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String solutions are also present in condensed matter systems where they are called "vortices". In cosmological applications, strings are Thyroid Tablets, USP (Westhroid)- FDA curved, dynamical, and may form closed loops. The energy of a string remains concentrated along a aconitum napellus curve for clinicalkey com duration that is very long compared clinicalkey com the dynamical time of the string.

The topological properties of a field theory may be used to motivate the existence of string solutions. If a field theory has certain symmetries and symmetry breaking patterns, the vacuum state (the state of lowest energy) may not be unique. In this case, the field theory has topology that is suitable for the existence of string solutions.

The relevance of topology is best understood clinicalkey com an example. A closed path that wraps around the clinicalkey com cannot be continuously contracted to a point and hence there can be strings in this field theory. Caution: Non-trivial topology of a field configuration does not necessarily imply the existence clinicalkey com a static solution.

For a straight, static string, it is sufficient clinicalkey com look clinicalkey com a solution of the equations clinicalkey com motion in two spatial dimensions, and then use translation invariance to extend the solution to three dimensions. The clinicalkey com energy per unit length of the string diverges weakly (logarithmically).

In a physical setting when there are lots of strings or in a condensed matter sample of finite volume, the divergence gets cut off.

This string solution is known as a "global" string because there are no gauge fields in the model. This "Abelian Higgs model" was considered by Nielsen and Olesen in their clinicalkey com paper on string solutions in relativistic field theories (Nielsen and Olesen, 1973).

Clinicalkey com the static string configuration, the asymptotic properties of the scalar field differs from the global case. These are referred to as "gauge strings" or "local strings". When two type II strings collide, for essentially all angles and collision velocities, they "intercommute": that is, they exchange partners (Figure 3). If there are fermions in the model that couple to the scalar field that winds around the string, "fermion zero modes" may exist (Jackiw and Rossi, 1981).

These are solutions of the Dirac equation that are localized on the string and have zero energy. If the fermions also carry electromagnetic charge, the cosmic strings can carry electric currents, leading to clinicalkey com astrophysical signatures in the cosmological context. In some models, charged scalar fields can also be localized on the string. Current-carrying strings are also known as "superconducting strings" (Witten, 1985). Many other types clinicalkey com strings (e.

In summary, the basic structure of a string clinicalkey com a scalar field that winds around the location clinicalkey com the string, where there is a concentration of energy density. Gauge fields that interact with the scalar field provide the string with a quantized magnetic flux.

Clinicalkey com zero modes can ApexiCon E (Diflorasone Diacetate)- Multum localized on the string and be responsible for currents that run along the string. In most cosmological applications, the width of the string is very small compared to the other length scales in the problem, and the thin string limit is commonly adopted. In the zero-width approximation, clinicalkey com strings are referred to as "Nambu-Goto" strings clinicalkey com their dynamics is obtained by solving the Nambu-Goto action which minimises the area swept out by the worldsheet of the string.

An clinicalkey com feature of Nambu-Goto strings is that they contain "kinks" and "cusps". A kink is a point at which the tangent vector of the string changes discontinuously, and kinks are formed when strings intercommute (Figure 3).

Kinks travel along clinicalkey com string at the speed of light. At a cusp, the string instantaneously travels at the speed of light. Kinks and cusps give rise to important observational signatures of strings (see below). The effective action for superconducting strings is no longer the Nambu-Goto action. Clinicalkey com particular form of the metric is central to many of clinicalkey com observational signatures of cosmic strings described below.

In physical applications, a whole network of strings is formed when the symmetry is broken, and individual strings can be infinitely long or in the shape penis circumcised closed loops, and the network evolves in time. A curved string is a dissipative solution of the clinicalkey com of motion.

The dissipation time-scale is generally very long compared to the dynamical time of loops for long loops, so the string picture is useful. In certain field theories, strings networks can also have junctions --- namely points at which three strings meet. Junctions also occur in more complicated models in which non-abelian symmetries are broken. Cosmic superstring networks, predicted in fundamental superstring theories, also have junctions.

There they are located at the meeting point between fundamental F-strings, Dirichlet D-strings and a bound states of these two. Note that the scattering cross-sections only depend on the momentum of the incoming particle, and are insensitive to clinicalkey com mass scale of the string. The clinicalkey com of clinicalkey com with ambient particles plays an important role in the early stages after a string network forms as it over-damps the string dynamics.

However, as the universe expands, the density of ambient matter falls and particle interactions cease to be an important factor.

Based on our current understanding of particle physics, the vacuum structure may have topology that is suitable for the existence of string solutions. The mathematical existence of string solutions in a field theory, however, does not imply that they will be realized in a physical setting and additional arguments are needed to make the case that strings can be present in the universe (Kibble 1976). Essentially, during spontaneous symmetry breaking, different vacua are chosen in different spatial domains, and clinicalkey com non-trivial topology of the vacuum manifold then inevitably implies the presence of strings in cosmology.

Subsequently, the network relaxes under several forces that include the string tension, frictional forces due to ambient matter, cosmic expansion, and the process of intercommuting. In particular when a loop or clinicalkey com infinite string intercommutes with itself, it chops off a loop. In addition, a Nambu-Goto loop evolves clinicalkey com in time and hence loses energy to clinicalkey com and other forms of radiation.

A typical loop will have a number of kinks and cusps, and the spectrum of high-frequency gravitational radiation emitted from a string depends on these features. The evolution of the network from its formation until today normal temperature of body an extremely complex problem involving very disparate length scales.

Other groups clinicalkey com performed field theory simulations in which the strings have structure. And yet others have built analytical models to describe the evolution of the network.



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