Some remarks about intrinsic parity in Ryder’s derivation of the Dirac equation

Gaioli, Fabian H.; Álvarez, Edgardo

doi:10.1119/1.17979

Cited by 44 publications

(22 citation statements)

References 9 publications

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“…The momentum-space wave equation satisfied by ψ(p) thus constructed follows uniquely [32,59,60] from the interplay of…”

Section: The Dirac Constructmentioning

confidence: 99%

“…We present a unified method which applies not only to the Elko but equally well to the Dirac framework. The method is a generalization of the textbook procedure to obtain 'wave operators' [32] with corrections noted in [20,59,60,72]. We introduce a general (1/2, 0) ⊕ (0, 1/2) spinor,…”

Section: Non-trivial Connection Between the Spin Sums And Wave Operatmentioning

confidence: 99%

“…Our walk in search of this operator is leisurely, and we do not refrain from stopping to look at other aspects which these operators may carry. In a particle's rest frame, by definition [32,59,60,72,84],…”

Section: Non-trivial Connection Between the Spin Sums And Wave Operatmentioning

confidence: 99%

“…59) 60) where the O λ S,A (p) are now written without invoking the second equality in equation (5.49), but instead are defined using equation (5.48) -the only difference being that now no dispersion relation is invoked explicitly. Then, P S P A = 0 implies the dispersion relation.…”

Section: The O For Elkomentioning

confidence: 99%

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Spin-half fermions with mass dimension one: theory, phenomenology, and dark matter

Ahluwalia

Grumiller

2005

J. Cosmol. Astropart. Phys.

180

260

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Abstract:We provide the first details on the unexpected theoretical discovery of a spinone-half matter field with mass dimension one. It is based upon a complete set of dualhelicity eigenspinors of the charge conjugation operator. Due to its unusual properties with respect to charge conjugation and parity, it belongs to a non-standard Wigner class. Consequently, the theory exhibits non-locality with (CP T ) 2 = −I. We briefly discuss its relevance to the cosmological 'horizon problem'. Because the introduced fermionic field is endowed with mass dimension one, it can carry a quartic self-interaction. Its dominant interaction with known forms of matter is via Higgs, and with gravity. This aspect leads us to contemplate the new fermion as a prime dark matter candidate. Taking this suggestion seriously we study a supernova-like explosion of a galactic-mass dark matter cloud to set limits on the mass of the new particle and present a calculation on relic abundance to constrain the relevant cross-section. The analysis favours light mass (roughly 20 MeV) and relevant cross-section of about 2 pb. Similarities and differences with the WIMP and mirror matter proposals for dark matter are enumerated. In a critique of the theory we bare a hint on non-commutative aspects of spacetime, and energy-momentum space.Keywords: dark matter, quantum field theory on curved space.To celebrate the birthday of my wife Dr I S Ahluwalia-Khalilova and in memory of my father Shri B S Ahluwalia (1933-1977

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“…The momentum-space wave equation satisfied by ψ(p) thus constructed follows uniquely [32,59,60] from the interplay of…”

Section: The Dirac Constructmentioning

confidence: 99%

Section: Non-trivial Connection Between the Spin Sums And Wave Operatmentioning

confidence: 99%

Section: Non-trivial Connection Between the Spin Sums And Wave Operatmentioning

confidence: 99%

Section: The O For Elkomentioning

confidence: 99%

See 2 more Smart Citations

Spin-half fermions with mass dimension one: theory, phenomenology, and dark matter

Ahluwalia

Grumiller

2005

J. Cosmol. Astropart. Phys.

180

260

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“…In [147] the derivation of [130] was repeated together with taking into account the physical meaning of the negative energies and the relative intrinsic parity of the elementary particles. The authors believe that the derivation from [130] is improved.…”

Section: Briefly On the Different Ways Of The Dirac Equation Derivationmentioning

confidence: 99%

On the Relativistic Canonical Quantum Mechanics and Field Theory of Arbitrary Spin

Simulik¹

2017

ujpa

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The new relativistic equations of motion for the particles with arbitrary spin and nonzero mass, suggested by author in years 2014-2016, are under consideration. The complete version of brief paper in J. Phys: Conf. Ser., 670 (2016) 012047(1-16) is given. The axiomatic level description of the relativistic canonical quantum mechanics of an arbitrary mass and spin has been given. The 64-dimensional Cl R (0,6) algebra in terms of Dirac gamma matrices has been suggested. The interpretation of the 28-dimensional gamma matrix representation of SO(8) algebra over the field of real numbers is given. The link between the relativistic canonical quantum mechanics of the arbitrary spin and the covariant local field theory in the form of extended Foldy-Wouthuysen transformation has been found. Different methods of the Dirac equation derivation have been reviewed. The manifestly covariant field equation for an arbitrary spin, that follows from the corresponding equation of relativistic canonical quantum mechanics, has been considered. The found equations are without redundant components. The partial examples for spin s=3/2 and s=2 are presented. The covariant local field theory equations for spin s = (3/2,3/2) particle-antiparticle doublet and spin s = (2,2) particle-antiparticle doublet have been introduced. The Maxwell and slightly generalized Maxwell-like equations containing mass member have been considered as well.

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Fermions, Bosons, and Locality in Special Relativity with Two Invariant Scales

Ahluwalia-Khalilova

2004

Beyond the Desert 2003

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We present a Master equation for description of fermions and bosons for special relativities with two invariant scales (c and λP ). We introduce canonically-conjugate variables χ 0 , χ to (ǫ, π) of Judes-Visser. Together, they bring in a formal element of linearity and locality in an otherwise nonlinear and non-local theory. Special relativities with two invariant scales provide all corrections, say, to the standard model of the high energy physics, in terms of one fundamental constant, λP . It is emphasized that spacetime of special relativities with two invariant scales carries an intrinsic quantum-gravitational character.

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Some remarks about intrinsic parity in Ryder’s derivation of the Dirac equation

Cited by 44 publications

References 9 publications

Spin-half fermions with mass dimension one: theory, phenomenology, and dark matter

Spin-half fermions with mass dimension one: theory, phenomenology, and dark matter

On the Relativistic Canonical Quantum Mechanics and Field Theory of Arbitrary Spin

Fermions, Bosons, and Locality in Special Relativity with Two Invariant Scales

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