{"title":"The Noncommutative Geometry of Configuration Spaces and the Problem of Reconciling General Relativity With Quantum Field Theory","authors":"Johannes Aastrup, Jesper Møller Grimstrup","doi":"10.1002/prop.70023","DOIUrl":"https://doi.org/10.1002/prop.70023","url":null,"abstract":"<p>In this paper a candidate for a spectral triple on a quotient space of gauge connections modulo gauge transformations is construted and it is shown that it is related to a Kasparov type bi-module over two canonical algebras: the <span></span><math>\u0000 <semantics>\u0000 <mi>HD</mi>\u0000 <annotation>$mathbf {HD}$</annotation>\u0000 </semantics></math>-algebra, which is a non-commutative <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>C</mi>\u0000 <mo>∗</mo>\u0000 </msup>\u0000 <annotation>$C^*$</annotation>\u0000 </semantics></math>-algebra generated by parallel transports along flows of vectorfields, and an exterior algebra on a space of gauge transformations. The latter algebra is related to the ghost sector in a BRST quantisation scheme. It is Previously shown that the key elements of bosonic and fermionic quantum field theory on a curved background emerge from a spectral triple of this type. In this paper it is shown that a dynamical metric on the underlying manifold also emerges from the construction. We first rigourously construct a Dirac type operator on the a quotient space of gauge connections modulo gauge transformations, and the commutator between this Dirac type operator and the <span></span><math>\u0000 <semantics>\u0000 <mi>HD</mi>\u0000 <annotation>$mathbf {HD}$</annotation>\u0000 </semantics></math>-algebra is discussed. To do this a gauge-covariant metric on the configuration space is first constructed and it is used to construct the triple. The key step is that the volume of the quotient space to required to be finite, which amounts to an ultra-violet regularisation. Since the metric on the configuration space is dynamical with respect to the time-evolution generated by the Dirac type operator, The regularisation is interpreted as a physical feature (as opposed to static regularisations, which are always computational artefacts). Finally, a Bott–Dirac operator that connects our construction with quantum Yang-Mills theory is constructed.</p>","PeriodicalId":55150,"journal":{"name":"Fortschritte Der Physik-Progress of Physics","volume":"73 8","pages":""},"PeriodicalIF":7.8,"publicationDate":"2025-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144870061","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":"Issue Information: Fortschritte der Physik 7 / 2025","authors":"","doi":"10.1002/prop.70022","DOIUrl":"https://doi.org/10.1002/prop.70022","url":null,"abstract":"","PeriodicalId":55150,"journal":{"name":"Fortschritte Der Physik-Progress of Physics","volume":"73 7","pages":""},"PeriodicalIF":5.6,"publicationDate":"2025-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/prop.70022","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144705558","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"2-Adic Quantum Mechanics, Continuous-Time Quantum Walks, and the Space Discreteness","authors":"W. A. Zúñiga-Galindo","doi":"10.1002/prop.70019","DOIUrl":"https://doi.org/10.1002/prop.70019","url":null,"abstract":"<p>The authors show that a large class of 2-adic Schrödinger equations is the scaling limit of certain continuous-time quantum Markov chains (CTQMCs). Practically, a discretization of such an equation gives a CTQMC. As a practical result, new types of continuous-time quantum walks (CTQWs) on graphs using two symmetric matrices are constructed. The transport between nodes in one direction is described by one matrix, while the transport between nodes in the opposite direction. This construction includes, as a particular case, the CTQWs constructed using adjacency matrices. The final goal of this work is to contribute to the understanding of the foundations of quantum mechanics (QM) and the role of the hypothesis of the discreteness of space. The connection between 2-adic QM and CTQWs shows that 2-adic QM has a physical meaning. 2-Adic QM is a nonlocal theory because the Hamiltonians used are nonlocal operators, and consequently, spooky actions at a distance are allowed. However, this theory is not a mathematical toy. The violation of Bell's inequality is experimentally confirmed, which implies that realism is allowed by this theory. The authors pointed out several new research problems connected with the foundations of QM.</p>","PeriodicalId":55150,"journal":{"name":"Fortschritte Der Physik-Progress of Physics","volume":"73 8","pages":""},"PeriodicalIF":7.8,"publicationDate":"2025-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/prop.70019","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144869365","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Luis A. Anchordoqui, Ignatios Antoniadis, Dieter Lüst
