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Papers by Dharam Vir Ahluwalia

Recent theoretical work reporting the construction of a new quantum field of spin one half fermio... more Recent theoretical work reporting the construction of a new quantum field of spin one half fermions with mass dimension one requires that Weinberg's no go theorem must be evaded. Here we show how this comes about. The essence of the argument is to first define a quantum field with due care being taken in fixing the locality phases attached to each of the expansion coefficients. The second ingredient is to systematically construct the adjoint/dual of the field. The Feynman-Dyson propagator constructed from the vacuum expectation value of the field and its adjoint then yields the mass dimensionality of the field. For a quantum field constructed from a complete set of eigenspinors of the charge conjugation operator, with locality phases judiciously chosen, the Feynman-Dyson propagator has mass dimension one. The Lorentz symmetry is preserved, locality anticommutators are satisfied, without violating fermionic statistics as needed for the spin one half field. Significance. In 1928 Dirac discovered a formalism to describe spin one half fermions. That formalism is generally considered unique and all matter fields of the standard model of high energy physics are formulated in terms of the Dirac's proposal. Here, we find an important theoretical crevice that allows a fundamentally different formalism to describe spin one half fermions. These new fermions have mass dimension one, as opposed to three halves of the Dirac fermions, and thus they cannot enter the standard model doublets. So, in effect, we here construct darkness of the dark matter.

We introduce a fermionic spin one-half quantum field with eigenspinors of the charge conjugation ... more We introduce a fermionic spin one-half quantum field with eigenspinors of the charge conjugation operator as its expansion coefficients. For the eigenspinors we make a very specific choice of the locality phases and provide their explicit expressions. We construct an analytic proof that these do not satisfy Dirac equation. Under the Dirac dual the naive expectation for the Lagrangian density fails and we use this fact to motivate and undertake a mathematical theory of duals for the spinors, and provide the correct spinorial Lagrangian density. We use the new dual to introduce an adjoint for the introduced quantum field. It differs from the standard adjoint given, for example, in Weinberg's classic on the theory of quantum fields. Without reference to any Lagrangian density or a wave equation we evaluate the Feynman-Dyson propagator for the field. It is determined not only by the knowledge of the quantum field but also by the definition of the field adjoint. It establishes the mass dimensionality of the field to be 1, and not 3/2, thus leading to an unexpected Lagrangian density for the new fermions. This allows us to evaluate the locality anti-commutators. The result of calculations presented here shows the new field to be local in the sense of Schwinger. The entire formalism is Lorentz covariant. 1

A consistent phenomenology of the interaction of particles of arbitrary spin requires covariant s... more A consistent phenomenology of the interaction of particles of arbitrary spin requires covariant spinors, eld operators, propagators and model interactions. Guided by an approach originally proposed by Weinberg, we construct from group theoretical arguments the (j; 0) (0; j) covariant spinors and the eld operators for a massive particles. Speci c examples are worked out in the familiar language of the Bjorken and Drell text for the case of the (1; 0) (0; 1), (3=2; 0) (0; 3=2) and (2; 0) (0; 2) matter elds. The m ! 0 limit of the covariant spinors is shown to have the expected structure. The algebra of the matrices associated with the (1; 0) (0; 1) matter elds is presented, and the conserved current derived. The procedure readily extends to higher spins. The causality problem associated with the j 1 wave equations is discussed in detail and a systematic procedure to construct causal propagators is provided. As an example a spin two wave equation satis ed by the (2; 0) (0; 2), covariant spinors is found to support not only ten correct and causal solutions, but also thirty physically unacceptable acausal solutions. However, we demonstrate how to construct the Feynman propagator for the higher spin particles directly from the spinors and thus avoid the shortcomings of the wave equation in building a phenomenology. The same exercise is repeated for the (1; 0) (0; 1) and (3=2; 0) (0; 3=2) matter elds, and the same conclusions obtained.

In this essay, an ab initio study of the self/anti-self charge conjugate (1/2, 0) ⊕ (0, 1/2) repr... more In this essay, an ab initio study of the self/anti-self charge conjugate (1/2, 0) ⊕ (0, 1/2) representation space is presented. Incompatibility of self/anti-self charge conjugation with helicity eigenstates and gauge interactions is demonstrated. Parity violation is seen as an intrinsic part of the self/anti-self charge conjugate construct. From a phenomenological point of view, an essential part of the theory is the Bargmann-Wightman-Wigner-type boson, where a boson and its antiboson carry opposite relative intrinsic parity.

The recently introduced mechanism of flavor-oscillation clocks has been used to emphasize observa... more The recently introduced mechanism of flavor-oscillation clocks has been used to emphasize observability of constant gravitational potentials and thereby to question completeness of the theory of general relativity. An inequality has been derived to experimentally test the thesis presented.

