Invariant Theoretical Interpretation of Interaction

Utiyama, Ryôyû

doi:10.1103/physrev.101.1597

Cited by 1,473 publications

(1,337 citation statements)

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“…The solution to this equation yields the affine connection in terms of its independent antisymmetric part B 1 2 ÿ ÿ ÿ in addition to the derivative of the metric [7] …”

Section: The Coset Constructionmentioning

confidence: 99%

“…Indeed a mth-rank contravariant local Lorentz and nth-rank covariant Einstein tensor, T m 1 m m 1 n , is defined to transform as [7] T 0m 0…”

Section: The Coset Constructionmentioning

confidence: 99%

“…Consider the covariant derivative of the Lorentz tensor T mn Converting the Lorentz index n to a space-time index using the vierbein, the covariant derivative for mixed tensors is obtained 2.28) where the spin connection ! mn M and ÿ are related according to [7] ÿ e ÿ1 n @ e n ÿ e ÿ1 n ! nr M e s rs : (2.29) (Note that this relation as well follows from the requirement that the covariant derivative of the vielbein vanishes, r e m 0).…”

Section: The Coset Constructionmentioning

confidence: 99%

“…It includes the vierbein as well as the locally covariant derivatives of the Goldstino fields which involve the gravitino fields and the spin (and hence affine) connections. The general covariant derivatives of these covariant one-forms are used as the building blocks of the action [7]. In Sec.…”

Section: Introductionmentioning

confidence: 99%

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Gauging nonlinear supersymmetry

et al. 2006

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Coset methods are used to construct the action describing the dynamics associated with the spontaneous breaking of the local supersymmetries. The resulting action is an invariant form of the Einstein-Hilbert action, which in addition to the gravitational vierbein, also includes a massive gravitino field. Invariant interactions with matter and gauge fields are also constructed. The effective Lagrangian describing processes involving the emission or absorption of a single light gravitino is analyzed.

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“…The solution to this equation yields the affine connection in terms of its independent antisymmetric part B 1 2 ÿ ÿ ÿ in addition to the derivative of the metric [7] …”

Section: The Coset Constructionmentioning

confidence: 99%

“…Indeed a mth-rank contravariant local Lorentz and nth-rank covariant Einstein tensor, T m 1 m m 1 n , is defined to transform as [7] T 0m 0…”

Section: The Coset Constructionmentioning

confidence: 99%

Section: The Coset Constructionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Gauging nonlinear supersymmetry

et al. 2006

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“…The particle concept within the EPS-axiomatics lost credibility when during the emergence of gauge theories of gravity (which started in 1956 with Utiyama [61] even before the EPS-framework had been set up in 1972) the first quantized wave function Ψ for matter entered the scene as an elementary and "irreducible" concept in gravity theory. When neutron interference in an external gravitational field was discovered experimentally in 1975 by Collella, Overhauser, and Werner (COW) [7], see also [52], Sec.7, it was clear that the point particle concept in the EPS-framework became untenable from a physical point of view.…”

Section: Discussionmentioning

confidence: 99%

Spacetime Metric from Local and Linear Electrodynamics: A New Axiomatic Scheme

Hehl

Obukhov

Lecture Notes in Physics

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Summary. We consider spacetime to be a 4-dimensional differentiable manifold that can be split locally into time and space. No metric, no linear connection are assumed. Matter is described by classical fields/fluids. We distinguish electrically charged from neutral matter. Electric charge and magnetic flux are postulated to be conserved. As a consequence, the inhomogeneous and the homogeneous Maxwell equations emerge expressed in terms of the excitation H = (H, D) and the field strength F = (E, B), respectively. H and F are assumed to fulfill a local and linear "spacetime relation" with 36 constitutive functions. The propagation of electromagnetic waves is considered under such circumstances in the geometric optics limit. We forbid birefringence in vacuum and find the light cone including its Lorentzian signature. Thus the conformally invariant part of the metric is recovered. If one sets a scale, one finds the pseudo-Riemannian metric of spacetime.

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Group Theory

Gilmore

2015

Digital Encyclopedia of Applied Physics

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The article conbtains sections titled: Introduction Precursors to Group Theory Classical Geometry Dimensional Analysis Scaling Dynamical Similarity Groups: Definitions Group Axioms Isomorphisms and Homomorphisms Examples of Discrete Groups Finite Groups Infinite Discrete Groups Examples of Matrix Groups Translation Groups Heisenberg Group Rotation Group Lorentz Group Lie Groups Lie Algebras Structure Constants Constructing Lie Algebras by Linearization Constructing Lie Groups by Exponentiation Cartan Metric Operator Realizations of Lie Algebras Disentangling Results Riemannian Symmetric Spaces Applications in Classical Physics Principle of Relativity Making Mechanics and Electrodynamics Compatible Gravitation Reflections Linear Representations Maps to Matrices Group Element–Matrix Element Duality Classes and Characters Fourier Analysis on Groups Irreps of Crystal Field Theory Symmetry Groups Dynamical Groups Conformal Symmetry Atomic Shell Structure Nuclear Shell Structure Dynamical Models Gauge Theory Group Theory and Special Functions Summary of Some Properties Relation with Lie Groups Spherical Harmonics and Differential and Recursion Relations Differential Equation Addition Theorems Generating Functions Summary Glossary

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Invariant Theoretical Interpretation of Interaction

Cited by 1,473 publications

References 4 publications

Gauging nonlinear supersymmetry

Gauging nonlinear supersymmetry

Spacetime Metric from Local and Linear Electrodynamics: A New Axiomatic Scheme

Group Theory

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