相关论文: Probability Collectives for Unstable Particles
Symmetries impose structure on the Hilbert space of a quantum mechanical model. The mathematical units of this structure are the irreducible representations of symmetry groups and I consider how they function as conceptual units of…
Motivated by the debate of possible definitions of mass and width of resonances for $Z$-boson and hadrons, we suggest a definition of unstable particles by ``minimally complex'' semigroup representations of the Poincar\'e group…
Ground state energies and decay widths of particle unstable nuclei are calculated within the Hartree-Fock approximation by performing a complex scaling of the many-body Hamiltonian. Through this transformation, the wave functions of the…
We present the probability preserving description of the decaying particle within the framework of quantum mechanics of open systems taking into account the superselection rule prohibiting the superposition of the particle and vacuum. In…
The unitary group $\mathrm U(\mathcal H)$ on an infinite dimensional complex Hilbert space $\mathcal H$ in its strong topology is a topological group and has some further nice properties, e.g. it is metrizable and contractible if $\mathcal…
We formulate a new bootstrap principle which allows for the construction of particle spectra involving unstable as well as stable particles. We comment on the general Lie algebraic structure which underlies theories with unstable particles…
We study the survival probability of moving relativistic unstable particles with definite momentum $\vec{p} \neq 0$. The amplitude of the survival probability of these particles is calculated using its integral representation. We found…
The structure of subspaces of a Hilbert space that are invariant under unitary representations of a discrete group is related to a notion of Hilbert modules endowed with inner products taking values in spaces of unbounded operators. A…
We show how the state of an unstable particle can be defined in terms of stable asymptotic states. This general definition is used to discuss and to solve some old problems connected with the short-time and large-time behaviour of the…
The self-assembly of particles into organized structures is a key feature of living organisms and a major engineering challenge. While it may proceed through the binding of perfectly matched, puzzle-pieces-like particles, many other…
For a quantum particle with a single degree of freedom, we derive preparational sum and product uncertainty relations satisfied by $N$ linear combinations of position and momentum observables. The state-independent bounds depend on their…
The top-quark, $W$ and $Z^0$ bosons have widths that are a sizable fraction of their masses and will be produced copiously at upcoming accelerators. Yet S-matrix theory cannot treat unstable particles as external states. Dealing with…
We define predictive states and predictive complexity for quantum systems composed of distinct subsystems. This complexity is a generalization of entanglement entropy. It is inspired by the statistical or forecasting complexity of…
We explore physics of unstable particles when mother particle mass is around the sum of its daughter particle masses. In this case, the conventional wave function renormalization factor is ill-defined. We propose a simple resolution of the…
We study entropies caused by the unstable part of partially hyperbolic systems. We define unstable metric entropy and unstable topological entropy, and establish a variational principle for partially hyperbolic diffeomorphsims, which states…
As physics searches for invariants in observations, this paper looks for invariants of probabilistic observation without assuming physical structure. Structure emerges from the basic assumption of science that new information shall lead to…
We establish character rigidity for all non-uniform higher-rank irreducible lattices in semisimple groups of characteristic other than 2. This implies stabilizer rigidity for probability measure preserving actions and rigidity of invariant…
This article is dedicated to the study of diagonal hyperbolic systems in one space dimension, with cumulative distribution functions, or more generally nonconstant monotonic bounded functions, as initial data. Under a uniform strict…
In this work, we study the analytic properties of S-matrix for unstable particles, which is defined as the residues on the unphysical sheets where unstable poles reside. We demonstrate that anomalous thresholds associated with UV physics…
In a statistical analysis in Particle Physics, nuisance parameters can be introduced to take into account various types of systematic uncertainties. The best estimate of such a parameter is often modeled as a Gaussian distributed variable…