International Journal of Geometric Methods in Modern Physics最新文献

{"title":"Revisiting Legendre transformations in Finsler geometry","authors":"Ernesto Rodrigues, Iarley P. Lobo","doi":"10.1142/s021988782450155x","DOIUrl":"https://doi.org/10.1142/s021988782450155x","url":null,"abstract":"<p>In this paper, we discuss the conditions for mapping the geometric description of the kinematics of particles that probe a given Hamiltonian in phase space to a description in terms of Finsler geometry (and vice-versa).</p>","PeriodicalId":50320,"journal":{"name":"International Journal of Geometric Methods in Modern Physics","volume":"10 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2024-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140124172","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A note on generalized weakly ℋ-symmetric manifolds and relativistic applications","authors":"Sameh Shenawy, Nasser Bin Turki, Carlo Mantica","doi":"10.1142/s0219887824501536","DOIUrl":"https://doi.org/10.1142/s0219887824501536","url":null,"abstract":"<p>In this work, generalized weakly <span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><mi mathvariant=\"cal\">ℋ</mi></math></span><span></span>-symmetric space-times (GWHS)<span><math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><msub><mrow></mrow><mrow><mi>n</mi></mrow></msub></math></span><span></span> are investigated, where <span><math altimg=\"eq-00004.gif\" display=\"inline\" overflow=\"scroll\"><mi mathvariant=\"cal\">ℋ</mi></math></span><span></span> is any symmetric <span><math altimg=\"eq-00005.gif\" display=\"inline\" overflow=\"scroll\"><mo stretchy=\"false\">(</mo><mn>0</mn><mo>,</mo><mn>2</mn><mo stretchy=\"false\">)</mo></math></span><span></span> tensor. It is proved that, in a nontrivial (GWHS)<span><math altimg=\"eq-00006.gif\" display=\"inline\" overflow=\"scroll\"><msub><mrow></mrow><mrow><mi>n</mi></mrow></msub></math></span><span></span> space-time, the tensor <span><math altimg=\"eq-00007.gif\" display=\"inline\" overflow=\"scroll\"><mi mathvariant=\"cal\">ℋ</mi></math></span><span></span> has a perfect fluid form. Accordingly, sufficient conditions for a nontrivial generalized weakly Ricci symmetric space-time (GWRS)<span><math altimg=\"eq-00008.gif\" display=\"inline\" overflow=\"scroll\"><msub><mrow></mrow><mrow><mi>n</mi></mrow></msub></math></span><span></span> to be either an Einstein space-time or a perfect fluid space-time are obtained. Also, conditions for space-times admitting either a generalized weakly symmetric energy-momentum tensor or a generalized weakly symmetric <span><math altimg=\"eq-00009.gif\" display=\"inline\" overflow=\"scroll\"><mi mathvariant=\"cal\">𝒵</mi></math></span><span></span> tensor to be Einstein or perfect fluid space-times are provided.</p>","PeriodicalId":50320,"journal":{"name":"International Journal of Geometric Methods in Modern Physics","volume":"9 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2024-02-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140124176","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Observation constraints on scalar field cosmological model in anisotropic universe","authors":"Vinod Kumar Bhardwaj, Anil Kumar Yadav","doi":"10.1142/s0219887824501445","DOIUrl":"https://doi.org/10.1142/s0219887824501445","url":null,"abstract":"&lt;p&gt;In this study, we have explored a scalar field cosmological model in the axially symmetric Bianchi type-I universe. In this study, our aim is to constrain the scalar field dark energy model in an anisotropic background. For this purpose, the explicit solution of the developed field equations for the model is determined and analyzed. Constraints on the cosmological model parameters are established utilizing Markov Chain Monte Carlo (MCMC) analysis and using the latest observational datasets of OHD, BAO, and Pantheon. For the combined dataset (OHD, BAO, and Pantheon), the best-fit values of Hubble and density parameters are estimated as &lt;span&gt;&lt;math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;7&lt;/mn&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;mn&gt;5&lt;/mn&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;mo stretchy=\"false\"&gt;±&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mn&gt;8&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt;&lt;span&gt;&lt;/span&gt;, &lt;span&gt;&lt;math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi mathvariant=\"normal\"&gt;Ω&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mn&gt;6&lt;/mn&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo stretchy=\"false\"&gt;±&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt;&lt;span&gt;&lt;/span&gt;&lt;span&gt;&lt;math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi mathvariant=\"normal\"&gt;Ω&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;ϕ&lt;/mi&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;mn&gt;7&lt;/mn&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo stretchy=\"false\"&gt;±&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;mn&gt;6&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt;&lt;span&gt;&lt;/span&gt; and &lt;span&gt;&lt;math altimg=\"eq-00004.gif\" display=\"inline\" overflow=\"scroll\"&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi mathvariant=\"normal\"&gt;Ω&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;σ&lt;/mi&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mn&gt;6&lt;/mn&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo stretchy=\"false\"&gt;±&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mn&gt;6&lt;/mn&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt;&lt;span&gt;&lt;/span&gt;. The model shows a flipping nature and redshift transition occurs at &lt;span&gt;&lt;math altimg=\"eq-00005.gif\" display=\"inline\" overflow=\"scroll\"&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;z&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;mn&gt;6&lt;/mn&gt;&lt;mn&gt;9&lt;/mn&gt;&lt;mn&gt;6&lt;/mn&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo stretchy=\"false\"&gt;−&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mn&gt;6&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo stretchy=\"false\"&gt;+&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mn&gt;6&lt;/mn&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;/math&gt;&lt;/span&gt;&lt;span&gt;&lt;/span&gt;, and the present value of decelerated parameter is computed to be &lt;span&gt;&lt;math altimg=\"eq-00006.gif\" display=\"inline\" overflow=\"scroll\"&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;q&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo stretchy=\"false\"&gt;−&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;mn&gt;6&lt;/mn&gt;&lt;mn&gt;9&lt;/mn&gt;&lt;mn&gt;6&lt;/mn&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;mo stretchy=\"false\"&gt;±&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mn&gt;8&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt;&lt;span&gt;&lt;/span&gt; for the combined dataset. We have explored characteristics like the univ","PeriodicalId":50320,"journal":{"name":"International Journal of Geometric Methods in Modern Physics","volume":"84 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2024-02-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140124112","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"From the classical Frenet–Serret apparatus to the curvature and torsion of quantum-mechanical evolutions. Part I. Stationary Hamiltonians","authors":"Paul M. Alsing, Carlo Cafaro","doi":"10.1142/s0219887824501524","DOIUrl":"https://doi.org/10.1142/s0219887824501524","url":null,"abstract":"&lt;p&gt;It is known that the Frenet–Serret apparatus of a space curve in three-dimensional Euclidean space determines the local geometry of curves. In particular, the Frenet–Serret apparatus specifies important geometric invariants, including the curvature and the torsion of a curve. It is also acknowledged in quantum information science that low complexity and high efficiency are essential features to achieve when cleverly manipulating quantum states that encode quantum information about a physical system.&lt;/p&gt;&lt;p&gt;In this paper, we propose a geometric perspective on how to quantify the bending and the twisting of quantum curves traced by dynamically evolving state vectors. Specifically, we propose a quantum version of the Frenet–Serret apparatus for a quantum trajectory in projective Hilbert space traced by a parallel-transported pure quantum state evolving unitarily under a stationary Hamiltonian specifying the Schrödinger equation. Our proposed constant curvature coefficient is given by the magnitude squared of the covariant derivative of the tangent vector &lt;span&gt;&lt;math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;mo stretchy=\"false\"&gt;〉&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;&lt;span&gt;&lt;/span&gt; to the state vector &lt;span&gt;&lt;math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi mathvariant=\"normal\"&gt;Ψ&lt;/mi&gt;&lt;mo stretchy=\"false\"&gt;〉&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;&lt;span&gt;&lt;/span&gt; and represents a useful measure of the bending of the quantum curve. Our proposed constant torsion coefficient, instead, is defined in terms of the magnitude squared of the projection of the covariant derivative of the tangent vector &lt;span&gt;&lt;math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;mo stretchy=\"false\"&gt;〉&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;&lt;span&gt;&lt;/span&gt;, orthogonal to both &lt;span&gt;&lt;math altimg=\"eq-00004.gif\" display=\"inline\" overflow=\"scroll\"&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;mo stretchy=\"false\"&gt;〉&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;&lt;span&gt;&lt;/span&gt; and &lt;span&gt;&lt;math altimg=\"eq-00005.gif\" display=\"inline\" overflow=\"scroll\"&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi mathvariant=\"normal\"&gt;Ψ&lt;/mi&gt;&lt;mo stretchy=\"false\"&gt;〉&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;&lt;span&gt;&lt;/span&gt;. The torsion coefficient provides a convenient measure of the twisting of the quantum curve. Remarkably, we show that our proposed curvature