{"title":"Two Micron-Size Dark Dimensions","authors":"Luis A. Anchordoqui, Ignatios Antoniadis, Dieter Lüst","doi":"10.1002/prop.70015","DOIUrl":"https://doi.org/10.1002/prop.70015","url":null,"abstract":"<p>Two extra dimensions of micron scale might simultaneously address the gauge and cosmological hierarchy problems. In this paper various observational bounds in scenarios with one and two large extra dimensions are examined, to see if they are compatible with the micron scale. The authors show that consistency with astrophysical observations requires that two extra dimensions of micron scale must not admit isometries, whereby conservation of the extra dimensional momentum is violated, allowing the massive Kaluza–Klein modes of the graviton to decay to other lighter graviton modes. However, to remain consistent with cosmological observations two extra dimensions of micron scale require a delicately fine tuning of the temperature at which the universe enters the radiation dominated epoch. Diving into this fine-tuned scenario the authors also show that primordial black holes with masses in the range <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mn>10</mn>\u0000 <mn>8</mn>\u0000 </msup>\u0000 <mo>≲</mo>\u0000 <msub>\u0000 <mi>M</mi>\u0000 <mi>BH</mi>\u0000 </msub>\u0000 <mo>/</mo>\u0000 <mi>g</mi>\u0000 <mo>≲</mo>\u0000 <msup>\u0000 <mn>10</mn>\u0000 <mn>21</mn>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$10^8 lesssim M_{rm BH}/{rm g} lesssim 10^{21}$</annotation>\u0000 </semantics></math> could make all cosmological dark matter.</p>","PeriodicalId":55150,"journal":{"name":"Fortschritte Der Physik-Progress of Physics","volume":"73 8","pages":""},"PeriodicalIF":7.8,"publicationDate":"2025-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/prop.70015","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144869364","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Maximum Mass Limit of Generalized MIT Compact Star: A Theoretical Study of Thin Shell Dynamics and Gravitational Lensing","authors":"Sayantan Ghosh, Sneha Pradhan, Pradyumn Kumar Sahoo","doi":"10.1002/prop.70020","DOIUrl":"https://doi.org/10.1002/prop.70020","url":null,"abstract":"<p>In this study, the properties, equilibrium, and stability of compact objects within the framework of teleparallel gravity with the generalized MIT bag model are investigated. By incorporating the modified field equations, the influence of the generalized bag constant on the structure and physical characteristics of quark stars and neutron stars is analyzed. A key focus of the work is the examination of the Israel junction conditions for the first time in the literature, which are employed to study the stability of the thin-shell interface separating the interior quark matter from the exterior vacuum or surrounding medium. A detailed stability analysis is conducted by evaluating the adiabatic index, Herrera's cracking criteria to determine the viability of the interior stellar configurations. To validate results, the predictions of our extended MIT Bag model are compared with observational constraints, including the compact object detected in GW190814, whose mass lies within the range of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>2.5</mn>\u0000 <mo>−</mo>\u0000 <mn>2.67</mn>\u0000 <mspace></mspace>\u0000 <msub>\u0000 <mi>M</mi>\u0000 <mo>⊙</mo>\u0000 </msub>\u0000 </mrow>\u0000 <annotation>$2.5-2.67nobreakspace M_{odot }$</annotation>\u0000 </semantics></math>. Furthermore, our findings with well-documented neutron stars (NSTRs) are compared, such as 4U 1608-52 <span></span><math>\u0000 <semantics>\u0000 <mfenced>\u0000 <mn>1</mn>\u0000 <mo>.</mo>\u0000 <msubsup>\u0000 <mn>74</mn>\u0000 <mrow>\u0000 <mo>−</mo>\u0000 <mn>0.14</mn>\u0000 </mrow>\u0000 <mrow>\u0000 <mo>+</mo>\u0000 <mn>0.14</mn>\u0000 </mrow>\u0000 </msubsup>\u0000 <mspace></mspace>\u0000 <msub>\u0000 <mi>M</mi>\u0000 <mo>⊙</mo>\u0000 </msub>\u0000 </mfenced>\u0000 <annotation>$left(1.74_{-0.14}^{+0.14}nobreakspace M_{odot }right)$</annotation>\u0000 </semantics></math> and PSR J0952-0607 <span></span><math>\u0000 <semantics>\u0000 <mfenced>\u0000 <mn>2</mn>\u0000 <mo>.</mo>\u0000 <msubsup>\u0000 <mn>35</mn>\u0000 <mrow>\u0000 <mo>−</mo>\u0000 <mn>0.17</mn>\u0000 </mrow>\u0000 <mrow>\u0000 <mo>+</mo>\u0000 <mn>0.17</mn>\u0000 </mrow>\u0000 </msubsup>\u0000 <ms","PeriodicalId":55150,"journal":{"name":"Fortschritte Der Physik-Progress of Physics","volume":"73 8","pages":""},"PeriodicalIF":7.8,"publicationDate":"2025-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/prop.70020","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144869243","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Gregory Patellis, Danai Roumelioti, Stelios Stefas, George Zoupanos
