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K. Urbanowski

Publications and source records attributed to K. Urbanowski.

At least 37 records · Page 2Linked to original sources
arXiv2013

Cosmology with a decaying vacuum

Properties of unstable false vacuum states are analyzed from the point of view of the quantum theory of unstable states. Some of false vacuum states survive up to times when their survival probability has a non-exponential form. At times much latter than the transition time, when contributions to the survival probability of its exponential and non-exponential parts are comparable, the survival probability as a function of time t has an inverse power-like form. We show that at this time region the instantaneous energy of the false vacuum states tends to the energy of the true vacuum state as $1/t^{2}$ for $t \to \infty$.

gr-qc↗
arXiv2010

Long time deviations from the exponential decay law: possible effects in particle physics and cosmology

An effect generated by the nonexponential behavior of the survival amplitude of an unstable state in the long time region is considered. We find that the instantaneous energy of the unstable state for a large class of models of unstable states tends to the minimal energy of the system ${\cal E}_{min}$ as $t\rightarrow\infty$ which is much smaller than the energy of this state for $t$ of the order of the lifetime of the considered state. Analyzing the transition time region between exponential and non-exponential form of the survival amplitude we find that the instantaneous energy of the considered unstable state can take large values, much larger than the energy of this state for $t$ from the exponential time region. Taking into account results obtained for a model considered, it is hypothesized that this purely quantum mechanical effect may be responsible for the properties of broad resonances such as $σ$ meson as well as having astrophysical and cosmological consequences.

hep-ph↗
arXiv2009

Energy of unstable states at long times

An effect generated by the nonexponential behavior of the survival amplitude of an unstable state in the long time region is considered. In 1957 Khalfin proved that this amplitude tends to zero as $t\to\infty$ more slowly than any exponential function of $t$. For a time-dependent decay rate $γ(t)$ Khalfin's result means that this $γ(t)$ is not a constant for large $t$ but that it tends to zero as $t\to\infty$. We find that a similar conclusion can be drawn for the instantaneous energy of the unstable state for a large class of models of unstable states: This energy tends to the minimal energy of the system ${\cal E}_{min}$ as $t\to\infty$ which is much smaller than the energy of this state for $t$ of the order of the lifetime of the considered state. Analyzing the transition time region between exponential and non-exponential form of the survival amplitude we find that the instantaneous energy of a considered unstable state can take large values, much larger than the energy of this state for $t$ from the exponential time region. Taking into account results obtained for a model considered, it is hypothesized that this purely quantum mechanical effect may be responsible for the properties of broad resonances such as $σ$ meson as well as having astrophysical and cosmological consequences.

hep-ph↗
arXiv2009

General properties of the evolution of unstable states at long times

An effect generated by the nonexponential behavior of the survival amplitude of an unstable state at the long time region is considered. It is known that this amplitude tends to zero as $t$ goes to the infinity more slowly than any exponential function of $t$. Using methods of asymptotic analysis we find the asymptotic form of this amplitude in the long time region in a general model independent case. We find that the long time behavior of this amplitude affects the form of the energy of unstable states: This energy should be much smaller for suitably long times $t$ than the energy of this state for $t$ of the order of the lifetime of the considered unstable state.

quant-ph↗
arXiv2008

On a possible quantum contribution to the red shift

We consider an effect generated by the nonexponential behavior of the survival amplitude of an unstable state in the long time region: In 1957 Khalfin proved that this amplitude tends to zero as $t$ goes to the infinity more slowly than any exponential function of $t$. This effect can be described in terms of time-dependent decay rate $γ(t)$ and then the Khalfin result means that this $γ(t)$ is not a constant for long times but that it tends to zero as $t$ goes to the infinity. It appears that a similar conclusion can be drawn for the energy of the unstable state for a large class of models of unstable particles: This energy should be much smaller for suitably long times $t$ than the energy of this state for $t$ of the order of the lifetime of the considered state. Within a given model we show that the energy corrections in the long ($t \to \infty$) and relatively short (lifetime of the state) time regions, are different. It is shown that these corrections decrease to ${\cal E} = {\cal E}_{min} < {\cal E}_ϕ$ as $t \to \infty$, where ${\cal E}_ϕ$ is the energy of the system in the state $|ϕ>$ measured at times $t \sim τ_ϕ= \frac{\hbar}γ$. This is a purely quantum mechanical effect. It is hypothesized that there is a possibility to detect this effect by analyzing the spectra of distant astrophysical objects. The above property of unstable states may influence the measured values of astrophysical and cosmological parameters.

