Group Theoretical Derivation of Consistent Massless Particle Theories

Nisticò, Giuseppe

doi:10.1007/s10701-021-00494-1

Cited by 2 publications

(3 citation statements)

References 18 publications

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“…For the zero mass case the helicity operator λ = J•P p 0 plays an important role. Theorem 4.1 and (5) imply [16] that λ = 0 for the triplets in I ± 0 . Using theorem 4.1 we see that λ = − m 2 for every triplet of I −+ 0 with U + irreducible.…”

Section: Scipost Physicsmentioning

confidence: 93%

“…The mathematical group structural properties of P imply [12], [16] that each irreducible triplet (U, S, T) is characterized by a number µ ∈ I C, called mass, with µ 2 ∈ IR, such that P 2 0 − P 2 = µ 2 1I.…”

Section: Quantum Theoretical Implications For An Elementary Free Part...mentioning

confidence: 99%

“…In [16] the irreducible triplets of I + 0 and I − 0 with U irreducible, and of I −+ 0 with U + irreducible are completely identified. The results are collected by the following statement.…”

Section: Zero Mass Irreducible Tripletsmentioning

confidence: 99%

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Group Theoretical Derivation of Consistent Free Particle Theories

Nisticò

2020

Found Phys

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The difficulties of relativistic particle theories formulated by means of canonical quantization, such as those of Klein-Gordon and Dirac, ultimately led theoretical physicists to turn to quantum field theory to model elementary particle physics. In order to overcome these difficulties, the theories of the present approach are developed deductively from the physical principles that specify the system, without making use of canonical quantization. For a free particle these starting assumptions are invariance of the theory and covariance of position with respect to Poincaré transformations. In pursuing the approach, the effectiveness of group theoretical methods is exploited. The coherent development of our program has shown that robust classes of representations of the Poincaré group, discarded by the known particle theories, can in fact be taken as bases for perfectly consistent theories. For massive spin zero particles, six inequivalent theories have been determined, two of which do not correspond to any of the current ones; all of these theories overcome the difficulties of Klein-Gordon one. The present lack of the explicit transformation properties of position with respect to boosts prevents the complete determination of non zero spin particle theories. In the past a particular form of these transformation properties was adopted by Jordan and Mukunda. We check its consistency within the present approach and find that for spin 1 2 particles there is only one consistent theory, which is unitarily related to Dirac's; yet, once again, it requires classes of irreducible representations previously discarded. 1 Motivations and Overview Canonical quantization was the primary method for formulating specific relativistic particle theories [1-3]; unlike the non-relativistic case, the results were affected by problems. The first problem was the order of the wave equation for a spin zero free B Giuseppe Nisticò

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Section: Scipost Physicsmentioning

confidence: 93%

Section: Quantum Theoretical Implications For An Elementary Free Part...mentioning

confidence: 99%

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Group Theoretical Derivation of Consistent Free Particle Theories

Nisticò

2020

Found Phys

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Group theoretical derivation of consistent particle theories

Nisticò

2023

SciPost Phys. Proc.

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Current quantum theories of an elementary free particle assume unitary space inversion and anti-unitary time reversal operators. In so doing robust classes of possible theories are discarded. The present work shows that consistent theories can be derived through a strictly deductive development from the principle of relativistic invariance and position covariance, also with anti-unitary space inversion and unitary time reversal operators. In doing so the class of possible consistent theories is extended for positive but also zero mass particles. In particular, consistent theories for a Klein-Gordon particle are derived and the non-localizability theorem for a non zero helicity massless particle is extended.

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Group Theoretical Derivation of Consistent Massless Particle Theories

Cited by 2 publications

References 18 publications

Group Theoretical Derivation of Consistent Free Particle Theories

Group Theoretical Derivation of Consistent Free Particle Theories

Group theoretical derivation of consistent particle theories

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