Pub Date : 2023-11-24DOI: 10.21468/scipostphysproc.14.048
Iryna Yehorchenko
We find extensions of realisations of some low-dimensional Lie algebras, in particular, for the Poincaré algebra for one space dimension. Using inequivalent extensions, we performed comprehensive classification of relative differential invariants for these Lie algebras. We show difference between classification of extensions of realisations, and classification of nonlinear realisations of Lie algebras.
{"title":"Extensions of realisations for low-dimensional Lie algebras","authors":"Iryna Yehorchenko","doi":"10.21468/scipostphysproc.14.048","DOIUrl":"https://doi.org/10.21468/scipostphysproc.14.048","url":null,"abstract":"We find extensions of realisations of some low-dimensional Lie algebras, in particular, for the Poincaré algebra for one space dimension. Using inequivalent extensions, we performed comprehensive classification of relative differential invariants for these Lie algebras. We show difference between classification of extensions of realisations, and classification of nonlinear realisations of Lie algebras.","PeriodicalId":355998,"journal":{"name":"SciPost Physics Proceedings","volume":" 37","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139240239","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-23DOI: 10.21468/scipostphysproc.14.021
Manuel Calixto, A. Mayorgas, J. Guerrero
Using the Lieb–Mattis ordering theorem of electronic energy levels, we identify and construct the Hilbert space of the low energy sector of U(N) quantum Hall/Heisenberg ferromagnets at filling factor M for L Landau/lattice sites. The carrier Hilbert space of irreducible representations of U(N) is described by rectangular Young tableaux of M rows and L columns, and associated with Grassmannian phase spaces U(N)/U(M)×U(N-M). Replacing U(N)-spin operators by their expectation values in a Grassmannian coherent state allows for a semi-classical treatment of the low energy U(N)-spin-wave coherent excitations (skyrmions) of U(N) quantum Hall ferromagnets in terms of Grasmannian nonlinear sigma models.
利用电子能级的利布-马蒂斯排序定理，我们确定并构建了 L 个兰道/晶格位点填充因子为 M 的 U(N) 量子霍尔/海森堡铁磁体低能段的希尔伯特空间。U(N) 不可还原表征的载波希尔伯特空间由 M 行 L 列的矩形杨表描述，并与格拉斯曼相空间 U(N)/U(M)×U(N-M) 相关联。用它们在格拉斯曼相干态中的期望值代替 U(N)-spin 算子，就可以用格拉斯曼非线性西格玛模型对 U(N) 量子霍尔铁磁体的低能 U(N)-spin 波相干激发（skyrmions）进行半经典处理。
{"title":"Hilbert space structure and classical limit of the low energy sector of U(N) quantum Hall ferromagnets","authors":"Manuel Calixto, A. Mayorgas, J. Guerrero","doi":"10.21468/scipostphysproc.14.021","DOIUrl":"https://doi.org/10.21468/scipostphysproc.14.021","url":null,"abstract":"Using the Lieb–Mattis ordering theorem of electronic energy levels, we identify and construct the Hilbert space of the low energy sector of U(N) quantum Hall/Heisenberg ferromagnets at filling factor M for L Landau/lattice sites. The carrier Hilbert space of irreducible representations of U(N) is described by rectangular Young tableaux of M rows and L columns, and associated with Grassmannian phase spaces U(N)/U(M)×U(N-M). Replacing U(N)-spin operators by their expectation values in a Grassmannian coherent state allows for a semi-classical treatment of the low energy U(N)-spin-wave coherent excitations (skyrmions) of U(N) quantum Hall ferromagnets in terms of Grasmannian nonlinear sigma models.","PeriodicalId":355998,"journal":{"name":"SciPost Physics Proceedings","volume":"16 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139242811","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-23DOI: 10.21468/scipostphysproc.14.015
Marcelo Tozo Araujo, J. Chahine, E. Drigo Filho, Regina Maria Ricotta
Recently, a mathematical method to solve the Fokker Plank equation (FPE) enabled the analysis of the protein folding kinetics, through the construction of the temporal evolution of the probability density. A symmetric tri-stable potential function was used to describe the unfolded and folded states of the protein as well as an intermediate state of the protein. In this paper, the main points of the methodology are reviewed, based on the algebraic Supersymmetric Quantum Mechanics (SQM) formalism, and new results on the kinetics of the evolution of the system characterized in terms of the diffusion parameter are presented.
