Related papers: Remarks on the conformal transformations
Large language models exhibit sophisticated capabilities, yet understanding how they work internally remains a central challenge. A fundamental obstacle is that training selects for behavior, not circuitry, so many weight configurations can…
Having in mind that physical systems have different levels of structure we develop the concept of external, internal and total improper Lorentz transformation (space inversion and time reversal). A particle obtained from the ordinary one by…
We reconsider the description for property transitions due to perfect measurements, viewing them as a special case of general transitions that are due to an externally imposed change. We propose a corresponding syntax involving operational…
While conformal transformations of the plane preserve Laplace's equation, Lorentz-conformal mappings preserve the wave equation. We discover how simple geometric objects, such as quadrilaterals and pairs of crossing curves, are transformed…
The dynamics of "dipolar particles", i.e. particles endowed with a four-vector mass dipole moment, is investigated using an action principle in general relativity. The action is a specific functional of the particle's world line, and of the…
Crystals form regular and robust structures that under extreme conditions can melt and recrystallize into different arrangements in a process that is called crystal metamorphism. While crystals exist due to the breaking of a continuous…
Determinantal and permanental processes are point processes with a correlation function given by a determinant or a permanent. Their atoms exhibit mutual attraction of repulsion, thus these processes are very far from the uncorrelated…
An effective method for generating linear equations of maximal symmetry in their much general normal form is obtained. In the said normal form, the coefficients of the equation are differential functions of the coefficient of the term of…
An appeal for symmetry is made to build established notions of specific representation and specific nonlinearity of measurement (often called model error) into a canonical linear regression model. Additive components are derived from the…
This article presents an exhaustive classification of metric-affine theories according to their scale symmetries. First it is clarified that there are three relevant definitions of a scale transformation. These correspond to a projective…
Fractional action-like variational problems have recently gained importance in studying dynamics of nonconservative systems. In this note we address multi-dimensional fractional action-like problems of the calculus of variations.
A Legendre transform of the recently discovered conformal fixed-point equation is constructed, providing an unintegrated equation encoding full conformal invariance within the framework of the effective average action.
Causality imposes strong restrictions on the type of operators that may be observables in relativistic quantum theories. In fact, causal violations arise when computing conditional probabilities for certain partial causally connected…
Conformal prediction is a popular, modern technique for providing valid predictive inference for arbitrary machine learning models. Its validity relies on the assumptions of exchangeability of the data, and symmetry of the given model…
We argue that 4D gravity is drastically modified at distances larger than the horizon scale, due to the large infrared quantum fluctuations of the conformal part of the metric. The infrared dynamics of the conformal factor is generated by…
The main topic of this article is a discussion about the best way to show students that the proportionality of mass and weight, strictly true for point-like particles, is an excellent approximation for objects of "normal" size. The usual…
In unified field theories with more than four dimensions, the form of the equations of physics in spacetime depends in general on the choice of coordinates in higher dimensions. The reason is that the group of coordinate transformations in…
We show that the requirement of gauge invariance is not enough to fix the form of interactions between unparticles and gauge fields, thus revealing a wide new class of gauged unparticle actions. Our approach also allows us to construct…
We investigate the conformal and superconformal properties of a non-relativistic spinning particle propagating in a curved background coupled to a magnetic field and with a scalar potential. We derive the conditions on the couplings for a…
We consider the problem of quantum behavior in the finite background. Introduction of continuum or other infinities into physics leads only to technical complications without any need for them in description of empirical observations. The…