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Register a new userNeutrino oscillations: Quantum mechanics vs. quantum field theory
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Authors
Evgeny Kh. Akhmedov
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A consistent description of neutrino oscillations requires either the quantum-mechanical (QM) wave packet approach or a quantum field theoretic (QFT) treatment. We compare these two approaches to neutrino oscillations and discuss the correspondence between them. In particular, we derive expressions for the QM neutrino wave packets from QFT and relate the free parameters of the QM framework, in particular the effective momentum uncertainty of the neutrino state, to the more fundamental parameters of the QFT approach. We include in our discussion the possibilities that some of the neutrinos interaction partners are not detected, that the neutrino is produced in the decay of an unstable parent particle, and that the overlap of the wave packets of the particles involved in the neutrino production (or detection) process is not maximal. Finally, we demonstrate how the properly normalized oscillation probabilities can be obtained in the QFT framework without an ad hoc normalization procedure employed in the QM approach.
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We consider neutrino oscillations in vacuum in the framework of quantum field theory in which neutrino production and detection processes are part of a single Feynman diagram and the corresponding cross section is computed in the standard way, i.e. with final states represented by plane waves. We use assumptions which are realized in actual experiments and concentrate on the detection process. Moreover, we also allow for a finite time interval of length $tau$ during which the detector records neutrino events. In this context we are motivated by accelerator-neutrino oscillation experiments where data taking is synchronized in time with the proton spill time of the accelerator. Given the final momenta and the direction of neutrino propagation, we find that in the oscillation amplitude---for all practical purposes---the neutrino energy $Q$ is fixed, apart from an interval of order $2pihbar/tau$ around a mean energy $bar Q$; this is an expression of energy non-conservation or the time-energy uncertainty relation in the detection process due to $tau < infty$. We derive in excellent approximation that in the amplitude the oscillation effect originates from massive neutrinos with the same energy $bar Q$, i.e. oscillations take place in space without any decoherece effect, while the remaining integration over $Q$ in the interval of order $2pihbar/tau$ around $bar Q$ results in a time-correlation function expressing the time delay between neutrino production and detection.
Neutrino mixing and oscillations in quantum field theory framework had been studied before, which shew that the Fock space of flavor states is unitarily inequivalent to that of mass states (inequivalent vacua model). A paradox emerges when we use these neutrino weak states to calculate the amplitude of $W$ boson decay. The branching ratio of W(+) -> e(+) + nu_mu to W(+) -> e(+) + nu_e is approximately at the order of O({m_i^2}/{k^2}). The existence of flavor changing currents contradicts to the Hamiltonian we started from, and the usual knowledge about weak processes. Also, negative energy neutrinos (or violating the principle of energy conservation) appear in this framework. We discuss possible reasons for the appearance of this paradox.
We review the application of the relativistic quantum mechanics method for the description of neutrino oscillations for the studies of spin-flavor oscillations in background matter under the influence of a plane electromagnetic wave. Basing on the new exact solution of the Dirac-Pauli equation for a massive neutrino in the given external fields, we derive the transition probabilities for spin and spin-flavor oscillations. The obtained expressions are analyzed for different types of the neutrino magnetic moments. Our results are compared with findings of other authors.
We show that the combinatorial numbers known as {em Bell numbers} are generic in quantum physics. This is because they arise in the procedure known as {em Normal ordering} of bosons, a procedure which is involved in the evaluation of quantum functions such as the canonical partition function of quantum statistical physics, {it inter alia}. In fact, we shall show that an evaluation of the non-interacting partition function for a single boson system is identical to integrating the {em exponential generating function} of the Bell numbers, which is a device for encapsulating a combinatorial sequence in a single function. We then introduce a remarkable equality, the Dobinski relation, and use it to indicate why renormalisation is necessary in even the simplest of perturbation expansions for a partition function. Finally we introduce a global algebraic description of this simple model, giving a Hopf algebra, which provides a starting point for extensions to more complex physical systems.
We study neutrino oscillations in a medium of dark matter which generalizes the standard matter effect. A general formula is derived to describe the effect of various mediums and their mediators to neutrinos. Neutrinos and anti-neutrinos receive opposite contributions from asymmetric distribution of (dark) matter and anti-matter, and thus it could appear in precision measurement of neutrino or anti-neutrino oscillations. Furthermore, the standard neutrino oscillation can occur from the symmetric dark matter effect even for massless neutrinos.
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