Determining a Quantum Theory of the Infinite-Component Majorana Field

TL;DR

This paper formulates a quantum theory for the infinite-component Majorana field, proposing that higher energy states are composite systems involving bradyons and tachyons, and explores their interactions within a CPT-invariant framework.

Contribution

It introduces a novel quantum field model for infinite-component Majorana fields, incorporating interactions and consistent with fundamental symmetries, potentially explaining new matter forms beyond the standard model.

Findings

Energy states are composite systems of bradyons and tachyons.

The quantum field is an infinite sum of four-spinor operators.

The theory is CPT invariant and consistent with spin-statistics.

Abstract

In this paper, the quantum theory of the infinite-component Majorana field for the fermionic tower is formulated. This study proves that the energy states with increasing spin are simply composite systems made by a bradyon and antitachyons with half-integer spin. The quantum field describing these exotic states is obtained by the infinite sum of four-spinor operators, which each operator depends on the spin and the rest mass of the bradyon in its fundamental state. The interaction between bradyon-tachyon, tachyon-tachyon and tachyon-luxon has also been considered and included in the total Lagrangian. The obtained theory is consistent with the CPT invariance and the spin-statistics theorem and could explain the existence of new forms of matter not predictable within the standard model.