Related papers: Beyond basis invariants
A symmetry transformation is well defined in the case of an invariant theory, being the corresponding operator undetermined otherwise. However, we show that, even with CP violation, it is possible to determine the CP transformation by…
The two-Higgs-doublet model can be constrained by imposing Higgs-family symmetries and/or generalized CP symmetries. It is known that there are only six independent classes of such symmetry-constrained models. We study the CP properties of…
We present a new scheme of defining invariant observables for general relativistic systems. The scheme is based on the introduction of an observer which endowes the construction with a straightforward physical interpretation. The…
This paper considers a generalization of the notion of quantum observables in ontological models of quantum mechanics. Within this framework it is possible to construct physical models where quantum noncommutativity can arise dynamically.…
The application of the notion of `observable' from gauge theory to diffeomorphism-invariant theories -- most relevantly to general relativity -- has led to numerous conceptual and technical issues when interpreting classical theories with…
The procedure to find gauge invariant variables for two-parameter nonlinear perturbations in general relativity is considered. For each order metric perturbation, we define the variable which is defined by the appropriate combination with…
It is emphasized that a many-worlds interpretation of quantum theory exists only to the extent that the associated basis problem is solved. The core basis problem is that the robust enduring states specified by environmental decoherence…
Emergent modified gravity has shown that the canonical formulation of general relativity gives rise to a larger class of covariant modifications than action-based approaches, so far in symmetry-reduced models. This outcome is made possible…
It is shown that the action for Hamiltonian equations of motion can be brought into invariant symplectic form. In other words, it can be formulated directly in terms of the symplectic structure $\omega$ without any need to choose some…
This thesis is concerned with the theory of invariant bilinear differential pairings on parabolic geometries. It introduces the concept formally with the help of the jet bundle formalism and provides a detailed analysis. More precisely,…
Based on the recent result that, if the masses of timelike fields are point-dependent fields themselves, the action of matter fields is conformal form-invariant in its standard form, and on the active and passive approaches to conformal…
One of basic difficulties of machine learning is handling unknown rotations of objects, for example in image recognition. A related problem is evaluation of similarity of shapes, for example of two chemical molecules, for which direct…
It is possible that fundamental constants may not be constant at all. There is a generally accepted view that one can only talk about variations of dimensionless quantities, such as the fine structure constant $\alpha_{\rm e}\equiv…
Using the gauge-invariant but path-dependent variables formalism, we examine the effect of the space-time dimensionality on a physical observable in the unparticle scenario. We explicitly show that long-range forces between particles…
Physical systems are characterized by their structure and dynamics. But the physical laws only express relations, and their symmetries allow any possible relational structure to be also possible in a different parametrization or basis of…
Due to the availability of large molecular data-sets, covariance models are increasingly used to describe the structure of genetic variation as an alternative to more heavily parametrised biological models. We focus here on a class of…
Starting from the concept of involution of field equations, a universal method is proposed for constructing consistent interactions between the fields. The method equally well applies to the Lagrangian and non-Lagrangian equations and it is…
The geometrical arrangement of a set of quantum states can be completely characterized using relational information only. This information is encoded in the pairwise state overlaps, as well as in Bargmann invariants of higher degree written…
We find new families of shape invariant potentials depending on n>=1 parameters subject to translation by the inclusion of non-trivial invariants. New dependencies of the spectra are found, and it opens the door to the engineering of…
Based on the gauge invariant variables proposed in our previous paper [K. Nakamura, Prog. Theor. Phys. vol.110 (2003), 723.], some formulae of the perturbative curvatures of each order are derived. We follow the general framework of the…