quant-ph↗
arXiv2008

A quantum long time energy red shift: a contribution to varying $α$ theories

By analyzing the survival probability amplitude of an unstable state we show that the energy corrections to this state in the long ($t \to \infty$) and relatively short (lifetime of the state) time regions, are different. It is shown that in the considered model the above corrections decrease to zero as $t \to \infty$. It is hypothesized that this property could be detected by analyzing the spectra of distant astrophysical objects. The above property of unstable states may influence the measured values of possible deviations of the fine structure constant $α$ as well as other astrophysical and cosmological parameters.

hep-ph↗
arXiv2007

Unitarity and real properties of the neutral meson complex

The proof of the Khalfin Theorem for neutral meson complex is analyzed. It is shown that the unitarity of the time evolution operator for the total system under considerations assures that the Khalfin's Theorem holds. The consequences of this Theorem for the neutral mesons system are discussed: it is shown, eg., that diagonal matrix elements of the exact effective Hamiltonian for the neutral meson complex can not be equal if CPT symmetry holds and CP symmetry is violated. Properties of time evolution governed by a time--independent effective Hamiltonian acting in the neutral mesons subspace of states are considered. Using the Khalfin's Theorem it is shown that if such Hamiltonian is time--independent then the evolution operator for the total system containing the neutral meson complex can not be a unitary operator. It is shown graphically for a given specific model how the Khalfin's Theorem works. It is also shown for this model how the difference of the mentioned diagonal matrix elements of the effective Hamiltonian varies in time.

hep-ph↗
arXiv2007

Khalfin's Theorem and neutral mesons subsystem

We analyze the proof of the Khalfin Theorem for neutral meson complex. The consequences of this Theorem are discussed: using this Theorem we find, eg., that diagonal matrix elements of the exact effective Hamiltonian for the neutral meson complex can not be equal if CPT symmetry holds and CP symmetry is violated. The Properties of time evolution governed by a time--independent effective Hamiltonian acting in the neutral mesons subspace of states are considered. By means of the Khalfin's Theorem we show that if such Hamiltonian is time--independent then the evolution operator for the total system containing neutral meson complex can not be a unitary operator. Within a given specific model we examine numerically the Khalfin's Theorem. We show for this model in a graphic form how the Khalfin's Theorem works. We also show for this model how the difference of the mentioned diagonal matrix elements of the effective Hamiltonian varies in time.

hep-ph↗
arXiv2006

On the Khalfin's improvement of the LOY effective Hamiltonian for neutral meson complex

The general properties of the effective Hamiltonian for neutral meson system improved by L.A. Khalfin in 1980 are studied. It is shown that contrary to the standard result of the Lee--Oehme--Yang (LOY) theory, the diagonal matrix elements of this effective Hamiltonian can not be equal in a CPT invariant system. It is also shown that the scalar product of short, $|K_{S}>$, and long, $|K_{L}>$, living superpositions of neutral kaons can not be real when CPT symmetry is conserved in the system under considerations whereas within the LOY theory such a scalar product is real.

hep-ph↗
arXiv2005

On the scalar product of short and long living states of neutral kaons in the CPT invariant system

This paper contains a detailed analysis of the properties of the scalar product of short and long living superpositions of neutral $|K_{0}>$, $|{\bar{K}}_{0}>$ mesons. It is shown for the exact effective Hamiltonian for neutral meson subsystem that the scalar product of its eigenvectors, which correspond with these short and long living superpositions, can not be real with the assumption of CPT conserved and CP violated. The standard conclusion obtained within the Lee-Oehme-Yang theory of neutral kaons is that in this case such a product should be real.

hep-ph↗
arXiv2004

Subsystem of neutral mesons beyond the Lee-Oehme-Yang approximation

General properties of eigenvectors and eigenvalues for an effective Hamiltonian governing time evolution in a two state subspace of the state space of the total system under consideration are discussed. The Lee, Oehme and Yang (LOY) theory of time evolution in such a subspace and CP-- and CPT--symmetry properties of the LOY effective Hamiltonian are considered. The CPT transformation properties of the exact effective Hamiltonian for two state subspace are discussed also. Using the Khalfin Theorem we show that contrary to the properties of the LOY theory, the diagonal matrix elements of the exact effective Hamiltonian governing the time evolution in the subspace of states of an unstable particle and its antiparticle need not be equal at for $t > t_{0}$ ($t_{0}$ is the instant of creation of the pair) when the total system under consideration is CPT invariant but CP noninvariant. Using the more accurate approximation than the LOY one we show that the interpretation of the tests measuring the difference between the $K_{0}$ mass and the ${\bar K}_{0}$ mass as the CPT--symmetry test is wrong.

