Related papers: Quantization of massive fermions in vacuum and ext…
Two mathematical models based on Pauli transformations including U(1) chiral group and Pauli SU(2) group, that mixes particle and antiparticle states, are developed for description of Majorana properties of neutral particles. The first one…
We generalize Koopman-von Neumann classical mechanics to poly-symplectic fields and recover De Donder-Weyl theory. Comparing with Dirac's Hamiltonian density inspires a new Hamiltonian formulation with a canonical momentum field that is…
Cosmic background neutrinos ($C_{\nu}B)$ helicity composition is different for Dirac or Majorana neutrinos making detectors based on $C_{\nu}B$ capture sensitive to the nature of neutrinos. We calculate, for the first time, the helicity…
The fermionic nature of neutrinos and the origin of their tiny masses remain unresolved issues in particle physics, intrinsically connected to lepton number symmetry-conserved for Dirac, violated for Majorana, and effectively pseudo-Dirac…
We study the effect of a background flux string on the vacuum energy of massive Dirac fermions in 3+1 dimensions confined to a finite spatial region through MIT boundary conditions. We treat two admissible self-adjoint extensions of the…
Massive neutrinos are guaranteed to have nonzero electromagnetic moments and, since there are at least three neutrino species, these dipole moments define a matrix. Here, we estimate the current upper bounds on all independent neutrino…
The Dirac equation for massive free electrically neutral spin 1/2 particles in a gravitation field is considered. The secondary quantization procedure is applied to it and the Hilbert space of multiparticle quantum states is constructed.
We consider the algebra of massive fermions restricted to a diamond in two-dimensional Minkowski spacetime, and in the Minkowski vacuum state. While the massless modular Hamiltonian is known for this setting, the derivation of the massive…
Free noncommutative fields constitute a natural and interesting example of constrained theories with higher derivatives. The quantization methods involving constraints in the higher derivative formalism can be nicely applied to these…
Light-Front quantization is one of the most promising and physical tools towards studying deep inelastic scattering on the basis of quark gluon degrees of freedom. The simplified vacuum structure (nontrivial vacuum effects can only appear…
The statistical mechanics of nonrelativistic fermions in a constant magnetic field is considered from the quantum field theory point of view. The fermionic determinant is computed using a general procedure that contains all possible…
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…
An algebraic formalism for the study of a system of charged particles interacting with an external quantum field is developed. The notion of monoidal categories with duality is used for the description of composite systems and corresponding…
Dirac neutrino masses require two distinct neutral Weyl spinors per generation, with a special arrangement of masses and interactions with charged leptons. Once this arrangement is perturbed, lepton number is no longer conserved and…
We derive the neutrino oscillation probabilities including sterile neutrinos by using the Dirac equation. If neutrinos have both the Dirac and the Majorana mass terms, left-handed neutrino $\nu_L$ and right-handed anti-neutrino $\nu_R^c$…
The formulation of classical mechanics applicable to fermionic degrees of freedom is presented in mathematically rigorous terms, including a description of how the mathematical structure relates to the quantization of the theory. Canonical…
Recent research has revealed that the CRT symmetry for fermions exhibits a fractionalization distinct from the $\mathbb{Z}_2^{\mathcal{C}}\times\mathbb{Z}_2^{\mathcal{R}}\times\mathbb{Z}_2^{\mathcal{T}}$ for scalar bosons. In fact, the CRT…
In various dimensional Euclidean lattice gauge theories, we examine a compatibility of the Majorana decomposition and the charge conjugation property of lattice Dirac operators. In $8n$ and $1+8n$ dimensions, we find a difficulty to…
We present an open system interaction formalism for the Dirac equation. Overcoming a complexity bottleneck of alternative formulations, our framework enables efficient numerical simulations (utilizing a typical desktop) of relativistic…
We compute the effective action for stationary and spatially constant magnetic fields, when coupled anomalously to charge neutral fermions, by integrating out the fermions. From this the grand canonical partition function and potential of…