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String Theory (Dimentions)

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CP violation. It plays an important role both in the attempts of cosmology to explain the dominance of matter over antimatter in the present Universe, and in the study of weak interactions in particle physics.

CP violation

CP-symmetry[edit] The idea behind parity symmetry is that the equations of particle physics are invariant under mirror inversion. This leads to the prediction that the mirror image of a reaction (such as a chemical reaction or radioactive decay) occurs at the same rate as the original reaction. Parity symmetry appears to be valid for all reactions involving electromagnetism and strong interactions.

Until 1956, parity conservation was believed to be one of the fundamental geometric conservation laws (along with conservation of energy and conservation of momentum). Overall, the symmetry of a quantum mechanical system can be restored if another symmetry S can be found such that the combined symmetry PS remains unbroken. CP violation in the Standard Model[edit] and , and their antiparticles . . . .

The Lattice A15+ Cyclic model. A cyclic model (or oscillating model) is any of several cosmological models in which the universe follows infinite, or indefinite, self-sustaining cycles.

Cyclic model

For example, the oscillating universe theory briefly considered by Albert Einstein in 1930 theorized a universe following an eternal series of oscillations, each beginning with a big bang and ending with a big crunch; in the interim, the universe would expand for a period of time before the gravitational attraction of matter causes it to collapse back in and undergo a bounce. Basic Ideas of Superstring Theory. The Official String Theory Web Site. Brian Greene: Making sense of string theory.

Symmetry (physics) Symmetric group. Although symmetric groups can be defined on infinite sets as well, this article discusses only the finite symmetric groups: their applications, their elements, their conjugacy classes, a finite presentation, their subgroups, their automorphism groups, and their representation theory.

Symmetric group

For the remainder of this article, "symmetric group" will mean a symmetric group on a finite set. The symmetric group is important to diverse areas of mathematics such as Galois theory, invariant theory, the representation theory of Lie groups, and combinatorics. Cayley's theorem states that every group G is isomorphic to a subgroup of the symmetric group on G. Definition and first properties[edit] The symmetric group on a finite set X is the group whose elements are all bijective functions from X to X and whose group operation is that of function composition.[1] For finite sets, "permutations" and "bijective functions" refer to the same operation, namely rearrangement.

Applications[edit] Elements[edit] M-theory. Membrane (M-theory) In string theory and related theories, D-branes are an important class of branes that arise when one considers open strings.

Membrane (M-theory)

As an open string propagates through spacetime, its endpoints are required to lie on a D-brane. The letter "D" in D-brane refers to the fact that we impose a certain mathematical condition on the system known as the Dirichlet boundary condition. The study of D-branes has led to important results, such as the anti-de Sitter/conformal field theory correspondence, which has shed light on many problems in quantum field theory. See also[edit] References[edit] Jump up ^ Moore, Gregory (2005). Calabi–Yau manifold. A 2D slice of the 6D Calabi-Yau quintic manifold.

Calabi–Yau manifold

Calabi–Yau manifolds are complex manifolds that are higher-dimensional analogues of K3 surfaces. They are sometimes defined as compact Kähler manifolds whose canonical bundle is trivial, though many other similar but inequivalent definitions are sometimes used. They were named "Calabi–Yau spaces" by Candelas et al. (1985) after E. Calabi (1954, 1957) who first studied them, and S. T. Definitions[edit] M Theory As A Matrix Model: A Conjecture By Banks, T., W. Fischler, S.H. Shenker, L. Susskind (1996)

High Energy Physics - M-Theory M.J. Duff. Magic, Mystery, and Matrix by Edward Witten. The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory: Brian Greene. Cambridge: M-theory, the theory formerly known as Strings. The Standard Model In the standard model of particle physics, particles are considered to be points moving through space, tracing out a line called the World Line.

Cambridge: M-theory, the theory formerly known as Strings

To take into account the different interactions observed in Nature one has to provide particles with more degrees of freedom than only their position and velocity, such as mass, electric charge, color (which is the "charge" associated with the strong interaction) or spin. The standard model was designed within a framework known as Quantum Field Theory (QFT), which gives us the tools to build theories consistent both with quantum mechanics and the special theory of relativity. With these tools, theories were built which describe with great success three of the four known interactions in Nature: Electromagnetism, and the Strong and Weak nuclear forces.

Modeling in nanotechnology by using structural models of the atoms. BSM Application 4 Modeling in nanotechnology by using structural models of the atoms The reader not acquainted with the BSM theory should read first the article "Breaf Introduction to BSM theory" in order to understand the presented method of modeling. The physical models of the atoms provide a great opportunity for a modeling of different structures in nanotechnology.

Such modeling could serve as a preliminary design of molecular structures in which the building blocks are the selected atoms. In such design, not only the possible combinations could be examined, but the position and orientation of any quantum orbit can be identified. Fig. 1. provides an axonometric view of a part of single-walled carbon nanotube, as known by the current knowledge. Fig. 1. Comparison between images of Au crystal structure. Fig. 9 shows images of two crystal planes of gold layer obtained by one of the most powerful transmission electron microscope (Japan) Fig. 10 and Fig. 11 show two theoretical patterns corresponding to two possible spatial orders (or crystal planes) of Au atoms in the metal crystal lattice.