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Marek Nowakowski

Publications and source records attributed to Marek Nowakowski.

52 records · Page 3Linked to original sources
arXiv2007

Scales Set by the Cosmological Constant

The cosmological constant sets certain scales important in cosmology. We show that Lambda in conjunction with other parameters like the Schwarzschild radius leads to scales relevant not only for cosmological but also for astrophysical applications. Of special interest is the extension of orbits and velocity of test particles traveling over Mpc distances. We will show that there exists a lower and an upper cut-off on the possible velocities of test particles. For a test body moving in a central gravitational field Lambda enforces a maximal value of the angular momentum if we insist on bound orbits of the test body which move at a distance larger than the Schwarzschild radius.

gr-qc↗
arXiv2007

On astrophysical bounds of the cosmological constant

Astrophysical bounds on the cosmological constant are examined for spherically symmetric bodies. Similar limits emerge from hydrostatical and gravitational equilibrium and the validity of the Newtonian limit. It is argued that the bound coming from the analysis of exact solutions is not a feature of the relativistic theory since it also emerges from the Newtonian theory. The methods in use seem to be disjoint from the basic principles, however they have the same implication regarding the upper bounds. Therefore we will compare different inequalities and comment on the possible relationship between them.

gr-qc↗
arXiv2006

Dark Energy in an Astrophysical Context

We explore local consequences of a non-zero cosmological constant on astrophysical structures. We find that the effects are not only sensitive to the density of the configurations but also to the geometry. For non-homogeneous configurations, we calculate the effects for a polytropic configurations and the isothermal sphere. Special emphasis is put on the fact that the cosmological constant sets certain scales of length, time, mass and density. Sizable effects are established for non spherical systems such as elliptical galaxy clusters where the effects of $Λ$ are growing with the flatness of the system. The equilibrium of rotating ellipsoids is modified and the cosmological constant allows new configurations of equilibrium.

astro-ph↗
arXiv2005

All electromagnetic form factors

The electromagnetic form factors of spin-1/2 particles are known, but due to historical reasons only half of them are found in many textbooks. Given the importance of the general result, its model independence, its connection to discrete symmetries and their violations we made an effort to derive and present the general result based only on the knowledge of Dirac equation. We discuss the phenomenology connected directly with the form factors, and spin precession in external fields including time reversal violating terms. We apply the formalism to spin-flip synchrotron radiation and suggest pedagogical projects.

physics.ed-ph↗
arXiv2004

Charged Dual String Vacua from Interacting Rotating Black Holes Via Discrete and Nonlinear Symmetries

Using the stationary formulation of the toroidally compactified heterotic string theory in terms of a pair of matrix Ernst potentials we consider the four-dimensional truncation of this theory with no U(1) vector fields excited. Imposing one time-like Killing vector permits us to express the stationary effective action as a model in which gravity is coupled to a matrix Ernst potential which, under certain parametrization, allows us to interpret the matter sector of this theory as a double Ernst system. We generate a web of string vacua which are related to each other via a set of discrete symmetries of the effective action (some of them involve S-duality transformations and possess non-perturbative character). Some physical implications of these discrete symmetries are analyzed and we find that, in some particular cases, they relate rotating black holes coupled to a dilaton with no Kalb--Ramond field, static black holes with non-trivial dilaton and antisymmetric tensor fields, and rotating and static naked singularities. Further, by applying a nonlinear symmetry, namely, the so-called normalized Harrison transformation, on the seed field configurations corresponding to these neutral backgrounds, we recover the U(1)^n Abelian vector sector of the four-dimensional action of the heterotic string, charging in this way the double Ernst system which corresponds to each one of the neutral string vacua, i.e., the stationary and the static black holes and the naked singularities.

hep-th↗
arXiv2002

Quantum Instability for Mixed States

The analysis of the time evolution of unstable states which are linear superposition of other, observable, states can, in principle, be carried out in two distinct, non-equivalent ways. One of the methods, usually employed for the neutral kaon system, combines the mixing and instability into one single step which then results into unconventional properties of the mass-eigenstates. An alternative method is to remain within the framework of a Lagrangian formalism and to perform the mixing prior to the instability analysis. Staying close to the $K^0-\bar{K^0}$ system, we compare both methods pointing out some of their shortcomings and advantages.

hep-ph↗
arXiv2001

Gravitational Equilibrium in the Presence of a Positive Cosmological Constant

We reconsider the virial theorem in the presence of a positive cosmological constant Lambda. Assuming steady state, we derive an inequality of the form rho >= A (Lambda / 4 pi GN) for the mean density rho of the astrophysical object. With a minimum at Asphere = 2, its value can increase by several orders of magnitude as the shape of the object deviates from a spherically symmetric one. This, among others, indicates that flattened matter distributions like e.g. clusters or superclusters, with low density, cannot be in gravitational equilibrium.

astro-ph↗
arXiv2000

Long Range Forces from Quantum Field Theory at Zero and Finite Temperature

We discuss the derivation of Newtonian potentials in the framework of quantum field theory. We focus on two particular points: on long range forces i.e. forces which fall off as $1/r^n$ being mediated by light quanta like neutrinos or Goldstone bosons and on possible temperature dependence of such forces arising in situations when the exchanged quanta are in a thermal heat bath. Examples of the latter are cosmic relic photons and relic neutrinos. Among other things, we will show that the existence of cosmic relic neutrinos modifies the long tail of the two-neutrino exchange Feinberg-Sucher force drastically. Results concerning the potential mediated by two Goldstone bosons are also presented.

hep-ph↗
arXiv2000

The Consistent Newtonian Limit of Einstein's Gravity with a Cosmological Constant

