Majorana Equations for Composite Systems

Bisiacchi, G.; Budini, P.

doi:10.1103/physrev.172.1508

Cited by 15 publications

(17 citation statements)

References 20 publications

(4 reference statements)

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“…Majorana formulated an equation for elementary particles; however, there are no restrictions to apply it to ordinary particles. The scientific literature includes uses of the Majorana equation to investigate composite systems like the hydrogen atom [16]. This also justifies the equation's use in this work.…”

Section: Methodological Approachmentioning

confidence: 67%

Space-like Particle Production: An Interpretation Based on the Majorana Equation

Nanni¹

2018

ujpa

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Section: Methodological Approachmentioning

confidence: 67%

Space-like Particle Production: An Interpretation Based on the Majorana Equation

Nanni¹

2018

ujpa

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“…The scientific literature includes uses of the Majorana equation to investigate composite systems like the hydrogen atom [16]. This also justifies the equation's use in this work.…”

Section: Methodological Approachmentioning

confidence: 87%

“…A relativistic quantum theory that includes tachyons requires an infinite-dimensional representation of the Lorentz group (1,3) [7][8][9][10][11][12][13][14][15][16][17]. Majorana formulated his equation using just this algebraical framework [14].…”

Section: Bradyons and Tachyons From The Perspective Of Majorana's Equmentioning

confidence: 99%

Space-Like Particle Production: an Interpretation Based on the Majorana Equation

Nanni¹

2016

Preprint

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This study reconsiders the decay of an ordinary particle in bradyons, tachyons and luxons in the field of the relativistic quantum mechanics. Lemke already investigated this from the perspective of covariant kinematics. Since the decay involves both space-like and time-like particles, the study uses the Majorana equation for particles with an arbitrary spin. The equation describes the tachyonic and bradyonic realms of massive particles, and approaches the problem of how space-like particles might develop. This method confirms the kinematic constraints that Lemke's theory provided and proves that some possible decays are more favourable than others are. IntroductionThe study of faster-than-light particles is a branch of theoretical physics still much debated. It leads to speculations and discussions ranging from a purely scientific scope to a metaphysicalphilosophical one [1][2][3][4][5]. In the second half of the last century, several physicists developed an intensive effort to extend the theory of relativity. Their goal was to apply it to massive particles travelling at velocities higher than the speed of light. Among these physicists, the names of Recami, Surdashan and Feinberg stand out [5][6][7]. They introduced the reinterpretation principle, similar to the one Feynman-Stueckelberg proposed to explain the negative energy of antiparticles in quantum field theory. This solved the superluminal propagation dilemma by restoring the principle of causality. Yet things do not go as well when we attempt to introduce the tachyon into quantum field theory. Problems such as vacuum instability and the violation of change, parity and time reversal (CPT) symmetry are hard to solve [6,[8][9][10]. Physicists have solved these issues separately; but so far, there is not a field theory able to explain the quantum behaviour of subluminal and superluminal massive particles without encountering the problems mentioned. For instance, if a theory imposed compliance with the CPT theorem, then the relationship between spin and statistics Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 4

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“…In other words, all spins are simultaneously representations of the inhomogeneous Lorentz groups obtained while only considering the spacetime symmetries [8]. The Majorana equation has two possible applications depending on the interpretation given to the wave function: particles with arbitrary spin or composite systems [8][9][10][11]. Therefore, this equation may be particularly useful in studying the structure of nuclear systems and their prospective high energy exotic states.…”

Section: Introductionmentioning

confidence: 99%

Determining a Quantum Theory of the Infinite-Component Majorana Field

Nanni¹

2017

Preprint

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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 bradyontachyon, 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. IntroductionThe formulation of the quantum field theory based on the finite-dimensional representation of the Lorentz group led to the standard model (SM) and coherently explained most of the experimental results [1][2][3][4]. However, the representation is neither complete nor unitary [5,6]. This gap can be filled through an infinite-dimensional representation, where boosts and rotations take the form of infinite matrices. In principle, a theory whose equations are covariant with respect to the infinite-dimensional representations could predict new particles or new structures of matter not contemplated in the picture of the SM. Although with different aims, Majorana formulated in 1932 a relativistic equation for particle with arbitrary spin [7], which it is a universal equation that describes the physical nature of bosons, fermions and luxons that depends on the considered spin and mass. In other words, all spins are simultaneously representations of the inhomogeneous Lorentz groups obtained while only considering the spacetime symmetries [8]. The Majorana equation has two possible applications depending on the interpretation given to the wave function: particles with arbitrary spin or composite systems [8][9][10][11]. Therefore, this equation may be particularly useful in studying the structure of nuclear systems and their prospective high energy exotic states. However, the solution of the Majorana equation leads to results that contrast with physical reality (particle with only positive frequency, mass spectrum that asymptotically decreases with spin increasing, spacelike solutions) [12]. Moreover, the attempt to quantise the infinitecomponent Majorana field violates CPT invariance and is inconsistent with the spin-statistic Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted:

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Majorana Equations for Composite Systems

Cited by 15 publications

References 20 publications

Space-like Particle Production: An Interpretation Based on the Majorana Equation

Space-like Particle Production: An Interpretation Based on the Majorana Equation

Space-Like Particle Production: an Interpretation Based on the Majorana Equation

Determining a Quantum Theory of the Infinite-Component Majorana Field

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