As discussed in previous papers,1 the nonlocal field was introduced in order to describe relativistically a system which was elementary in the sense that it could no longer be decomposed into more elementary constituents, but was so substantial, nevertheless, as to be able to contain implicitly a great variety of particles with different masses, spins, and other intrinsic properties. However, the conclusions reached so far were very unsatisfactory in many respects.2 Among other things, the masses of the particles associated with the irreducible nonlocal fields remained completely arbitrary and simple and plausible assumptions concerning the interaction between fields did not result in the expected convergence of self-energies. It seems to the author that these disappointing consequences are not inherent in nonlocal field theory, in general, but are rather related to the particular type of field to which the author restricted himself. Instead, if we start anew from less restricted nonlocal fields, a more promising aspect of possible nonlocal theories is revealed, as shown in the following.

Structure and Mass Spectrum of Elementary particles. I. General Considerations

In a model with B − L gauge symmetry, right-handed neutrinos may have exotic local B − L charge assignments: two of them with B − L = −4 and the other one having B − L = 5. Then, it is natural to accommodate the right-handed neutrinos with the same B − L charge in a doublet of the discrete S3 symmetry, and the third one in a singlet. If the Yukawa interactions involving right-handed neutrinos are invariant under S3, the quasi-Dirac neutrino scheme arises naturally in this model. However, we will show how in this scheme it is possible to give a value for θ13 in agreement with the Daya Bay results. For example the S3 symmetry has to be broken in the Yukawa interactions involving right-handed charged leptons.

Quasi-Dirac neutrinos in a model with local B - L symmetry

On the CP -noninvariant equations for the particle with zero mass and spin s = 1/2

https://www.imath.kiev.ua/~fushchych/papers/1970_2.pdf

On the P- and T-non-invariant two-component equation for the neutrino

Elko spinors are eigenspinors of the charge conjugation operator. In this work we use the Clifford algebra of the physical space in order to formulate the theory of Elko spinors and use a procedure analog to Ryder’s derivation of Dirac equation to come up with an equation for Elko spinor fields. Unlike other works in the literature where an equation for Elko spinor fields has been studied, in this work we obtain a first order differential equation for Elko spinor fields, which resembles but is different from the Dirac equation.

The Clifford Algebra of Physical Space and Elko Spinors

A new wave equation of a neutrino, which is a natural counterpart of the electromagnetic equation, is proposed. Though the ordinary two-component neutrino equation is itself P- and C-invariant, the new equation is not invariant against parity and charge conjugation separately but is CP-invariant. The accepted V-A interaction is explained as a potential interaction of our neutrino. The field is quantized only by generalizing the Hilbert space.

A Proposal of Neutrino Equation

A quantization of a spinor field is analyzed on the basis of the general Lagrangian, which gives the Dirac equation, in the generalized Hilbert space. The Lagrangian is classified into three; the first one is essentially equivalent to the Dirac one except for sign and is rather docile, the second is a new type and the field considered should be quantized essentially in an indefinite metric space, and the third is the Majorana one. It is also shown that the first field is a mixture of two definite or two indefinite Majorana fields and the second is a mixture of a definite and an indefinite Majorana fields. The expansion of a field in momentum space to get a particle interpretation is rather obvious for the first field but not for the second.

A quantization of a spinor field in the generalized Hilbert space

Spinor Field and Its Transformations

/pdf/some-remarks-on-the-non-local-field-theory-1yue95yih3.pdf

Zensuke Tokuoka

Papers

A Proposal of Neutrino Equation

A quantization of a spinor field in the generalized Hilbert space

Spinor Field and Its Transformations

Some Remarks on the Non-local Field Theory