{"title":"The impact of the diffusion parameter on the passage time of the folding process","authors":"Marcelo Tozo Araujo, J. Chahine, E. Drigo Filho, Regina Maria Ricotta","doi":"10.21468/scipostphysproc.14.015","DOIUrl":"https://doi.org/10.21468/scipostphysproc.14.015","url":null,"abstract":"Recently, a mathematical method to solve the Fokker Plank equation (FPE) enabled the analysis of the protein folding kinetics, through the construction of the temporal evolution of the probability density. A symmetric tri-stable potential function was used to describe the unfolded and folded states of the protein as well as an intermediate state of the protein. In this paper, the main points of the methodology are reviewed, based on the algebraic Supersymmetric Quantum Mechanics (SQM) formalism, and new results on the kinetics of the evolution of the system characterized in terms of the diffusion parameter are presented.","PeriodicalId":355998,"journal":{"name":"SciPost Physics Proceedings","volume":"78 5","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139243594","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-23DOI: 10.21468/scipostphysproc.14.004
Gilles Cohen-Tanoudji, J. Gazeau
The LambdaΛCDM standard model of cosmology involves two dark components of the universe, dark energy and dark matter. Whereas dark energy is usually associated with the (positive) cosmological constant LambdaΛ associated with a de Sitter geometry, we propose to explain dark matter as a pure QCD effect, namely a gluonic Bose Einstein condensate with the status of a Cosmic Gluonic Background (CGB). This effect is due to the trace anomaly viewed as an effective negative cosmological constant determining an Anti de Sitter geometry and accompanying baryonic matter at the hadronization transition from the quark gluon plasma phase to the colorless hadronic phase. Our approach also allows to assume a ratio Dark/Visible equal to 11/2.
{"title":"Dark matter as a QCD effect in an anti de Sitter geometry: Cosmogonic implications of de Sitter, anti de Sitter and Poincaré symmetries","authors":"Gilles Cohen-Tanoudji, J. Gazeau","doi":"10.21468/scipostphysproc.14.004","DOIUrl":"https://doi.org/10.21468/scipostphysproc.14.004","url":null,"abstract":"The LambdaΛCDM standard model of cosmology involves two dark components of the universe, dark energy and dark matter. Whereas dark energy is usually associated with the (positive) cosmological constant LambdaΛ associated with a de Sitter geometry, we propose to explain dark matter as a pure QCD effect, namely a gluonic Bose Einstein condensate with the status of a Cosmic Gluonic Background (CGB). This effect is due to the trace anomaly viewed as an effective negative cosmological constant determining an Anti de Sitter geometry and accompanying baryonic matter at the hadronization transition from the quark gluon plasma phase to the colorless hadronic phase. Our approach also allows to assume a ratio Dark/Visible equal to 11/2.","PeriodicalId":355998,"journal":{"name":"SciPost Physics Proceedings","volume":"116 ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139242835","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-23DOI: 10.21468/scipostphysproc.14.002
María Antonia Lledó Barrena
Erik Panzer, from the University of Oxford, has been awarded the 2020 Hermann Weyl Prize of the International Colloquium on Group Theoretical Methods in Physics, for “his pioneering achievements in the calculation of amplitudes in gauge theories, for developing new mathematical structures that exploit the language of symmetries, and for his contribution to the description of important physical phenomena present in nature.”
{"title":"Laudatio of Dr. Erik Panzer, 2020 Hermann Weyl Prize","authors":"María Antonia Lledó Barrena","doi":"10.21468/scipostphysproc.14.002","DOIUrl":"https://doi.org/10.21468/scipostphysproc.14.002","url":null,"abstract":"Erik Panzer, from the University of Oxford, has been awarded the 2020 Hermann Weyl Prize of the International Colloquium on Group Theoretical Methods in Physics, for “his pioneering achievements in the calculation of amplitudes in gauge theories, for developing new mathematical structures that exploit the language of symmetries, and for his contribution to the description of important physical phenomena present in nature.”","PeriodicalId":355998,"journal":{"name":"SciPost Physics Proceedings","volume":"3 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139245960","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-23DOI: 10.21468/scipostphysproc.14.024
Won S. Chung, M. N. Hounkonnou
We define new velocity and acceleration having dimension of (Length)^{alpha}/(Time)(Length)α/(Time) and (Length)^{alpha}/(Time)^2,(Length)α/(Time)2, respectively, based on the fractional addition rule. We discuss the formulation of fractional Newton mechanics, Galilean relativity and special relativity in the same setting. We show the conservation of the fractional energy, characterize the Lorentz transformation and group, and derive the expressions of the energy and momentum. The two body decay is discussed as a concrete illustration.
