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Register a new userTheory of Classical Higgs Fields. III. Metric-affine gauge theory
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Added by
Gennady Sardanashvily
Publication date
2014
fields
Physics
and research's language is
English
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We consider classical gauge theory with spontaneous symmetry breaking on a principal bundle $Pto X$ whose structure group $G$ is reducible to a closed subgroup $H$, and sections of the quotient bundle $P/Hto X$ are treated as classical Higgs fields. Its most comprehensive example is metric-affine gauge theory on the category of natural bundles where gauge fields are general linear connections on a manifold $X$, classical Higgs fields are arbitrary pseudo-Riemannian metrics on $X$, and matter fields are spinor fields. In particular, this is the case of gauge gravitation theory.
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Higgs fields are attributes of classical gauge theory on a principal bundle $Pto X$ whose structure Lie group $G$ if is reducible to a closed subgroup $H$. They are represented by sections of the quotient bundle $P/Hto X$. A problem lies in description of matter fields with an exact symmetry group $H$. They are represented by sections of a composite bundle which is associated to an $H$-principal bundle $Pto P/H$. It is essential that they admit an action of a gauge group $G$.
We consider classical gauge theory with spontaneous symmetry breaking on a principal bundle $Pto X$ whose structure group $G$ is reducible to a closed subgroup $H$, and sections of the quotient bundle $P/Hto X$ are treated as classical Higgs fields. In this theory, matter fields with an exact symmetry group $H$ are described by sections of a composite bundle $Yto P/Hto X$. We show that their gauge $G$-invariant Lagrangian necessarily factorizes through a vertical covariant differential on $Y$ defined by a principal connection on an $H$-principal bundle $Pto P/H$.
A new variational principle for General Relativity, based on an action functional $I/(Phi, abla)/$ involving both the metric $Phi/$ and the connection $ abla/$ as independent, emph{unconstrained/} degrees of freedom is presented. The extremals of $I/$ are seen to be pairs $/(Phi, abla)/$ in which $Phi/$ is a Ricci flat metric, and $ abla/$ is the associated Riemannian connection. An application to Kaluzas theory of interacting gravitational and electromagnetic fields is discussed.
We study the metric-affi
We present an identity satisfied by the kinematic factors of diagrams describing the tree amplitudes of massless gauge theories. This identity is a kinematic analog of the Jacobi identity for color factors. Using this we find new relations between color-ordered partial amplitudes. We discuss applications to multi-loop calculations via the unitarity method. In particular, we illustrate the relations between different contributions to a two-loop four-point QCD amplitude. We also use this identity to reorganize gravity tree amplitudes diagram by diagram, offering new insight into the structure of the KLT relations between gauge and gravity tree amplitudes. This can be used to obtain novel relations similar to the KLT ones. We expect this to be helpful in higher-loop studies of the ultraviolet properties of gravity theories.
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