and torsion coefficients coincide with those existing in the literature, although introduced in a completely different manner. Interestingly, not only we establish that zero curvature corresponds to unit geodesic efficiency during the quantum transportation in projective Hilbert space, but we also find that the concepts of curvature and torsion help enlighten the statistical structure of quantum theory. Indeed, while the former concept can be essentially defined in terms of the concept of kurtosis, the positivity of the latter can be regarded as a restatement of the well-known Pearson inequality that involves both the concepts of kurtosis and skewness in mathematical statistics. Finally, not only do we present illustrative examples with no","PeriodicalId":50320,"journal":{"name":"International Journal of Geometric Methods in Modern Physics","volume":"9 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2024-02-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140124143","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The equivalence principle as a Noether symmetry","authors":"Salvatore Capozziello, Carmen Ferrara","doi":"10.1142/s0219887824400140","DOIUrl":"https://doi.org/10.1142/s0219887824400140","url":null,"abstract":"<p>The equivalence principle is considered in the framework of metric-affine gravity. We show that it naturally emerges as a Noether symmetry starting from a general non-metric theory. In particular, we discuss the Einstein equivalence principle and the strong equivalence principle showing their relations with the non-metricity tensor. Possible violations are also discussed pointing out the role of non-metricity in this debate.</p>","PeriodicalId":50320,"journal":{"name":"International Journal of Geometric Methods in Modern Physics","volume":"68 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2024-02-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140124147","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Solitons and traveling waves structure for the Schrödinger–Hirota model in fluids","authors":"Fazal Badshah, Kalim U. Tariq, Jian-Guo Liu, S. M. Raza Kazmi","doi":"10.1142/s0219887824501457","DOIUrl":"https://doi.org/10.1142/s0219887824501457","url":null,"abstract":"<p>The Schrödinger–Hirota equation is one of the most important models of contemporary physics which is popular throughout the broad fields of fluid movement as well as in the study of thick-water crests, liquid science, refractive optical components and so on. In this paper, we utilize the Hirota bilinear technique and the unified technique to attain various soliton solutions of the governing model analytically. These approaches are robust, powerful and unique also have many applications in different fields of mathematical physics. The solutions attained from these techniques are highly valuable and useful in various fields of sciences specially in the transmissions of optical fibers, also they give different behaviors including V-shaped and periodic soliton solution behavior. Further, the approaches applied here are not applied in this model previously. Therefore, ours is a new work, which summarizes its novelty. The 3D, 2D and contour plots are included to grasp the understanding of solutions’ behavior. These findings are valuable in electronic communications such as elliptical circuits and in investigation of solitude controlling.</p>","PeriodicalId":50320,"journal":{"name":"International Journal of Geometric Methods in Modern Physics","volume":"54 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2024-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140124113","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Spacetime metric from quantum-gravity corrected Feynman propagators","authors":"P. Fernández de Córdoba, J. M. Isidro, Rudranil Roy","doi":"10.1142/s0219887824501391","DOIUrl":"https://doi.org/10.1142/s0219887824501391","url":null,"abstract":"<p>Differentiation of the scalar Feynman propagator with respect to the spacetime coordinates yields the metric on the background spacetime that the scalar particle propagates in. Now Feynman propagators can be modified in order to include quantum-gravity corrections as induced by a zero-point length <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mi>L</mi><mo>&gt;</mo><mn>0</mn></math></span><span></span>. These corrections cause the length element <span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><msqrt><mrow><msup><mrow><mi>s</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></msqrt></math></span><span></span> to be replaced with <span><math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><msqrt><mrow><msup><mrow><mi>s</mi></mrow><mrow><mn>2</mn></mrow></msup><mo stretchy=\"false\">+</mo><mn>4</mn><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></msqrt></math></span><span></span> within the Feynman propagator. In this paper, we compute the metrics derived from both the quantum-gravity free propagators and from their quantum-gravity corrected counterparts. We verify that the latter propagators yield the same spacetime metrics as the former, provided one measures distances greater than the quantum of length <span><math altimg=\"eq-00004.gif\" display=\"inline\" overflow=\"scroll\"><mi>L</mi></math></span><span></span>. We perform this analysis in the case of the background spacetime <span><math altimg=\"eq-00005.