{"title":"Unification of Conformal and Fuzzy Gravities With Internal Interactions Resulting in SO(10) and a Possible Probe Through Stochastic Gravitational Wave Background","authors":"Gregory Patellis, Danai Roumelioti, Stelios Stefas, George Zoupanos","doi":"10.1002/prop.70014","DOIUrl":"https://doi.org/10.1002/prop.70014","url":null,"abstract":"<p>The unification of conformal and fuzzy gravities with internal interactions is based on the facts that i) the tangent group of a curved manifold and the manifold itself do not necessarily have the same dimensions and ii) both gravitational theories considered here have been formulated in a gauge theoretic way. The gauge-theoretic approach of gravities, commenting in particular on their diffeomorphism invariance, and the construction of conformal and noncommutative (fuzzy) gravity using the gauge-theoretic framework are reviewed. Based on an extension of the four-dimensional tangent group, unification of both gravities with the internal interactions is achieved. Both unified schemes are examined at 1-loop level considering suitable spontaneous symmetry breakings to a <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>S</mi>\u0000 <mi>O</mi>\u0000 <mo>(</mo>\u0000 <mn>10</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$SO(10)$</annotation>\u0000 </semantics></math> grand unified theory and consequently down to the Standard Model of particle physics through four specific spontaneous symmetry breaking channels. Each channel is examined against proton lifetime experimental bounds and its observation potential through gravitational signal from cosmic strings production is discussed.</p>","PeriodicalId":55150,"journal":{"name":"Fortschritte Der Physik-Progress of Physics","volume":"73 9-10","pages":""},"PeriodicalIF":7.8,"publicationDate":"2025-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/prop.70014","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145243120","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Iqra Ibrar, Eman M. Moneer, Muhammad Sharif, Euaggelos E. Zotos
{"title":"Compact Star Structure Under Hybrid and Logarithmic \u0000 \u0000 \u0000 f\u0000 (\u0000 Q\u0000 ,\u0000 T\u0000 )\u0000 \u0000 $f(mathbb {Q},mathcal {T})$\u0000 Rastall Gravity","authors":"Iqra Ibrar, Eman M. Moneer, Muhammad Sharif, Euaggelos E. Zotos","doi":"10.1002/prop.70016","DOIUrl":"https://doi.org/10.1002/prop.70016","url":null,"abstract":"<p>Spherically symmetric anisotropic solutions that describe compact stellar objects within the framework of modified Rastall <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>f</mi>\u0000 <mo>(</mo>\u0000 <mi>Q</mi>\u0000 <mo>,</mo>\u0000 <mi>T</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$f(mathbb {Q},mathcal {T})$</annotation>\u0000 </semantics></math> gravity are explored in this manuscript, where the non-metricity scalar represented by <span></span><math>\u0000 <semantics>\u0000 <mi>Q</mi>\u0000 <annotation>$mathbb {Q}$</annotation>\u0000 </semantics></math> and the trace of the energy-momentum tensor is denoted by <span></span><math>\u0000 <semantics>\u0000 <mi>T</mi>\u0000 <annotation>$mathcal {T}$</annotation>\u0000 </semantics></math>. To achieve this, the Karmarkar condition is applied and a relationship between the metric functions to solve the resulting field equations is established. In this framework, the field equations are constructed and the behavior of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>h</mi>\u0000 <mo>(</mo>\u0000 <mi>Q</mi>\u0000 <mo>,</mo>\u0000 <mi>T</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$h(mathbb {Q},mathcal {T})$</annotation>\u0000 </semantics></math> under two different scenarios is investigated. In the first scenario, a hybrid form <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>f</mi>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>Q</mi>\u0000 <mo>,</mo>\u0000 <mi>T</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <mo>=</mo>\u0000 <mi>ψ</mi>\u0000 <msup>\u0000 <mi>Q</mi>\u0000 <mi>n</mi>\u0000 </msup>\u0000 <msup>\u0000 <mi>e</mi>\u0000 <mrow>\u0000 <mi>Q</mi>\u0000 <mi>m</mi>\u0000 </mrow>\u0000 </msup>\u0000 <mo>+</mo>\u0000 <mi>η</mi>\u0000 <mi>T</mi>\u0000 </mrow>\u0000 <annotation>$f(mathbb {Q},mathcal {T}) = psi mathbb {Q}^n e^{mathbb {Q} m} + eta mathcal {T}$</annotation>\u0000 </semantics></math> is employed along with a linear equation of state <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>p</mi>\u0000 <mi>r</mi>\u0000 </msub>\u0000 <mo>=</mo>\u0000 <mi>a</mi>\u0000 <mi>ρ</mi>\u0000 <mo>+</mo>\u0000 <mi>b</mi>\u0000 </mrow>\u0000 <annotatio","PeriodicalId":55150,"journal":{"name":"Fortschritte Der Physik-Progress of Physics","volume":"73 8","pages":""},"PeriodicalIF":7.8,"publicationDate":"2025-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144869201","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}