Chinese Journal of Physics- Taipei-

ABSTRACT

Nature

Theories of quantum gravity attempt to combine quantum mechanics -which reigns supreme at the ato... more Theories of quantum gravity attempt to combine quantum mechanics -which reigns supreme at the atomic scale -and the classical theory of general relativity, which governs planets and galaxies. The era of quantum gravity began about 50 years ago with the pioneering work of Chandrasekhar, when it was realized that quantum mechanics and gravitation combine in a fundamental manner to form white dwarfs -the Earth-sized stars of roughly a solar mass. That singular discovery had to wait another 25 years for the excitement to begin afresh with the ideas put forward by Bekenstein, Hawking, Unruh, and Wheeler, among others. Yet, the present activity runs the danger of evolving into a mathematical science fiction in the absence of an experimental counterpart. For the last quarter of a century an important, though limited, experimental quantum-gravity programme has existed. Giovanni Amelino-Camelia's paper on page 216 of this issue[1] adds to this in a fundamental and significant manner by suggesting that the fuzziness of space-time is experimentally accessible. Using existing data from a certain type of gravity wave detector he is able to set significant bounds on proposed quantum properties of space-time. Instruments under construction promise to take us far beyond.

Recent results on neutrinoless double beta decay, as reported by Klapdor-Kleingrothaus et al., ta... more Recent results on neutrinoless double beta decay, as reported by Klapdor-Kleingrothaus et al., take us for the first time into the realm of Majorana spacetime structure. However, this structure has either been treated as an afterthought to the Dirac construct; or, when it has been attended to in its own right, its physical and mathematical content was never fully unearthed. In this Letter, we undertake to remedy the existing situation. We present a detailed formalism required for the description of the non-trivial spacetime structure underlying the ν ⇋ ν metamorphosis -where ν generically represents a massive Majorana neutrino, or a massive gaugino.

In a 1996 JRO Fellowship Research Proposal (Los Alamos), the author suggested that neutrino oscil... more In a 1996 JRO Fellowship Research Proposal (Los Alamos), the author suggested that neutrino oscillations may provide a powerful indirect energy transport mechanism to supernovae explosions. The principal aim of this addendum is to present the relevant unedited text of Section 1 of that proposal. We then briefly remind, (a) of an early suggestion of Mazurek on vacuum neutrino oscillations and their relevance to supernovae explosion, and (b) Wolfenstein's result on suppression of the effect by matter effects. We conclude that whether or not neutrino oscillations play a significant role in supernovae explosions shall depend if there are shells/regions of space in stellar collapse where matter effects play no essential role. Should such regions exist in actual astrophysical situations, the final outcome of neutrino oscillations on supernovae explosions shall depend, in part, on whether or not the LNSD signal is confirmed. Importantly, the reader is reminded that neutrino oscillations form a set of flavor-oscillation clocks and these clock suffer gravitational redshift which can be as large as 20 percent. This effect must be incorporated fully into any calculation of supernova explosion.

In this talk I review a series of recent conceptual developments at the interface of the quantum ... more In this talk I review a series of recent conceptual developments at the interface of the quantum and gravitational realms. Wherever possible, I comment on the possibility to probe the interface experimentally. It is concluded that the underlying spacetime for a quantum theory of gravity must be non-commutative, that wave-particle duality suffers significant modification at the Planck scale, and that the latter forbids probing spacetime below Planck length. Furthermore, study of quantum test particles in classical and quantum sources of gravity puts forward theoretical challenges and new experimental possibilities. It is suggested that existing technology may allow to probe gravitationally-modified wave particle duality in the laboratory,

We show that Majorana particles belong to the Wigner class of fermions in which the charge conjug... more We show that Majorana particles belong to the Wigner class of fermions in which the charge conjugation and the parity operators commute, rather than anticommute. Rigorously speaking, Majorana spinors do not satisfy the Dirac equation [a result originally due to M. Kirchbach, which we re-render here]. Instead, they satisfy a different wave equation, which we derive. This allows us to reconcile Stückelberg-Feynman interpretation with the Majorana construct. We present several new properties of neutral particle spinors and argue that discovery of Majorana particles constitutes dawn of a new era in spacetime structure.

We argue that existing doubly special relativities may not be operationally distinguishable from ... more We argue that existing doubly special relativities may not be operationally distinguishable from the special relativity. In the process we point out that some of the phenomenologically motivated modifications of dispersion relations, and arrived conclusions, must be reconsidered. Finally, we reflect on the possible conceptual issues that arise in quest for a theory of spacetime with two invariant scales.