hep-ph↗
arXiv2003

A new interpretation of one CPT violation test for $K_0 - \bar{K}_0$ system

Using a more accurate approximation than that applied by Lee--Oehme--Yang we show that the interpretation of the tests measuring the difference between the $K_{0}$ mass and the ${\bar K}_{0}$ mass as the CPT--symmetry test is wrong. We find that in fact such tests are tests for the existence of the hypothetical interaction allowing the first order $|ΔS| = 2$ transitions $K_{0} \rightleftharpoons {\bar K}_{0}$.

hep-ph↗
arXiv2003

CPT symmetry and properties of the exact and approximate effective Hamiltonians for the neutral kaon complex

We start from a discussion of the general form and general CP-- and CPT-- transformation properties of the Lee--Oehme--Yang (LOY) effective Hamiltonian for the neutral kaon complex. Next we show that there exists an approximation which is more accurate than the LOY, and which leads to an effective Hamiltonian whose diagonal matrix elements posses CPT transformation properties, which differ from those of the LOY effective Hamiltonian. These properties of the mentioned effective Hamiltonians are compared with the properties of the exact effective Hamiltonian for the neutral kaon complex. We show that the diagonal matrix elements of the exact effective Hamiltonian governing the time evolution in the subspace of states of an unstable particle and its antiparticle need not be equal at for $t > t_{0}$ ($t_{0}$ is the instant of creation of the pair) when the total system under consideration is CPT invariant but CP noninvariant. The unusual consequence of this result is that, contrary to the properties of stable particles, the masses of the unstable particle "1" and its antiparticle "2" need not be equal for $t \gg t_{0}$ in the case of preserved CPT and violated CP symmetries.

hep-ph↗
arXiv2003

Need the masses of unstable particles and their antiparticles be equal in the CPT--invariant system?

We show that the real parts of diagonal matrix elements of the exact effective Hamiltonian governing the time evolution in the subspace of states of neutral kaons and similar particles can not be equal for $t > t_{0}$ ($t_{0}$ is the instant of creation of the pair $K_{0}, {\bar{K}}_{0}$) when the total system under consideration is CPT invariant but CP noninvariant. The unusual consequence of this result is that, contrary to the properties of stable particles, the masses of the unstable particle, e.g.. $K_{0}$, and its antiparticle, ${\bar{K}}_{0}$, need not be equal for $t \gg t_{0}$ in the case of preserved CPT and violated CP symmetries.

hep-ph↗
arXiv2003

Studying the Bell--Steinberger relation

The Bell--Steinberger relation is analyzed. The questionable points of the standard derivation of this relation are discussed. It is shown that the use of a more accurate approximation than the one usually used in the derivation of this relation can lead to corrections to the right hand side of the standard Bell--Steinberger relation.

hep-ph↗
arXiv2002

CPT and effective Hamiltonians for neutral kaon and similar complexes

We begin with a discussion of the general form and general CP-- and CPT-- transformation properties of the Lee--Oehme--Yang (LOY) effective Hamiltonian for the neutral kaon complex. Next, the properties of the exact effective Hamiltonian for this complex are discussed. Using the Khalfin Theorem we show that the diagonal matrix elements of the effective Hamiltonian governing the time evolution in the subspace of states of an unstable particle and its antiparticle need not be equal at for t > t_0 (t_0 is the instant of creation of the pair) when the total system under consideration is CPT invariant but CP noninvariant. The unusual consequence of this result is that, contrary to the properties of stable particles, the masses of the unstable particle "1" and its antiparticle "2" need not be equal for t >> t_0 in the case of preserved CPT and violated CP symmetries. We also show that there exists an approximation which is more accurate than the LOY, and which leads to an effective Hamiltonian whose diagonal matrix elements posses properties consistent with the conclusions for the exact effective Hamiltonian described above.

hep-ph↗
arXiv2002

On masses of unstable particles and their antiparticles in the CPT-invariant system

We show that the diagonal matrix elements of the effective Hamiltonian governing the time evolution in the subspace of states of an unstable particle and its antiparticle need not be equal at $t > t_{0}$ ($t_{0}$ is the instant of creation of the pair) when the total system under consideration is CPT invariant but CP noninvariant. To achieve this we use the transition amplitudes for transitions $|{\bf 1}> \to |{\bf 2}>$, $|{\bf 2}> \to |{\bf 1}>$ together with the identity expressing the effective Hamiltonian by these amplitudes and their derivatives with respect to time $t$. This identity must be fulfilled by any effective Hamiltonian (both approximate and exact) derived for the two state complex. The unusual consequence of this result is that, contrary to the properties of stable particles, the masses of the unstable particle "1" and its antiparticle "2" need not be equal for $t \gg t_{0}$ in the case of preserved CPT and violated CP symmetries.

hep-ph↗