The formation probability of multiple winding topological defects is calculated by phase and flux distribution analysis based on the Kibble mechanism. The core size of defects is taken into account so that when it is much larger than the correlation length of the Higgs field, high winding configuration can be realized. For example, if the self coupling constant of the Higgs field is smaller tha...

We introduce the category NCSet consisting of neutrosophic crisp sets and morphisms between them. And we study NCSet in the sense of a topological universe and prove that it is Cartesian closed over Set, where Set denotes the category consisting of ordinary sets and ordinary mappings between them. 2010 AMS Classification: 03E72, 18B05

Topological defects such as cosmic strings may have been formed at early-universe phase transitions. Direct tests of this idea are impossible, but the mechanism can be elucidated by studying analogous processes in low-temperature condensed-matter systems. Experiments on vortex formation in superfluid helium and in supercon-ductors have so far yielded somewhat confusing results. I shall discuss ...

Why do all electrons have the same charge and why do all protons have exactly the opposite charge? Dirac provided a possible answer by proposing the existence of magnetic monopoles. We propose a simple possible topological explanation of why charge is quantized, involving a tiny permanent magnetic field trapped in the topology of the universe. The idea apparently works for every possible compac...

In this contribution we discuss gravitational effects of global scalar fields and, especially, of global topological defects. We first give an introduction to the dynamics of global fields and the formation of defects. Next we investigate the induced gravitational fields, first in a flat background and then in the expanding universe. In flat space, we explicitly calculate the gravitational fiel...

A topological theory for the interactions in Nature is presented. The theory derives from the cyclic properties of the topological manifold Q = 2T 3 ⊕ 3S × S which has 23 intrinsic degrees of freedom, discrete Z3 and Z2 × Z3 internal groups, an SU(5) gauge group, and an anomalous U(1) symmetry. These properties reproduce the standard model with a stable proton, a natural place for CP violation ...

In three spacetime dimensions, general relativity drastically simplifies, becoming a "topological" theory with no propagating local degrees of freedom. Nevertheless, many of the difficult conceptual problems of quantizing gravity are still present. In this review, I summarize the rather large body of work that has gone towards quantizing (2 + 1)-dimensional vacuum gravity in the setting of a sp...

We study 2-d φF gauge theories with the objective to understand, also at the quantum level, the emergence of induced gravity. The wave functionals-representing the eigenstates of a vanishing flat potential-are obtained in the φ representation. The composition of the space they describe is then analyzed: the state corresponding to the singlet representation of the gauge group describes a topolog...

Topological defects are thought to be left behind by the cosmolog-ical phase transitions which occur as the universe expands and cools. Similar processes can be studied in the phase transitions which take place in the laboratory: " Cosmological " experiments in superfluid He 4 and in liquid crystals were carried out within the past few years, and their results shed a new light on the dynamics o...