Quantum field theory creates fermions via abstract operators exciting abstract fields, with a specific field for each type of specific particle. This operator algebra lends itself well to quantum statistics, neverthel...Quantum field theory creates fermions via abstract operators exciting abstract fields, with a specific field for each type of specific particle. This operator algebra lends itself well to quantum statistics, nevertheless, our physical understanding of this process is nonintuitive at best. In this paper we analyze the creation of fermions from primordial gauge field quantum gravity loops in the context of Calabi-Yau manifold theory. I extend a prior mass-gap treatment based on Yang-Mills gauge theory of higher order self-interaction to include the half-integral spin of fermions.展开更多
For each natural odd number n≥3,we exhibit a maximal family of n-dimensional Calabi-Yau manifolds whose Yukawa coupling length is 1.As a consequence,Shafarevich’s conjecture holds true for these families.Moreover,it...For each natural odd number n≥3,we exhibit a maximal family of n-dimensional Calabi-Yau manifolds whose Yukawa coupling length is 1.As a consequence,Shafarevich’s conjecture holds true for these families.Moreover,it follows from Deligne and Mostow(Publ.Math.IHÉS,63:5-89,1986)and Mostow(Publ.Math.IHÉS,63:91-106,1986;J.Am.Math.Soc.,1(3):555-586,1988)that,for n=3,it can be partially compactified to a Shimura family of ball type,and for n=5,9,there is a sub Q-PVHS of the family uniformizing a Zariski open subset of an arithmetic ball quotient.展开更多
We construct an N = 2 superconformal vertex algebra（SCVA） from a generalized Calabi-Yau manifold and compute the BRST cohomology of its associated topological vertex algebras. We show that the BRST cohomology coinci...We construct an N = 2 superconformal vertex algebra（SCVA） from a generalized Calabi-Yau manifold and compute the BRST cohomology of its associated topological vertex algebras. We show that the BRST cohomology coincides with the generalized Dobeault cohomology. We show that the two topological vertex algebras constructed from the N = 2 SCVA by A and B twist respectively are mirror pairs.展开更多
Math and physics proceed from assumptions to conclusions via a logical path. Artificial intelligence possesses the ability to follow logic, herein specifically applied to the problem of defining ontologically real 2D ...Math and physics proceed from assumptions to conclusions via a logical path. Artificial intelligence possesses the ability to follow logic, herein specifically applied to the problem of defining ontologically real 2D manifolds in a 3D continuum. Vortices and tori in fluids exhibit effective 2D surfaces, which, treated as manifolds, allow application of calculus on the boundaries of the structures. Recent papers in primordial field theory (PFT) have employed Calabi-Yau geometry and topology to develop a fermion structure. We desire a logical justification of this application and herein explore the use of artificial intelligence to assist in logic verification. A proof is outlined by the author and formalized by the AI.展开更多
A theory of quantum gravity has recently been developed by the author based on the concept that all forces converge to one at the moment of Creation. This primordial field can only interact with itself, as no other fi...A theory of quantum gravity has recently been developed by the author based on the concept that all forces converge to one at the moment of Creation. This primordial field can only interact with itself, as no other field exists, contrasting with the Standard Model of Particle Physics in which each elementary particle is an excitation in its own quantum field. The primordial field theory of quantum gravity has produced a model of a fermion with a mass gap, ½-integral spin, discrete charge, and magnetic moment. The mass gap is based on an existence theorem that is anchored in Yang-Mills, while Calabi-Yau anchors ½-integral spin, with charge and magnetic moment based on duality. Based on N-windings, this work is here extended to encompass fractional charge, with the result applied to quarks, yielding fermion mass and charge in agreement with experiment and novel size correlations and a unique quantum gravity-based ontological understanding of quarks.展开更多
In this paper we solve completely the well-known conjecture of Calabi onhyperbolic affine hyperspheres.The following Theorems are provedTheorem 1 Let M be a locally strongly convex,affine complete hyperbolicaffine hyp...In this paper we solve completely the well-known conjecture of Calabi onhyperbolic affine hyperspheres.The following Theorems are provedTheorem 1 Let M be a locally strongly convex,affine complete hyperbolicaffine hypersphere,then M is Euclidean complete.展开更多
In this article, we obtain Li-Yau-type gradient estimates with time dependent parameter for positive solutions of the heat equation that are different with the estimates by Li-Xu [21] and Qian [23]. As an application ...In this article, we obtain Li-Yau-type gradient estimates with time dependent parameter for positive solutions of the heat equation that are different with the estimates by Li-Xu [21] and Qian [23]. As an application of the estimate, we also obtained slight improvements of Davies' Li-Yau-type gradient estimate.展开更多
The latter half of the twentieth century yielded two tools of unprecedented power, both of which took decades to mature to their current states. The purpose of this research is to apply these to a theory of gravity an...The latter half of the twentieth century yielded two tools of unprecedented power, both of which took decades to mature to their current states. The purpose of this research is to apply these to a theory of gravity and develop the consequences of the model based on these tools. This paper presents such results without mathematical details, which are presented elsewhere. The tools are: Geometric Calculus, developed by David Hestenes, circa 1965 and Mathematica, released in 1988 by Steven Wolfram. Both tools have steep learning curves, requiring several years to acquire expertise in their use. This paper explains in what sense they are optimal.展开更多
文摘Quantum field theory creates fermions via abstract operators exciting abstract fields, with a specific field for each type of specific particle. This operator algebra lends itself well to quantum statistics, nevertheless, our physical understanding of this process is nonintuitive at best. In this paper we analyze the creation of fermions from primordial gauge field quantum gravity loops in the context of Calabi-Yau manifold theory. I extend a prior mass-gap treatment based on Yang-Mills gauge theory of higher order self-interaction to include the half-integral spin of fermions.
