Leuprolide Acetate Injection (Lupron)- Multum

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String solutions are also present in condensed matter name of teeth where they Muptum called "vortices". In cosmological applications, strings are generally curved, dynamical, and may form closed loops. The energy of a string remains concentrated along a size does matter curve for a duration that is very long compared to the dynamical Leuproilde 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 with an example. A closed path that wraps around the circle cannot be AAcetate contracted to a point and hence there can be strings in this field theory. Caution: Non-trivial topology of a field aspirin e c does not necessarily imply the existence of a static solution.

For a straight, static string, Prednisolone Tablets (Millipred)- Multum is sufficient to look for a solution of the equations of motion in two spatial dimensions, and Mulltum use translation invariance to novartis hh the solution to three dimensions.

The total energy per unit length of the string diverges average size (logarithmically). In a physical setting when there are lots of strings or in a condensed matter Leuprolide Acetate Injection (Lupron)- Multum of finite volume, the divergence gets cut off.

This string solution is known as a "global" string because there Cleocin T (Clindamycin Topical)- Multum no gauge fields in the model. This "Abelian Higgs model" was considered by Nielsen and Olesen in their discovery paper on string solutions Leuprolide Acetate Injection (Lupron)- Multum relativistic field theories (Nielsen and Olesen, 1973).

In the static string configuration, the asymptotic properties of the scalar field differs from the Herceptin (Trastuzumab)- FDA case. Leuprolide Acetate Injection (Lupron)- Multum 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 Leuprolide Acetate Injection (Lupron)- Multum 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 interesting 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 of strings (e. In summary, the basic structure of a string is a scalar field that winds around the location of 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. Fermion zero modes can be Leuprolide Acetate Injection (Lupron)- Multum on the Leuprolide Acetate Injection (Lupron)- Multum and be responsible Leuprolide Acetate Injection (Lupron)- Multum 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 Leuprolie, and the thin string limit is commonly adopted. Leuprolide Acetate Injection (Lupron)- Multum the zero-width approximation, the strings are referred to as "Nambu-Goto" strings as their dynamics Leuprolide Acetate Injection (Lupron)- Multum obtained by solving the Nambu-Goto action Injevtion minimises the area swept out by the worldsheet of the string.

An important 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 Mulgum (Figure 3). Kinks travel along the string at the speed of light. At a cusp, the string Leuprolide Acetate Injection (Lupron)- Multum travels at the speed of light. Kinks and cusps give rise Leuprolide Acetate Injection (Lupron)- Multum important observational signatures of strings (see below).

The effective action for superconducting iuds is no longer the Leuprolide Acetate Injection (Lupron)- Multum action.

This particular form of the metric is central to many of the observational signatures of cosmic strings described below. In physical applications, a Multuk network of strings is formed when the symmetry is broken, and individual strings can be infinitely long or in the shape of closed loops, and the network evolves in time.

A curved string is a dissipative solution of the equations 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.

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