Results presented in a recent paper Which is the Quantum Decay Law of Relativistic particles?, arXiv: 1412.3346v2 [quant--ph]], are analyzed. We show that approximations used therein to derive the main final formula for the survival probability of fi
nding a moving unstable particle to be undecayed at time $t$ force this particle to almost stop moving, that is that, in fact, the derived formula is approximately valid only for $gamma cong 1$, where $gamma = 1/sqrt{1-beta^{2}}$ and $beta = v/c$, or in other words, for the velocity $v simeq 0$.
A new quantum effect connected with the late time behavior of decaying states is described and its possible observational consequences are analyzed: It is shown that charged unstable particles as well as neutral unstable particles with non--zero magn
etic moment which live sufficiently long may emit electromagnetic radiation. This mechanism is due to the nonclassical behavior of unstable particles at late times (at the post exponential time region). Analyzing the transition times region between exponential and non-exponential form of the survival amplitude it is found that the instantaneous energy of the unstable particle can take very large values, much larger than the energy of this state at times from the exponential time region. Based on the results obtained for the model considered, it is shown that this new purely quantum mechanical effect may be responsible for causing unstable particles produced by astrophysical sources and moving with relativistic velocities to emit electromagnetic--, $X$-- or $gamma$--rays at some time intervals from the transition time regions.
We study the survival probability of moving relativistic unstable particles with definite momentum $vec{p} eq 0$. The amplitude of the survival probability of these particles is calculated using its integral representation. We found decay curves of
such particles for the quantum mechanical models considered. These model studies show that late time deviations of the survival probability of these particles from the exponential form of the decay law, that is the transition times region between exponential and non-expo-nen-tial form of the survival probability, should occur much earlier than it follows from the classical standard approach resolving itself into replacing time $t$ by $t/gamma$ (where $gamma$ is the relativistic Lorentz factor) in the formula for the survival probability and that the survival probabilities should tend to zero as $trightarrow infty$ much slower than one would expect using classical time dilation relation. Here we show also that for some physically admissible models of unstable states the computed decay curves of the moving particles have fluctuating form at relatively short times including times of order of the lifetime.
Late time properties of moving relativistic particles are studied. Within the proper relativistic treatment of the problem we find decay curves of such particles and we show that late time deviations of the survival probability of these particles fro
m the exponential form of the decay law, that is the transition times region between exponential and non-expo-nen-tial form of the survival amplitude, occur much earlier than it follows from the classical standard approach boiled down to replace time $t$ by $t/gamma_{L}$ (where $gamma_{L}$ is the relativistic Lorentz factor) in the formula for the survival probability. The consequence is that fluctuations of the corresponding decay curves can appear much earlier and much more unstable particles have a chance to survive up to these times or later. It is also shown that fluctuations of the instantaneous energy of the moving unstable particles has a similar form as the fluctuations in the particle rest frame but they are seen by the observer in his rest system much earlier than one could expect replacing $t$ by $t/gamma_{L}$ in the corresponding expressions for this energy and that the amplitude of these fluctuations can be even larger than it follows from the standard approach. All these effects seems to be important when interpreting some accelerator experiments with high energy unstable particles and the like (possible connections of these effects with GSI anomaly are analyzed) and some results of astrophysical observations.
Recent LHC results concerning the mass of the Higgs boson indicate that the vacuum in our Universe may be unstable. We analyze properties of unstable vacuum states from the point of view of the quantum theory of unstable states. From the literature i
t is known that some of false vacuum states may 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 $t to infty$. Properties of the instantaneous energy at transition times are also analyzed for a given model. It is shown that at this time region large and rapid fluctuations of the instantaneous energy take place. This suggests analogous behavior of the cosmological constant at these time regions.
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 $t to infty$.
