Search results for "Proper time"
showing 10 items of 13 documents
(F, G) -summed form of the QED effective action
2021
We conjecture that the proper-time series expansion of the one-loop effective Lagrangian of quantum electrodynamics can be summed in all terms containing the field-strength invariants $\mathcal{F}=\frac{1}{4}{F}_{\ensuremath{\mu}\ensuremath{\nu}}{F}^{\ensuremath{\mu}\ensuremath{\nu}}(x)$, $\mathcal{G}=\frac{1}{4}{\stackrel{\texttildelow{}}{F}}_{\ensuremath{\mu}\ensuremath{\nu}}{F}^{\ensuremath{\mu}\ensuremath{\nu}}(x)$, including those also possessing derivatives of the electromagnetic field strength. This partial resummation is exactly encapsulated in a factor with the same form as the Heisenberg-Euler Lagrangian density, except that now the electric and magnetic fields can depend arbitrar…
Hot spots and gluon field fluctuations as causes of eccentricity in small systems
2021
We calculate eccentricities in high energy proton-nucleus collisions, by calculating correlation functions of the energy density field of the Glasma immediately after the collision event at proper time tau = 0. We separately consider the effects of color charge and geometrical hot spot fluctuations, analytically performing the averages over both in a dilute-dense limit. We show that geometric fluctuations of hot spots inside the proton are the dominant source of eccentricity whereas color charge fluctuations only give a negligible correction. The size and number of hot spots are the most important parameters characterizing the eccentricities.
Evolution of initial stage fluctuations in the glasma
2021
We perform a calculation of the one- and two-point correlation functions of energy density and axial charge deposited in the glasma in the initial stage of a heavy ion collision at finite proper time. We do this by describing the initial stage of heavy ion collisions in terms of freely evolving classical fields whose dynamics obey the linearized Yang-Mills equations. Our approach allows us to systematically resum the contributions of high momentum modes that would make a power series expansion in proper time divergent. We evaluate the field correlators in the McLerran-Venugopalan model using the glasma graph approximation, but our approach for the time dependence can be applied to a general…
A quantum model of Schwarzschild black hole evaporation
1996
We construct a one-loop effective metric describing the evaporation phase of a Schwarzschild black hole in a spherically symmetric null-dust model. This is achieved by quantising the Vaidya solution and by chosing a time dependent quantum state. This state describes a black hole which is initially in thermal equilibrium and then the equilibrium is switched off, so that the black hole starts to evaporate, shrinking to a zero radius in a finite proper time. The naked singularity appears, and the Hawking flux diverges at the end-point. However, a static metric can be imposed in the future of the end-point. Although this end-state metric cannot be determined within our construction, we show tha…
Positioning with stationary emitters in a two-dimensional space-time
2006
The basic elements of the relativistic positioning systems in a two-dimensional space-time have been introduced in a previous work [Phys. Rev. D {\bf 73}, 084017 (2006)] where geodesic positioning systems, constituted by two geodesic emitters, have been considered in a flat space-time. Here, we want to show in what precise senses positioning systems allow to make {\em relativistic gravimetry}. For this purpose, we consider stationary positioning systems, constituted by two uniformly accelerated emitters separated by a constant distance, in two different situations: absence of gravitational field (Minkowski plane) and presence of a gravitational mass (Schwarzschild plane). The physical coord…
A missing link: What is behind de Broglie's "Periodic phenomenon"?
1996
The present work constitutes an attempt to give the interpretation of de Broglie's internal periodic phenomenon which ascribes the frequencym0c2/h to each single entity in its eigensystem of coordinates. This phenomenon provides existence in principle of the ideal proper-time scale, making it possible to identify the geometric proper-time interval with a physically existing one, thus ensuring the realization of basic postulates of the relativity theory. According to the latter, neither time nor de Broglie's frequency are invariant with respect to the Lorentz transformation of the coordinate system. A search for the fundamental invariant demands passing over to dimensionless quantities, and …
A Numbers-Based Approach to a Free Particle's Spacetime
2020
A possibility is proposed to define the proper spacetime of a free nonzerorest- mass m_0 particle based on the connection of its lasting proper time to an open sequence of natural numbers counting de Broglie time periods (h/c^2)(m^(-1)_ 0 ) [see R. Ferber, A Missing Link: What is Behind de Broglie's" Periodic Phenomenon"?, Foundations of Physics Letters 9, 575 (1996)]. It is suggested to define a set of twodirectional intervals of the particle's proper space (proper distances) following the construction of positive and negative integers from the ordered pairs of the natural numbers, which belong to the sequence 1, 2, ..., n defining the elapsed interval of de Broglie time t_n. Corresponding…
Reply to "Comment on 'Insensitivity of Hawking radiation to an invariant Planck-scale cutoff' "
2010
We clarify the relationship between the conclusions of the previous Comment of A. Helfer and that of our Brief Report.
Particle in Harmonic E-Field E ( t ) = E sin ω 0 t $$E(t)= E \sin \omega _0 t$$ ; Schwinger–Fock Proper-Time Method
2020
Since the Green’s function of a Dirac particle in an external field, which is described by a potential Aμ(x), is given by
Measurement of the and B− meson lifetimes
1993
Abstract The lifetimes of the B 0 and B − mesons have been measured with the ALEPH detector at LEP. Semileptonic decays of B 0 and B − mesons were partially reconstructed by identifying events containing a lepton with an associated D ∗+ or D 0 meson. The proper time of the B meson was estimated from the measured decay length and the momentum and mass of the D -lepton system. A fit to the proper time of 77 D ∗+ l − and 77 D 0 l − candidates, combined with a constraint on the lifetime ratio ( τ − τ 0 ) arising from the relative rates of observed D ∗+ l − and D 0 l − events, yielded the following lifetimes: τ 0 =1.52 −0.18 +0.20 ( stat. ) −0.13 +0.07 ( syst. ) ps , τ − = 1.47 −0.19 +0.22 ( sta…