{"title":"Newton mechanics, Galilean relativity, and special relativity in $alpha$-deformed binary operation setting","authors":"Won S. Chung, M. N. Hounkonnou","doi":"10.21468/scipostphysproc.14.024","DOIUrl":"https://doi.org/10.21468/scipostphysproc.14.024","url":null,"abstract":"<jats:p>We define new velocity and acceleration having dimension of <jats:inline-formula><jats:alternatives><jats:tex-math>(Length)^{alpha}/(Time)</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><mml:mrow><mml:msup><mml:mrow><mml:mo stretchy=\"true\" form=\"prefix\">(</mml:mo><mml:mi>L</mml:mi><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:mi>g</mml:mi><mml:mi>t</mml:mi><mml:mi>h</mml:mi><mml:mo stretchy=\"true\" form=\"postfix\">)</mml:mo></mml:mrow><mml:mi>α</mml:mi></mml:msup><mml:mi>/</mml:mi><mml:mrow><mml:mo stretchy=\"true\" form=\"prefix\">(</mml:mo><mml:mi>T</mml:mi><mml:mi>i</mml:mi><mml:mi>m</mml:mi><mml:mi>e</mml:mi><mml:mo stretchy=\"true\" form=\"postfix\">)</mml:mo></mml:mrow></mml:mrow></mml:math></jats:alternatives></jats:inline-formula> and <jats:inline-formula><jats:alternatives><jats:tex-math>(Length)^{alpha}/(Time)^2,</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><mml:mrow><mml:msup><mml:mrow><mml:mo stretchy=\"true\" form=\"prefix\">(</mml:mo><mml:mi>L</mml:mi><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:mi>g</mml:mi><mml:mi>t</mml:mi><mml:mi>h</mml:mi><mml:mo stretchy=\"true\" form=\"postfix\">)</mml:mo></mml:mrow><mml:mi>α</mml:mi></mml:msup><mml:mi>/</mml:mi><mml:msup><mml:mrow><mml:mo stretchy=\"true\" form=\"prefix\">(</mml:mo><mml:mi>T</mml:mi><mml:mi>i</mml:mi><mml:mi>m</mml:mi><mml:mi>e</mml:mi><mml:mo stretchy=\"true\" form=\"postfix\">)</mml:mo></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:mo>,</mml:mo></mml:mrow></mml:math></jats:alternatives></jats:inline-formula> respectively, based on the fractional addition rule. We discuss the formulation of fractional Newton mechanics, Galilean relativity and special relativity in the same setting. We show the conservation of the fractional energy, characterize the Lorentz transformation and group, and derive the expressions of the energy and momentum. The two body decay is discussed as a concrete illustration.</jats:p>","PeriodicalId":355998,"journal":{"name":"SciPost Physics Proceedings","volume":"3 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139245677","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-23DOI: 10.21468/scipostphysproc.14.010
G. Pogosyan, Mariano A. del Olmo
A personal view of the Mexican mathematical physicist Kurt Bernardo Wolf (1942-2022) is presented here.
这里介绍的是墨西哥数学物理学家库尔特-贝尔纳多-沃尔夫（1942-2022 年）的个人观点。
{"title":"Kurt Bernardo Wolf memorial lecture","authors":"G. Pogosyan, Mariano A. del Olmo","doi":"10.21468/scipostphysproc.14.010","DOIUrl":"https://doi.org/10.21468/scipostphysproc.14.010","url":null,"abstract":"A personal view of the Mexican mathematical physicist Kurt Bernardo Wolf (1942-2022) is presented here.","PeriodicalId":355998,"journal":{"name":"SciPost Physics Proceedings","volume":"229 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139244000","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-23DOI: 10.21468/scipostphysproc.14.023
E. Celeghini, M. Gadella, Mariano A. del Olmo
A generalisation of Euclidean and pseudo-Euclidean groups is presented, where the Weyl-Heisenberg groups, well known in quantum mechanics, are involved. A new family of groups is obtained including all the above-mentioned groups as subgroups. Symmetries, like self-similarity and invariance with respect to the orientation of the axes, are properly included in the structure of this new family of groups. Generalized Hermite functions on multidimensional spaces, which serve as orthogonal bases of Hilbert spaces supporting unitary irreducible representations of these new groups, are introduced.
