(Quantum) gravity effects via exotic ℝ4

Król, Jerzy

doi:10.1002/andp.201010446

Cited by 8 publications

(2 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As shown in [21,22] the existence of exotic smoothness has a tremendous impact on cosmology, further explored in [23]. Beginning with the work of Krol [24][25][26][27][28][29] on the relation between categorical constructions and exotic smoothness, the focus in the topic is shifted to show a direct relation between exotic smoothness and quantum gravity [30][31][32].…”

Section: Introductionmentioning

confidence: 99%

Exotic smoothness and quantum gravity

Asselmeyer-Maluga¹

2010

Class. Quantum Grav.

View full text Add to dashboard Cite

Abstract. Since the first work on exotic smoothness in physics, it was folklore to assume a direct influence of exotic smoothness to quantum gravity. Thus, the negative result of Duston [1] was a surprise. A closer look into the semi-classical approach uncovered the implicit assumption of a close connection between geometry and smoothness structure. But both structures, geometry and smoothness, are independent of each other.In this paper we calculate the "smoothness structure" part of the path integral in quantum gravity assuming that the "sum over geometries" is already given. For that purpose we use the knot surgery of Fintushel and Stern applied to the class E(n) of elliptic surfaces. We mainly focus our attention to the K3 surfaces E(2). Then we assume that every exotic smoothness structure of the K3 surface can be generated by knot or link surgery a la Fintushel and Stern. The results are applied to the calculation of expectation values. Here we discuss the two observables, volume and Wilson loop, for the construction of an exotic 4-manifold using the knot 5 2 and the Whitehead link W h. By using Mostow rigidity, we obtain a topological contribution to the expectation value of the volume. Furthermore we obtain a justification of area quantization.

show abstract

Section: Introductionmentioning

confidence: 99%

Exotic smoothness and quantum gravity

Asselmeyer-Maluga¹

2010

Class. Quantum Grav.

View full text Add to dashboard Cite

show abstract

“…Such an approach is the realization of the idea that superstring theory refers to physical 4-dimensions via its relation to exotic small R 4 's. New constraints reducing the multitude of possible superstring vacua are thus proposed [7,8,13,14,15].…”

Section: D Matter and Quantum Gravitymentioning

confidence: 99%

Untitled

Król¹

2011

Acta Phys. Pol. B

Self Cite

View full text Add to dashboard Cite

We present arguments that in 4-dimensions quantum matter, geometry and gravity are related in a special, new way. This is based on the geometry of exotic smooth R 4 k , k even, which on the one hand underlies the effective states of quantum matter, as in Kondo effect, and on the other, refers to exact superstring backgrounds. This kind of link of geometry and quantum matter allows for quantum treatment of gravity confined to exotic R 4 k .

show abstract

Model and Set-Theoretic Aspects of Exotic Smoothness Structures on $$\mathbb {R}^4$$ R 4

Król

2016

Fundamental Theories of Physics

View full text Add to dashboard Cite

Model-theoretic aspects of exotic smoothness were studied long ago uncovering unexpected relations to noncommutative spaces and quantum theory. Some of these relations were worked out in detail in later work. An important point in the argumentation was the forcing construction of Cohen but without a direct application to exotic smoothness. In this article we assign the set-theoretic forcing on trees to Casson handles and characterize small exotic smooth R 4 from this point of view. Moreover, we show how models in some Grothendieck toposes can help describing such differential structures in dimension 4. These results can be used to obtain the deformation of the algebra of usual complex functions to the noncommutative algebra of operators on a Hilbert space. We also discuss the results in the context of the Epstein-Glaser renormalization in QFT.

show abstract

(Quantum) gravity effects via exotic ℝ4

Cited by 8 publications

References 17 publications

Exotic smoothness and quantum gravity

Exotic smoothness and quantum gravity

Untitled

Model and Set-Theoretic Aspects of Exotic Smoothness Structures on $$\mathbb {R}^4$$ R 4

Contact Info

Product

Resources

About