Recent theoretical work reporting the construction of a new quantum field of spin one half fermio... more Recent theoretical work reporting the construction of a new quantum field of spin one half fermions with mass dimension one requires that Weinberg's no go theorem must be evaded. Here we show how this comes about. The essence of the argument is to first define a quantum field with due care being taken in fixing the locality phases attached to each of the expansion coefficients. The second ingredient is to systematically construct the adjoint/dual of the field. The Feynman-Dyson propagator constructed from the vacuum expectation value of the field and its adjoint then yields the mass dimensionality of the field. For a quantum field constructed from a complete set of eigenspinors of the charge conjugation operator, with locality phases judiciously chosen, the Feynman-Dyson propagator has mass dimension one. The Lorentz symmetry is preserved, locality anticommutators are satisfied, without violating fermionic statistics as needed for the spin one half field. Significance. In 1928 Dirac discovered a formalism to describe spin one half fermions. That formalism is generally considered unique and all matter fields of the standard model of high energy physics are formulated in terms of the Dirac's proposal. Here, we find an important theoretical crevice that allows a fundamentally different formalism to describe spin one half fermions. These new fermions have mass dimension one, as opposed to three halves of the Dirac fermions, and thus they cannot enter the standard model doublets. So, in effect, we here construct darkness of the dark matter.

We introduce a fermionic spin one-half quantum field with eigenspinors of the charge conjugation ... more We introduce a fermionic spin one-half quantum field with eigenspinors of the charge conjugation operator as its expansion coefficients. For the eigenspinors we make a very specific choice of the locality phases and provide their explicit expressions. We construct an analytic proof that these do not satisfy Dirac equation. Under the Dirac dual the naive expectation for the Lagrangian density fails and we use this fact to motivate and undertake a mathematical theory of duals for the spinors, and provide the correct spinorial Lagrangian density. We use the new dual to introduce an adjoint for the introduced quantum field. It differs from the standard adjoint given, for example, in Weinberg's classic on the theory of quantum fields. Without reference to any Lagrangian density or a wave equation we evaluate the Feynman-Dyson propagator for the field. It is determined not only by the knowledge of the quantum field but also by the definition of the field adjoint. It establishes the mass dimensionality of the field to be 1, and not 3/2, thus leading to an unexpected Lagrangian density for the new fermions. This allows us to evaluate the locality anti-commutators. The result of calculations presented here shows the new field to be local in the sense of Schwinger. The entire formalism is Lorentz covariant. 1

A consistent phenomenology of the interaction of particles of arbitrary spin requires covariant s... more A consistent phenomenology of the interaction of particles of arbitrary spin requires covariant spinors, eld operators, propagators and model interactions. Guided by an approach originally proposed by Weinberg, we construct from group theoretical arguments the (j; 0) (0; j) covariant spinors and the eld operators for a massive particles. Speci c examples are worked out in the familiar language of the Bjorken and Drell text for the case of the (1; 0) (0; 1), (3=2; 0) (0; 3=2) and (2; 0) (0; 2) matter elds. The m ! 0 limit of the covariant spinors is shown to have the expected structure. The algebra of the matrices associated with the (1; 0) (0; 1) matter elds is presented, and the conserved current derived. The procedure readily extends to higher spins. The causality problem associated with the j 1 wave equations is discussed in detail and a systematic procedure to construct causal propagators is provided. As an example a spin two wave equation satis ed by the (2; 0) (0; 2), covariant spinors is found to support not only ten correct and causal solutions, but also thirty physically unacceptable acausal solutions. However, we demonstrate how to construct the Feynman propagator for the higher spin particles directly from the spinors and thus avoid the shortcomings of the wave equation in building a phenomenology. The same exercise is repeated for the (1; 0) (0; 1) and (3=2; 0) (0; 3=2) matter elds, and the same conclusions obtained.

In this essay, an ab initio study of the self/anti-self charge conjugate (1/2, 0) ⊕ (0, 1/2) repr... more In this essay, an ab initio study of the self/anti-self charge conjugate (1/2, 0) ⊕ (0, 1/2) representation space is presented. Incompatibility of self/anti-self charge conjugation with helicity eigenstates and gauge interactions is demonstrated. Parity violation is seen as an intrinsic part of the self/anti-self charge conjugate construct. From a phenomenological point of view, an essential part of the theory is the Bargmann-Wightman-Wigner-type boson, where a boson and its antiboson carry opposite relative intrinsic parity.

The recently introduced mechanism of flavor-oscillation clocks has been used to emphasize observa... more The recently introduced mechanism of flavor-oscillation clocks has been used to emphasize observability of constant gravitational potentials and thereby to question completeness of the theory of general relativity. An inequality has been derived to experimentally test the thesis presented.