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mi>ℝ</mi></mrow><mrow><mi>D</mi></mrow></msup></math></span><span></span> in the Euclidean sector.</p>","PeriodicalId":50320,"journal":{"name":"International Journal of Geometric Methods in Modern Physics","volume":"6 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2024-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140124144","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Conformal η-Ricci–Bourguignon soliton in general relativistic spacetime","authors":"Santu Dey, Shyamal Kumar Hui, Soumendu Roy, Ali H. Alkhaldi","doi":"10.1142/s0219887824501482","DOIUrl":"https://doi.org/10.1142/s0219887824501482","url":null,"abstract":"<p>In this research paper, we determine the nature of conformal <span><math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><mi>η</mi></math></span><span></span>-Ricci–Bourguignon soliton on a general relativistic spacetime with torse forming potential vector field. Besides this, we evaluate a specific situation of the soliton when the spacetime admitting semi-symmetric energy–momentum tensor with respect to conformal <span><math altimg=\"eq-00004.gif\" display=\"inline\" overflow=\"scroll\"><mi>η</mi></math></span><span></span>-Ricci–Bourguignon soliton, whose potential vector field is torse-forming. Next, we explore some characteristics of curvature on a spacetime that admits conformal <span><math altimg=\"eq-00005.gif\" display=\"inline\" overflow=\"scroll\"><mi>η</mi></math></span><span></span>-Ricci–Bourguignon soliton. In addition, we turn up some physical perception of dust fluid, dark fluid and radiation era in a general relativistic spacetime in terms of conformal <span><math altimg=\"eq-00006.gif\" display=\"inline\" overflow=\"scroll\"><mi>η</mi></math></span><span></span>-Ricci–Bourguignon soliton. Finally, we examine necessary and sufficient conditions for a 1-form <span><math altimg=\"eq-00007.gif\" display=\"inline\" overflow=\"scroll\"><mi>η</mi></math></span><span></span>, which is the <span><math altimg=\"eq-00008.gif\" display=\"inline\" overflow=\"scroll\"><mi>g</mi></math></span><span></span>-dual of the vector field <span><math altimg=\"eq-00009.gif\" display=\"inline\" overflow=\"scroll\"><mi>ξ</mi></math></span><span></span> on general relativistic spacetime to be a solution of the Schrödinger–Ricci equation.</p>","PeriodicalId":50320,"journal":{"name":"International Journal of Geometric Methods in Modern Physics","volume":"56 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2024-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140124116","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Lie symmetries of Lemaitre–Tolman–Bondi metric","authors":"Jamshed Khan, Tahir Hussain, Ashfaque H. Bokhari, Muhammad Farhan","doi":"10.1142/s0219887824501329","DOIUrl":"https://doi.org/10.1142/s0219887824501329","url":null,"abstract":"<p>The aim of this paper is to investigate Lie symmetries including Killing, homothetic and conformal symmetries of Lemaitre–Tolman–Bondi (LTB) spacetime metric. To find all LTB metrics admitting these three types of symmetries, we have analyzed the set of symmetry equations by a Maple algorithm that provides some restrictions on the functions involved in LTB metric under which this metric admits the three mentioned symmetries. The solution of symmetry equations under these restrictions leads to the explicit form of symmetries. The stress–energy tensor is calculated for all the obtained metrics in order to discuss their physical significance. It is noticed that most of these metrics satisfy certain energy conditions and correspond to anisotropic fluids.</p>","PeriodicalId":50320,"journal":{"name":"International Journal of Geometric Methods in Modern Physics","volume":"14 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2024-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140124145","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The geometry of quantum computing","authors":"E. Ercolessi, R. Fioresi, T. Weber","doi":"10.1142/s0219887824400115","DOIUrl":"https://doi.org/10.1142/s0219887824400115","url":null,"abstract":"<p>In this expository paper, we present a brief introduction to the geometrical modeling of some quantum computing problems. After a brief introduction to establish the terminology, we focus on quantum information geometry and <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mi>Z</mi><mi>X</mi></math></span><span></span>-calculus, establishing a connection between quantum computing questions and quantum groups, i.e. Hopf algebras.</p>","PeriodicalId":50320,"journal":{"name":"International Journal of Geometric Methods in Modern Physics","volume":"111 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2024-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140124179","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}