL Dunwoodie. "Breaking symmetry: a clinical overview of left-right patterning". Clinical Genetics 65, n.º 6 (18 de mayo de 2004): 441–57. http://dx.doi.org/10.1111/j.0009-9163.2004.00258.x.

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50

Naviliat-Cuncic, O., T. A. Girard, J. Deutsch y N. Severijns. "Left-right symmetry breaking sensitivity of beta -asymmetry measurements". Journal of Physics G: Nuclear and Particle Physics 17, n.º 6 (1 de junio de 1991): 919–26. http://dx.doi.org/10.1088/0954-3899/17/6/013.

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