We derive an explicit manifestly covariant expression for the most general positivedefinite and Lorentz-invariant inner product on the space of solutions of the Klein-Gordon equation. This expression involves a one-parameter family of conserved current densities J µ a , with a ∈ (−1, 1), that are analogous to the chiral current density for spin half fields. The conservation of J µ a is related to a global gauge symmetry of the Klein-Gordon fields whose gauge group is U (1) for rational a and the multiplicative group of positive real numbers for irrational a. We show that the associated gauge symmetry is responsible for the conservation of the total probability of the localization of the field in space. This provides a simple resolution of the paradoxical situation resulting from the fact that the probability current density for free scalar fields is neither covariant nor conserved. Furthermore, we discuss the implications of our approach for free real scalar fields offering a direct proof of the uniqueness of the relativistically invariant positive-definite inner product on the space of real Klein-Gordon fields. We also explore an extension of our results to scalar fields minimally coupled to an electromagnetic field.

We use the formulation of the quantum mechanics of first quantized Klein-Gordon fields given in the first of this series of papers to study relativistic coherent states. In particular, we offer an explicit construction of coherent states for both charged and neutral (real) free Klein-Gordon fields as well as for charged fields interacting with a constant magnetic field. Our construction is free from the problems associated with charge-superselection rule that complicated the previous studies. We compute various physical quantities associated with our coherent states and present a detailed investigation of their classical (nonquantum) and nonrelativistic limits.

We construct the most general physically admissible positive-definite inner product on the space of Proca fields. Up to a trivial scaling this defines a five-parameter family of Lorentz invariant inner products that we use to construct a genuine Hilbert space for the quantum mechanics of Proca fields. If we identify the generator of time-translations with the Hamiltonian, we obtain a unitary quantum system that describes first-quantized Proca fields and does not involve the conventional restriction to the positive-frequency fields. We provide a rather comprehensive analysis of this system. In particular, we examine the conserved current density responsible for the conservation of the probabilities, explore the global gauge symmetry underlying the conservation of the probabilities, obtain a probability current density, construct position, momentum, helicity, spin, and angular momentum operators, and determine the localized Proca fields. We also compute the generalized parity (P), generalized time-reversal (T ), and generalized charge or chirality (C) operators for this system and offer a physical interpretation for its PT -, C-, and

The high-energy particles coming from the Sun with energies in the range of a few KeV to more than several GeV are called solar energetic particles (SEPs). Solar eruptions such as coronal mass ejections (CMEs) and solar flares are the important sources of SEPs (Gopalswamy et al., 2015;Krucker & Lin, 2000). Magnetic reconnection and waves are the crucial mechanisms for accelerating particles and the production of SEPs. Among SEPs, solar proton events (SPEs) are one of the most significant components of interplanetary streams and play an important role in space weather studies (Reames, 1999). SPEs can be spectacular as they are in auroras or be dangerous as they form solar storms. A solar storm is a flux of SEPs which is carried by the solar wind and can be detrimental to astronauts' health or damage the electrical devices in space or even on the Earth (Feynman & Gabriel, 2000;Jiggens et al., 2014). Simply, a geomagnetic storm can be defined as a major disturbance in the Earth's magnetic field that may be the result of sudden and drastic changes in the solar wind (Taran et al., 2019, and references therein), leading to changes in the current, plasma, and magnetic fields of the magnetosphere. It is accepted that the geomagnetic storms on the Earth may affect radio communication and cause hardware damage on satellites and the global positioning system (GPS). Obviously, not all CMEs can cause a geomagnetic storm; conditions on the strength and direction of the interplanetary magnetic field need to create an intense storm (Gonzalez et al., 1994). Also, large speed and width increase the probability for a CME to create a geomagnetic storm (Gopalswamy et al., 2010). However, strong geomagnetic storms are most likely associated with large CMEs or CMEs associated with X-class flares (Srivastava & Venkatakrishnan, 2002). Recently, machine learning methods have been developed for forecasting the geomagnetic indices (Camporeale, 2019) and the occurrence time of large solar flares (Alipour et al., 2019) which are open challenges for the space weather community.Several researchers examined the dependence of SEP characteristics on flare parameters (

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