We derive the `exact' Newtonian limit of general relativity with a positive cosmological constant $Λ$. We point out that in contrast to the case with $Λ= 0 $, the presence of a positive $Λ$ in Einsteins's equations enforces, via the condition $| Φ| \ll 1$, on the potential $Φ$, a range ${\cal R}_{max}(Λ) \gg r \gg {\cal R}_{min} (Λ)$, within which the Newtonian limit is valid. It also leads to the existence of a maximum mass, ${\cal M}_{max}(Λ)$. As a consequence we cannot put the boundary condition for the solution of the Poisson equation at infinity. A boundary condition suitably chosen now at a finite range will then get reflected in the solution of $Φ$ provided the mass distribution is not spherically symmetric.

gr-qc↗
arXiv1998

Bell-inequalities for Entangled Neutral Kaons

We extend the use of Bell-inequalities to $Φ\to K^0 \bar{K^0}$ decays by exploiting analogies and differences to the well-known and experimentally verified singlet-spin case. Contrasting with other analyses, our Bell-inequalities are violated by quantum mechanics and can strictly be derived from local realistic theories. In principle, quantum mechanics could then be tested using unstable, oscillating states governed by a CP-violating Hamiltonian.

hep-ph↗
arXiv1998

The Quantum Mechanical Current of the Pauli Equation

We argue that the process of constructing the quantum mechanical current of the Pauli equation by copying the line of arguments used in the spin-0 case, i.e. the Schrödinger equation, is ambiguous. We show that a non-relativistic reduction of the relativistic Dirac four-vector current is, however, capable of fully resolving the problem. This analysis reveals that the non-relativistic current of the Pauli equation should include an extra term of the form $\vec \nabla \vec \times (ψ^{\dagger} \vec σψ)$. We present an initial exploration of the potential consequences of this new 'spin-term' by solving the Pauli equation for crossed magnetic and electric fields and calculating the corresponding current.

physics.ed-ph↗
arXiv1998

The Electromagnetic Coupling in Kemmer-Duffin-Petiau Theory

We analyse the electromagnetic coupling in the Kemmer-Duffin-Petiau (KDP) equation. Since the KDP--equation which describes spin-0 and spin-1 bosons is of Dirac-type, we examine some analogies and differences from the Dirac equation. The main difference to the Dirac equation is that the KDP equation contains redundant components. We will show that as a result certain interaction terms in the Hamilton form of the KDP equation do not have a physical meaning and will not affect the calculation of physical observables. We point out that a second order KDP equation derived by Kemmer as an analogy to the second order Dirac equation is of limited physical applicability as (i) it belongs to a class of second order equations which can be derived from the original KDP equation and (ii) it lacks a back-transformation which would allow one to obtain solutions of the KDP equation out of solutions of the second order equation. We therefore suggest a different higher order equation which, as far as the solutions for the wave functions are concerned, is equivalent to the orginal first order KDP wave equation.

quant-ph↗
arXiv1995

W- and Z-Boson Interactions in Supersymmetric Models with Explicit R-Parity Violation

The minimal supersymmetric Standard Model with explicit R-parity nonconservation contains bilinear terms involving the left-handed lepton superfields and the Higgs chiral multiplet with hypercharge Y=+1, which cannot in general be rotated away in the presence of soft-supersymmetry- breaking interactions. These bilinear lepton-number-violating terms are found to give rise to non-zero vacuum expectation values of the scalar neutrinos. This leads to nonuniversal and flavour-violating tree-level couplings of the W and Z bosons to charged leptons and neutrinos. The parameter space of this novel scenario is systematically analyzed and further restricted by a number of laboratory, astrophysical, and cosmological constraints. The possibility that our minimal model can account for the KARMEN anomaly is examined.

hep-ph↗
arXiv1995

TIME EVOLUTION OF $K^0-\bar{K^0}$ SYSTEM IN SPECTRAL FORMULATION

We reanalyse the time evolution of the $K^0-\bar{K^0}$ system in the language of certain spectral function whose Fourier transforms give the time dependent survival and transition amplitudes. The reanalysis turned out to be necessary in view of the astonishing theorem by Khalfin on the possibility of vacuum regeneration of $K_S$ and $K_L$. The main reason for this unexpected behaviour is the non-orthogonality of $\ks$ and $\kl$. As a result of this theorem new contributions to the well known oscillatory terms will enter the time dependent transition probabilities. These new terms are not associated with small/large time behaviour of the amplitudes and therefore their magnitude is apriori unknown. Approximating the spectral functions by an one-pole ansatz Khalfin estimated the new effect in transition probabilities to be $4 \times 10^{-4}$. Whereas we agree with Khalfin on the general existence of vacuum regeneration of $K_S$ and $K_L$ we disagree on the size of the effect. A careful analysis of the one-pole approximation reveals that the effect is eleven orders of magnitude smaller than Khalfin's estimate and, in principle, its exact determination lies outside the scope of the one-pole ansatz. The present paper gives also insight into the limitation of the validity of one-pole approximation, not only for small/large time scales, but also for intermediate times where new effects, albeit small, are possible. It will be shown that the same validity restrictions apply to the known formulae of Weisskopf-Wigner approximation as well.

hep-ph↗
arXiv1994

Just so oscillations in supersymmetric standard model

We analyze the spectrum and mixing among neutrinos in the minimal supersymmetric standard model with explicit breaking of R parity. It is shown that ({\em i}) the mixing among neutrinos is naturally large and ({\em ii}) the non zero neutrino mass is constrained to be $\leq 10^{-5}$ eV from arguments based on baryogenesis. Thus vacuum oscillations of neutrinos in this model may offer a solution of the solar neutrino problem. The allowed space of the supersymmetric parameters consistent with this solution is determined.

hep-ph↗