相关论文: On Decompositions of Lorentz Transformations and t…

It is shown that the polar decomposition theorem of operators in (real) Hilbert spaces gives rise to the known decomposition in boost and spatial rotation part of any matrix of the orthochronous proper Lorentz group $SO(1,3)\uparrow$. This…

The Lorentz transformation (LT) is explained by changes occurring in the wave characteristics of matter as it changes inertial frame. This explanation is akin to that favoured by Lorentz, but informed by later insights, due primarily to de…

In this paper, a new general decomposition theory inspired from modular graph decomposition is presented. Our main result shows that, within this general theory, most of the nice algorithmic tools developed for modular decomposition are…

This paper describes a generalization of decomposition in orbifolds. In general terms, decomposition states that two-dimensional orbifolds and gauge theories whose gauge groups have trivially-acting subgroups decompose into disjoint unions…

The forward and inverse wavelet transform using the continuous Morlet basis may be symmetrized by using an appropriate normalization factor. The loss of response due to wavelet truncation is addressed through a renormalization of the…

A submarine moving at relativistic horizontal velocity sinks in Earth's rest frame due to length contraction while appearing to float in its own frame. Using spacetime geometry and the Lorentz transformations, we show that the resolution…

Recently, questions have been raised about the role of Lorentz invariance in false vacuum decay. It has been argued that infinities may arise in an integration over Lorentz-boosted final states. This suggestion motivates a Minkowski-space…

While an explicit basis is common in the study of Euclidean spaces, it is usually implied in the study of inertial relativistic systems. There are some conceptual advantages to including the basis in the study of special relativistic…

Decomposition of tomographic reconstructions has many different practical application. We propose two new reconstruction methods that combines the task of tomographic reconstruction with object decomposition. We demonstrate these…

We study the transformation of maximally entangled states under the action of Lorentz transformations in a fully relativistic setting. By explicit calculation of the Wigner rotation, we describe the relativistic analog of the Bell states as…

We generalize the Unruh-DeWitt detector model to second quantization. We illustrate this model by applying it to an excited particle in a superposition of relativistic velocities. We calculate, to first order, how its decay depends on…

We propose a new interpretation of doubly special relativity based on the distinction between the momenta and the translation generators in its phase space realization. We also argue that the implementation of the theory does not…

One possible ramification of unified theories of nature such as string theory that may underlie the conventional standard model is the possible spontaneous breakdown of Lorentz and CPT symmetry. In this talk, the formalism for inclusion of…

Wigner rotations and Iwasawa decompositions are manifestations of the internal space-time symmetries of massive and massless particles, respectively. It is shown to be possible to produce combinations of optical filters which exhibit…

Low-energy remnant fundamental symmetry violations may be present in nature at levels attainable in upcoming experiments. These effects may arise through spontaneous symmetry breaking in a more complete Lorentz covariant theory underlying…

The Helmholtz decomposition splits a sufficiently smooth vector field into a gradient field and a divergence-free rotation field. Existing decomposition methods impose constraints on the behavior of vector fields at infinity and require…

We consider transformations between uniformly accelerated systems, assuming that the Clock Hypothesis is false. We use the proper velocity-time description of events rather than the usual space-time description in order to obtain linear…

Motivated by a connection with the factorization of multivariate polynomials, we study integral convex polytopes and their integral decompositions in the sense of the Minkowski sum. We first show that deciding decomposability of integral…

A careful study is made of the operational meaning of the time symbols appearing in the space-time Lorentz transformation. Four distinct symbols, with different physical meanings, are needed to describe reciprocal measurements involving…

We give a general constructive proof for hierarchical coordinatizations (Lagrange Decompositions) of permutation groups. The generalization originates from the investigation of how the subgroup chains of finite permutation groups yield…