基金financial support was provided by the NSF under(Grant Nos.DMS-1362960 to JK and DMS-1901849 to CX)received support from the(Grant No.DMS-1440140)while in residence at MSRI during the Spring 2019 semester。
文摘We prove that the irreducible components of the moduli space of polarized Calabi–Yau pairs are projective.
文摘For each natural odd number n≥3,we exhibit a maximal family of n-dimensional Calabi-Yau manifolds whose Yukawa coupling length is 1.As a consequence,Shafarevich’s conjecture holds true for these families.Moreover,it follows from Deligne and Mostow(Publ.Math.IHÉS,63:5-89,1986)and Mostow(Publ.Math.IHÉS,63:91-106,1986;J.Am.Math.Soc.,1(3):555-586,1988)that,for n=3,it can be partially compactified to a Shimura family of ball type,and for n=5,9,there is a sub Q-PVHS of the family uniformizing a Zariski open subset of an arithmetic ball quotient.
文摘We construct an N = 2 superconformal vertex algebra（SCVA） from a generalized Calabi-Yau manifold and compute the BRST cohomology of its associated topological vertex algebras. We show that the BRST cohomology coincides with the generalized Dobeault cohomology. We show that the two topological vertex algebras constructed from the N = 2 SCVA by A and B twist respectively are mirror pairs.
文摘Math and physics proceed from assumptions to conclusions via a logical path. Artificial intelligence possesses the ability to follow logic, herein specifically applied to the problem of defining ontologically real 2D manifolds in a 3D continuum. Vortices and tori in fluids exhibit effective 2D surfaces, which, treated as manifolds, allow application of calculus on the boundaries of the structures. Recent papers in primordial field theory (PFT) have employed Calabi-Yau geometry and topology to develop a fermion structure. We desire a logical justification of this application and herein explore the use of artificial intelligence to assist in logic verification. A proof is outlined by the author and formalized by the AI.
文摘A theory of quantum gravity has recently been developed by the author based on the concept that all forces converge to one at the moment of Creation. This primordial field can only interact with itself, as no other field exists, contrasting with the Standard Model of Particle Physics in which each elementary particle is an excitation in its own quantum field. The primordial field theory of quantum gravity has produced a model of a fermion with a mass gap, ½-integral spin, discrete charge, and magnetic moment. The mass gap is based on an existence theorem that is anchored in Yang-Mills, while Calabi-Yau anchors ½-integral spin, with charge and magnetic moment based on duality. Based on N-windings, this work is here extended to encompass fractional charge, with the result applied to quarks, yielding fermion mass and charge in agreement with experiment and novel size correlations and a unique quantum gravity-based ontological understanding of quarks.
文摘In this paper we solve completely the well-known conjecture of Calabi onhyperbolic affine hyperspheres.The following Theorems are provedTheorem 1 Let M be a locally strongly convex,affine complete hyperbolicaffine hypersphere,then M is Euclidean complete.
基金partially supported by the Yangfan project from Guangdong ProvinceNSFC(11571215)
文摘In this article, we obtain Li-Yau-type gradient estimates with time dependent parameter for positive solutions of the heat equation that are different with the estimates by Li-Xu [21] and Qian [23]. As an application of the estimate, we also obtained slight improvements of Davies' Li-Yau-type gradient estimate.
文摘The latter half of the twentieth century yielded two tools of unprecedented power, both of which took decades to mature to their current states. The purpose of this research is to apply these to a theory of gravity and develop the consequences of the model based on these tools. This paper presents such results without mathematical details, which are presented elsewhere. The tools are: Geometric Calculus, developed by David Hestenes, circa 1965 and Mathematica, released in 1988 by Steven Wolfram. Both tools have steep learning curves, requiring several years to acquire expertise in their use. This paper explains in what sense they are optimal.
