相关论文: Generic composition of boosts: an elementary deriv…

We analyze the angular momentum balance for a particle undergoing Thomas precession. The relationships among relativistic torque, the center of mass, and the center of inertia for a spinning particle are clarified. We show that spin…

According to Wigner theorem, transformations of quantum states which preserve the probabilities are either unitary or antiunitary. This short communication presents an elementary proof of this theorem that significantly departs from the…

We construct general Wigner rotations for both massive and massless particles in $D$-dimensional spacetime. We work out the explicit expressions of these Wigner rotations for arbitrary Lorentz transformations. We study the relation between…

Classical model of light in helicity formalism is presented. Then quantum point of view at photons -- construction and interpretation of photon wave function is proposed. Quantum mechanics of photon is investigated. The Bia\l ynicki --…

We present a calculation of the imaginary part of the polarizability of a Wigner crystal using the Fluctuation-Dissipation theorem. The oscillations of the localized electrons about their equilibrium positions are treated in the harmonic…

A new method of derivation of Lorentz Transformation (LT) is given based on both axioms of special relativity (SR) and physical intuitions. The essence of the transformation is established and the crucial role played by the presumptions is…

In statistical mechanics, the generally called Stirling approximation is actually an approximation of Stirling's formula. In this article, it is shown that the term that is dropped is in fact the one that takes fluctuations into account.…

Weinberg relation can be explained by Newton laws. It can also be transformed into a relation between a gravitational cross section area, associated to a gravitational mass m, and the product of two gravitational radii corresponding to the…

Instantaneous derivation of the Thomas precession with only basic vector calculus.

Very special relativity (VSR) keeps the main features of special relativity but breaks rotational invariance. It can not be regarded as a fundamental symmetry of nature because many observed phenomena depend on the existence of Lorentz…

Compositional generalization-the systematic combination of known components into novel structures-remains a core challenge in cognitive science and machine learning. Although transformer-based large language models can exhibit strong…

We introduce the "wedge diagram," an intuitive way to illustrate how cosmological models with a classical (non-singular) bounce generically resolve fundamental problems in cosmology. These include the well-known horizon, flatness, and…

From a group action on a space, define a variant of the configuration space by insisting that no two points inhabit the same orbit. When the action is almost free, this "orbit configuration space" is the complement of an arrangement of…

In Poincare-Wigner-Dirac theory of relativistic interactions, boosts are dynamical. This means that - just like time translations - boost transformations have non-trivial effect on internal variables of interacting systems. This is…

Wigner's celebrated theorem, which is particularly important in the mathematical foundations of quantum mechanics, states that every bijective transformation on the set of all rank-one projections of a complex Hilbert space which preserves…

Perturbing resonant systems causes shifts in their associated scattering poles in the complex plane. In a previous study [arXiv: 2408.11360], we demonstrated that these shifts can be calculated numerically by analyzing the residue of a…

The truncated Wigner approximation is an established approach that describes the dynamics of weakly interacting Bose gases beyond the mean-field level. Although it allows a quantum field to be expressed by a stochastic c-number field, the…

A matrix approach to continuous iteration is proposed for general formal series. It leads, in particular, to an order{to{order iteration of the exponential function, and consequently to an algorithmic approach to tetration. Lower{order…

We discuss how the diffraction theory of a single translation bounded measure or a family of such measures can be understood within the framework of unitary group representations. This allows us to prove an orthogonality feature of measures…

Einstein's perihelion advance formula can be given a geometric interpretation in terms of the curvature of the ellipse. The formula can be obtained by splitting the constant term of an auxiliary polar equation for an elliptical orbit into…