{"title":"Generalized Heisenberg-Weyl groups and Hermite functions","authors":"E. Celeghini, M. Gadella, Mariano A. del Olmo","doi":"10.21468/scipostphysproc.14.023","DOIUrl":"https://doi.org/10.21468/scipostphysproc.14.023","url":null,"abstract":"A generalisation of Euclidean and pseudo-Euclidean groups is presented, where the Weyl-Heisenberg groups, well known in quantum mechanics, are involved. A new family of groups is obtained including all the above-mentioned groups as subgroups. Symmetries, like self-similarity and invariance with respect to the orientation of the axes, are properly included in the structure of this new family of groups. Generalized Hermite functions on multidimensional spaces, which serve as orthogonal bases of Hilbert spaces supporting unitary irreducible representations of these new groups, are introduced.","PeriodicalId":355998,"journal":{"name":"SciPost Physics Proceedings","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139244448","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-23DOI: 10.21468/scipostphysproc.14.016
Naruhiko Aizawa
We give a brief review on recent developments of mathbb{Z}_2^nℤ2n-graded symmetry in physics in which hidden mathbb{Z}_2^nℤ2n-graded symmetries and mathbb{Z}_2^nℤ2n-graded extensions of known systems are discussed. This elucidates physical relevance of the mathbb{Z}_2^nℤ2n-graded algebras. As an example of physically interesting algebra, we take mathbb{Z}_2^2ℤ22-graded supersymmetry (SUSY) algebras and consider their irreducible representations (irreps). A list of irreps for N = 1, 2N=1,2 algebras is presented and as an application of the irreps, mathbb{Z}_2^2ℤ22-graded SUSY classical actions are constructed.
{"title":"Irreducible representations of $mathbb{Z}_2^2$-graded supersymmetry algebra and their applications","authors":"Naruhiko Aizawa","doi":"10.21468/scipostphysproc.14.016","DOIUrl":"https://doi.org/10.21468/scipostphysproc.14.016","url":null,"abstract":"<jats:p>We give a brief review on recent developments of <jats:inline-formula><jats:alternatives><jats:tex-math>mathbb{Z}_2^n</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><mml:msubsup><mml:mi>ℤ</mml:mi><mml:mn>2</mml:mn><mml:mi>n</mml:mi></mml:msubsup></mml:math></jats:alternatives></jats:inline-formula>-graded symmetry in physics in which hidden <jats:inline-formula><jats:alternatives><jats:tex-math>mathbb{Z}_2^n</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><mml:msubsup><mml:mi>ℤ</mml:mi><mml:mn>2</mml:mn><mml:mi>n</mml:mi></mml:msubsup></mml:math></jats:alternatives></jats:inline-formula>-graded symmetries and <jats:inline-formula><jats:alternatives><jats:tex-math>mathbb{Z}_2^n</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><mml:msubsup><mml:mi>ℤ</mml:mi><mml:mn>2</mml:mn><mml:mi>n</mml:mi></mml:msubsup></mml:math></jats:alternatives></jats:inline-formula>-graded extensions of known systems are discussed. This elucidates physical relevance of the <jats:inline-formula><jats:alternatives><jats:tex-math>mathbb{Z}_2^n</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><mml:msubsup><mml:mi>ℤ</mml:mi><mml:mn>2</mml:mn><mml:mi>n</mml:mi></mml:msubsup></mml:math></jats:alternatives></jats:inline-formula>-graded algebras. As an example of physically interesting algebra, we take <jats:inline-formula><jats:alternatives><jats:tex-math>mathbb{Z}_2^2</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><mml:msubsup><mml:mi>ℤ</mml:mi><mml:mn>2</mml:mn><mml:mn>2</mml:mn></mml:msubsup></mml:math></jats:alternatives></jats:inline-formula>-graded supersymmetry (SUSY) algebras and consider their irreducible representations (irreps). A list of irreps for <jats:inline-formula><jats:alternatives><jats:tex-math>N = 1, 2</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><mml:mrow><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:math></jats:alternatives></jats:inline-formula> algebras is presented and as an application of the irreps, <jats:inline-formula><jats:alternatives><jats:tex-math>mathbb{Z}_2^2</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><mml:msubsup><mml:mi>ℤ</mml:mi><mml:mn>2</mml:mn><mml:mn>2</mml:mn></mml:msubsup></mml:math></jats:alternatives></jats:inline-formula>-graded SUSY classical actions are constructed.</jats:p>","PeriodicalId":355998,"journal":{"name":"SciPost Physics Proceedings","volume":"15 ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139245217","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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