In general relativity, a manifestly covariant equation is one in which all expressions are tensors. The operations of addition, tensor multiplication, tensor contraction, raising and lowering indices, and covariant differentiation may appear in the equation. Forbidden terms include but are not restricted to partial derivatives. Tensor densities, especially integrands and variables of integration, may be allowed in manifestly covariant equations if they are clearly weighted by the appropriate power of the determinant of the metric.
Writing an equation in manifestly covariant form is useful because it guarantees general covariance upon quick inspection. If an equation is manifestly covariant, and if it reduces to a correct, corresponding equation in special relativity when evaluated instantaneously in a local inertial frame, then it is usually the correct generalization of the special relativistic equation in general relativity.
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equation in manifestly covariant form is useful because it guarantees general covariance upon quick inspection. If an equation is manifestly covariant,...
gauge. This is because the proof of Goldstone's theorem requires manifest Lorentz covariance, a property not possessed by the radiation gauge. Wikinews has...
Cartesian coordinates. It's the covariant derivative which transforms in manifestcovariance, in Cartesian coordinates this happens to reduce to the partial derivatives...
covariant derivative Dμ is required to transform quark fields in manifestcovariance; the partial derivatives that form the four-gradient ∂μ alone are...
In physics, a covariance group is a group of coordinate transformations between frames of reference (see for example Ryckman (2005)). A frame of reference...
dynamical triangulation Coordinate-free Quantum field theory General covariance Rickles, Dean (2008). "Who's Afraid of Background Independence?". The...
example, if it is posited that there are two factors accounting for the covariance in the measures, and that these factors are unrelated to each other, the...
estimation approach that differs from the covariance-based structural equation modeling. Unlike covariance-based approaches to structural equation modeling...
the analysis. EFA is based on the common factor model. In this model, manifest variables are expressed as a function of common factors, unique factors...
Markham, Alex; Das, Richeek; Grosse-Wentrup, Moritz (2022). "A Distance Covariance-based Kernel for Nonlinear Causal Clustering in Heterogeneous Populations"...
form of the Lagrangian is manifestly invariant under redefinition of the spatial coordinates, it makes general covariance opaque. Since the lapse function...
Binomial / Poisson regressions Partition of variance Analysis of variance (ANOVA, anova) Analysis of covariance Multivariate ANOVA Degrees of freedom...
estimated based on either raw data (with FIML modelling) or on correlation or covariance matrices. Models can handle mixtures of continuous and ordinal data. The...
'general covariance' was used in the early formulation of general relativity, but the principle is now often referred to as 'diffeomorphism covariance'. Diffeomorphism...
These can be viewed either as the covariance between any offspring and any one of its parents (PO), or as the covariance between any offspring and the "mid-parent"...
compatibility. Computer programming portal Comparison of type systems Covariance and contravariance (computer science) Polymorphism in object-oriented...
was a consequence of his principle of general covariance and arises from the following. General covariance states that the laws of physics should take the...
to the subsequent development of theoretical physics, because manifest Lorentz covariance (time and space components of quantities enter equations in the...
related, have subtle and important differences. Understanding Lorentz covariance is simplified by keeping in mind the geometric character of the process...
preceding analysis. This is rather an artifact of breaking relativistic covariance by choosing a preferred time direction. To have physical degrees of freedom...
mean and covariance parameters. With a large number ( N {\displaystyle N} ) of observations, the ( N × N {\displaystyle N\times N} ) covariance matrix may...
} is the factor covariance matrix. Assuming that the noise terms for the returns and factors are uncorrelated, the mean and covariance for the returns...
possessing similar abilities, to respond differently to the item. It manifests when individuals from different groups, with comparable skill levels,...
quantum fields. Goldstone's theorem only applies to gauges having manifest Lorentz covariance, a condition that took time to become questioned. But the process...
relatively cheap tests that are given to large populations, none of whom manifest any clinical indication of disease (e.g., Pap smears). Testing involves...
p. There is a direct correspondence between these parameters and the covariance function of the process, and this correspondence can be inverted to determine...
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