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Dia 1
Dia 1

... Such an anomaly could jeopardize the renormalizability of massive vector theories. How can we assure that such anomalies stay harmless ? Should the small-distance behavior provide answers? This was an important reason for studying the scaling behavior of gauge theories. What is their small-distance ...
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... things we know that we know. There are known unknowns. That is to say, there are things that we know we don't know. But there are also unknown unknowns. There are things we don't know we don't know.” Donald Rumsfeld ...
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... other hand, is not renormalizable after quantization [1][2]. This is one of the reasons that general relativity was considered to be incompatible with quantum mechanics. In the quantized version of general relativity, one would not be able to reabsorb all the UV divergences into the coupling constan ...
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... 1. What type of particles are described by the Klein-Gordon equation? Is there any such particle in the SM? 2. What type of particles are described by the Dirac equation? 3. How many Dirac matrices are there? 4. There are four solutions to the Dirac equations. What do they represent? 5. How many ind ...
YANG-MILLS THEORY 1. Introduction In 1954, Yang and Mills
YANG-MILLS THEORY 1. Introduction In 1954, Yang and Mills

... subgroup of a larger simple group, such as SU (5). Theories of this kind, which attempt to unify interactions are sometimes known as grand unified theories (GUTs). Another possible GUT is based on the group SO(10). These theories are somewhat speculative and direct measurements are not possible toda ...
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PDF

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Physics 722, Spring 2007 Final Exam Due Friday, May 11, 5pm
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... are not asked to prove (but it is not difficult). This means that the variation of the variation of any field vanishes. For example, varying the antighost field once gives a term proportional to B a , and varying again, δB a =0. The existence of BRST invariance is helpful in proving renormalizabilit ...
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... particles this symmetry breaking would allow three of our four particles to have mass.  These four particles were found found to be our three weak bosons the, W+, W- and Z, and the massless particle that was left over is the photon of the electromagnetic force  Therefore, we had a unified theory o ...
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Title: Physics of gauge field and topology in spintronics, graphene
Title: Physics of gauge field and topology in spintronics, graphene

... We present an overview of gauge fields associated with spin transport and dynamics, focusing on their origin and physical consequences. Important topics, such as the geometric gauge fields associated with adiabatic quantum evolution, their “forceful” effects, and their topological implications are d ...
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Gauge theory

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—referred to as the symmetry 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 that 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 of quantum 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 the relativistic 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.
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