Angel "Java" Lopez en Blog

Publicado el 22 de Mayo, 2013, 17:05

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Un tema que sigo desde hace casi tres décadas. Recuerdo haberlo encontrado varias veces en los artículos de los ochenta de Investigación y Ciencia, por ejemplo, un artículo ya clásico de Gerard t'Hooft. Si se interesan en este tema, pasearan por gran parte de la física matemática moderna y clásica.

Les agrego dos enlaces: preparation for gauge theory, muy bueno, tiene todo gauge, group, lagrangian, dirac, electromagnetism, etc. para intrépidos aficionados a la física matemática. muy buena intro, algo habia leido antes, ver si lo tengo impreso de hooft, muy bueno la introducción más fácil

In physics, gauge invariance (also called gauge symmetry) is the property of a field theory in which different configurations of the underlying fields — which are not themselves directly observable — result in identical observable quantities. A theory with such a property is called a gauge theory. A transformation from one such field configuration to another is called a gauge transformation.[1][2]

Modern physical theories describe reality in terms of fields, e.g., the electromagnetic field, the gravitational field, and fields for the electron and all other elementary particles. A general feature of these theories is that none of these fundamental fields, which are the fields that change under a gauge transformation, can be directly measured. On the other hand, the observable quantities, namely the ones that can be measured experimentally — charges, energies, velocities, etc. — do not change under a gauge transformation, even though they are derived from the fields that do change. This (and any) kind of invariance under a transformation is called a symmetry.

For example, in electromagnetism the electric and magnetic fields, E and B, are observable, while the potentials V ("voltage") and A (the vector potential) are not.[3] Under a gauge transformation in which a constant is added to V, no observable change occurs in E or B.

With the advent of quantum mechanics in the 1920s, and with successive advances in quantum field theory, the importance of gauge transformations has steadily grown. Gauge theories constrain the laws of physics, because all the changes induced by a gauge transformation have to cancel each other out when written in terms of observable quantities. Over the course of the 20th century, physicists gradually realized that all forces (fundamental interactions) arise from the constraints imposed by local gauge symmetries, in which case the transformations vary from point to point in space and time. Perturbative quantum field theory (usually employed for scattering theory) describes forces in terms of force mediating particles called gauge bosons. The nature of these particles is determined by the nature of the gauge transformations. The culmination of these efforts is the Standard Model, a quantum field theory explaining all of the fundamental interactions except gravity.

Ahora, la lista original que había preparado:  

In physics, a gauge theory is a type of field theory in which the Lagrangian is invariant under a continuous group of local transformations.

The term gauge refers to redundant degrees of freedom in the Lagrangian. The transformations between possible gauges, called gauge transformations, form a Lie group which is referred to as thesymmetry group or the gauge group of the theory. Associated with any Lie group is the Lie algebra of group generators. For each group generator there necessarily arises a corresponding vector field called the gauge field. Gauge fields are included in the Lagrangian to ensure its invariance under the local group transformations (called gauge invariance). When such a theory is quantized, the quanta of the gauge fields are called gauge bosons. If the symmetry group is non-commutative, the gauge theory is referred to as non-abelian, the usual example being the Yang–Mills theory.

Many powerful theories in physics are described by Lagrangians which are invariant under some symmetry transformation groups. When they are invariant under a transformation identically performed at every point in the space in which the physical processes occur, they are said to have a global symmetry. The requirement of local symmetry, the cornerstone of gauge theories, is a stricter constraint. In fact, a global symmetry is just a local symmetry whose group's parameters are fixed in space-time.

Gauge theories are important as the successful field theories explaining the dynamics of elementary particles. Quantum electrodynamics is an abelian gauge theory with the symmetry group U(1)and has one gauge field, the electromagnetic four-potential, with the photon being the gauge boson. The Standard Model is a non-abelian gauge theory with the symmetry group U(1)×SU(2)×SU(3)and has a total of twelve gauge bosons: the photon, three weak bosons and eight gluons.

Gauge theories are also important in explaining gravitation in the theory of general relativity. Its case is somewhat unique in that the gauge field is a tensor, the Lanczos tensor. Theories ofquantum gravity, beginning with gauge gravitation theory, also postulate the existence of a gauge boson known as the graviton. Gauge symmetries can be viewed as analogues of the principle of general covariance of general relativity in which the coordinate system can be chosen freely under arbitrary diffeomorphisms of spacetime. Both gauge invariance and diffeomorphism invariance reflect a redundancy in the description of the system. An alternative theory of gravitation, gauge theory gravity, replaces the principle of general covariance with a true gauge principle with new gauge fields.

Historically, these ideas were first stated in the context of classical electromagnetism and later in general relativity. However, the modern importance of gauge symmetries appeared first in therelativistic quantum mechanics of electrons – quantum electrodynamics, elaborated on below. Today, gauge theories are useful in condensed matter, nuclear and high energy physics among other subfields.

Gauge symmetry (mathematics) - Wikipedia, the free encyclopedia

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The Stand-Up Physicist: Gauge Symmetries in the Lagrangian AND the Field Equations - YouTube

Gauge covariant derivative - Wikipedia, the free encyclopedia

Phys. Rev. D 24, 471 (1981): Incompatibility of unitarity and gauge symmetry in the SL(2,C) Yang-Mills field theory

Confusiones típicas de los físicos sobre el problema del salto de masa en teorías de Yang-Mills puras « Francis (th)E mule Science's News

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Emmy Noether and The Fabric of Reality - YouTube

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Teleparallelism - Wikipedia, the free encyclopedia

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Conference on Higher Gauge Theory, Quantum Gravity, and Topological Field Theory « Secret Blogging Seminar

Higher Gauge Theory, TQFT and Quantum Gravity in Lisbon | The n-Category Café

Phys. Rev. D 24, 471 (1981): Incompatibility of unitarity and gauge symmetry in the SL(2,C) Yang-Mills field theory

Introduction to gauge theory - Wikipedia, the free encyclopedia

An Invitation to Higher Gauge Theory (Again) | The n-Category Café

Division Algebras and Supersymmetry II | The n-Category Café

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Angel "Java" Lopez

Por ajlopez, en: Ciencia