Chinese Journal of Physics- Taipei-

ABSTRACT

Nature

Theories of quantum gravity attempt to combine quantum mechanics -which reigns supreme at the ato... more Theories of quantum gravity attempt to combine quantum mechanics -which reigns supreme at the atomic scale -and the classical theory of general relativity, which governs planets and galaxies. The era of quantum gravity began about 50 years ago with the pioneering work of Chandrasekhar, when it was realized that quantum mechanics and gravitation combine in a fundamental manner to form white dwarfs -the Earth-sized stars of roughly a solar mass. That singular discovery had to wait another 25 years for the excitement to begin afresh with the ideas put forward by Bekenstein, Hawking, Unruh, and Wheeler, among others. Yet, the present activity runs the danger of evolving into a mathematical science fiction in the absence of an experimental counterpart. For the last quarter of a century an important, though limited, experimental quantum-gravity programme has existed. Giovanni Amelino-Camelia's paper on page 216 of this issue[1] adds to this in a fundamental and significant manner by suggesting that the fuzziness of space-time is experimentally accessible. Using existing data from a certain type of gravity wave detector he is able to set significant bounds on proposed quantum properties of space-time. Instruments under construction promise to take us far beyond.

Recent results on neutrinoless double beta decay, as reported by Klapdor-Kleingrothaus et al., ta... more Recent results on neutrinoless double beta decay, as reported by Klapdor-Kleingrothaus et al., take us for the first time into the realm of Majorana spacetime structure. However, this structure has either been treated as an afterthought to the Dirac construct; or, when it has been attended to in its own right, its physical and mathematical content was never fully unearthed. In this Letter, we undertake to remedy the existing situation. We present a detailed formalism required for the description of the non-trivial spacetime structure underlying the ν ⇋ ν metamorphosis -where ν generically represents a massive Majorana neutrino, or a massive gaugino.

In a 1996 JRO Fellowship Research Proposal (Los Alamos), the author suggested that neutrino oscil... more In a 1996 JRO Fellowship Research Proposal (Los Alamos), the author suggested that neutrino oscillations may provide a powerful indirect energy transport mechanism to supernovae explosions. The principal aim of this addendum is to present the relevant unedited text of Section 1 of that proposal. We then briefly remind, (a) of an early suggestion of Mazurek on vacuum neutrino oscillations and their relevance to supernovae explosion, and (b) Wolfenstein's result on suppression of the effect by matter effects. We conclude that whether or not neutrino oscillations play a significant role in supernovae explosions shall depend if there are shells/regions of space in stellar collapse where matter effects play no essential role. Should such regions exist in actual astrophysical situations, the final outcome of neutrino oscillations on supernovae explosions shall depend, in part, on whether or not the LNSD signal is confirmed. Importantly, the reader is reminded that neutrino oscillations form a set of flavor-oscillation clocks and these clock suffer gravitational redshift which can be as large as 20 percent. This effect must be incorporated fully into any calculation of supernova explosion.

In this talk I review a series of recent conceptual developments at the interface of the quantum ... more In this talk I review a series of recent conceptual developments at the interface of the quantum and gravitational realms. Wherever possible, I comment on the possibility to probe the interface experimentally. It is concluded that the underlying spacetime for a quantum theory of gravity must be non-commutative, that wave-particle duality suffers significant modification at the Planck scale, and that the latter forbids probing spacetime below Planck length. Furthermore, study of quantum test particles in classical and quantum sources of gravity puts forward theoretical challenges and new experimental possibilities. It is suggested that existing technology may allow to probe gravitationally-modified wave particle duality in the laboratory,

We show that Majorana particles belong to the Wigner class of fermions in which the charge conjug... more We show that Majorana particles belong to the Wigner class of fermions in which the charge conjugation and the parity operators commute, rather than anticommute. Rigorously speaking, Majorana spinors do not satisfy the Dirac equation [a result originally due to M. Kirchbach, which we re-render here]. Instead, they satisfy a different wave equation, which we derive. This allows us to reconcile Stückelberg-Feynman interpretation with the Majorana construct. We present several new properties of neutral particle spinors and argue that discovery of Majorana particles constitutes dawn of a new era in spacetime structure.

We argue that existing doubly special relativities may not be operationally distinguishable from ... more We argue that existing doubly special relativities may not be operationally distinguishable from the special relativity. In the process we point out that some of the phenomenologically motivated modifications of dispersion relations, and arrived conclusions, must be reconsidered. Finally, we reflect on the possible conceptual issues that arise in quest for a theory of spacetime with two invariant scales.