arXiv subjects

E. G. Delgado-Acosta

Publications and source records attributed to E. G. Delgado-Acosta.

7 recordsLinked to original sources

arXiv2013

Second order theory of $(j,0)\oplus (0,j)$ single high spins as Lorentz tensors

We show that higher order differential equations and matrix spinor calculus are completely avoidable in the description of pure high spin-$j$ Weinberg-Joos states, $(j,0)\oplus (0,j)$. The case is made on the example of $(3/2,0)\oplus(0,3/2)$, for the sake of concreteness and without loss of generality. Namely, we use as a vehicle for the aforementioned covariant single spin-$3/2$ description the antisymmetric tensor of second rank with Dirac spinor components, $Ψ_{[μν]}=B_{[μν]}\otimesψ$. The $(3/2,0)\oplus(0,3/2)$ sector of interest is tracked down in two steps. First we search for spin-$3/2$ by means of a covariant spin projector constructed from the Casimir invariants of the Poincaré algebra, and then we identify the wanted irreducible representation space by means of a momentum independent (static) projector designed on the basis of the Casimir invariants of the Lorentz algebra. The latter projectors unambiguously identify any irreducible $so(1,3)$ subspace of any Lorentz tensor and without rising the order of the differential equation. The method proposed correctly reproduces the electromagnetic multipole moments earlier calculated for single spin-$3/2$ particles in treating it in the standard way as eight dimensional spinor. We furthermore calculate Compton scattering off the pure spin-$3/2$ under discussion, and show that the differential cross section satisfies unitarity in forward direction for a gyromagnetic ratio of $g=2/3$. Suggesting possible validity of Belinfante's conjecture for pure spin-states, while the natural value of $g=2$ seems more likely to characterize the highest spins in the Rarita-Schwinger representation spaces. The scheme straightforwardly extends to any $(j,0)\oplus (0,j)$ Weinberg-Joos state and brings the advantage of avoiding rectangular matrix couplings between states of different spins, replacing them by simple Lorentz contractions.

hep-ph↗

arXiv2013

Status of the lower spins in the Rarita-Schwinger four-vector spinor $ψ_μ$ within the method of the combined Lorentz- and Poincaré invariant projectors

We investigate the status of the lower spin-1/2 companions to spin-3/2 within the four-vector spinor, $ψ_μ$. According to its reducibility, $ψ_μ\longrightarrow \left[(1/2,1)\oplus (1,1/2)\right]\oplus [(1/2,0)\oplus (0,1/2)]$ this representation space contains two spin-1/2 sectors, the first one transforming as a genuine Dirac-spinor, $(1/2,0)\oplus (0,1/2)$, and the second as the companion to spin-3/2 in $(1/2,1)\oplus (1,1/2)$. In order to correctly identify the covariant spin-1/2 degrees of freedom in the Rarita-Schwinger field of interest we exploit the properties of the Casimir invariants of the Lorentz algebra to distinguish between the irreducible Dirac- and $(1/2,1)\oplus (1,1/2)$ representation spaces and construct corresponding momentum-independent (static) projectors which we then combine with a dynamical spin-1/2 Poincaré covariant projector. In so doing we obtain two spin-1/2 wave equation, and prove them to be causal within an electromagnetic field. We furthermore calculate Compton scattering off each one of the above states, and find that the amplitudes corresponding to the first spin-1/2 are identical to those of a Dirac particle and conclude on the observability of this state. Also for the second spin-1/2 we find finite cross sections in all directions in the ultra-relativistic limit, and conclude that its observability is not excluded neither by causality of propagation within an electromagnetic environment, nor by unitarity of the Compton scattering amplitudes in the ultraviolet. Finally, we notice that the method of the combined Lorentz- and Poincaré invariant projectors could be instrumental in opening a new avenue toward the consistent description of any spin by means of second order Lagrangians written in terms of sufficiently large reducible representation spaces equipped with separate Lorentz-- and Dirac indices.

hep-ph↗

arXiv2013

Compton scattering off massive fundamental bosons of pure spin 1

Relativistic particles with spins $J>0$ are described by means of multicomponent wave functions which transform covariantly according to Lorentz-group representations that contain at rest the spin of interest. The symmetry group of space-time provides not one but an infinity of such representations which are equivalent for free particles but yield different electromagnetic couplings upon gauging; thus the challenge is to develop criteria which allow us to select those of them which relate to physically detectable particles. We here take the position that the unitarity of the Compton scattering cross sections in the ultrarelativistic limit, when predicted by a consistent method for a spin-$1$ description, could provide such a criterion. We analyze the properties of massive fundamental spin-$1$ bosons transforming as antisymmetric tensors of second rank, $(1,0)\oplus(0,1)$. For this purpose, we employ the Poincaré covariant projector method, which provides consistent, causal, and representation specific Lagrangians. This formalism yields a twofold extension of the Proca Lagrangian for the description of spin-$1$ bosons, first from an in-built $g=1$ value of the gyromagnetic ratio to an unspecified $g\not=1$, and from, single-parity, to parity-doublet degrees of freedom. We find different results for Compton scattering in these theories and track the differences to the lack of universality of the vector-antisymmetric-tensor equivalence theorem which is specific only to Proca's framework, and valid for $g=1$, while it is violated within the covariant projector formalism. Our main result is that a finite Compton scattering differential cross section in the ultrarelativistic limit requires us to consider the contributions of both parities in $(1,0)\oplus(0,1)$. On that basis, we conclude that massive spin-$1$ bosons transforming as antisymmetric tensors are physical parity doublets.

hep-th↗

arXiv2012

Electromagnetic multipole moments of elementary spin-1/2, 1, and 3/2 particles

We study multipole decompositions of the electromagnetic currents of spin-1/2, 1, and 3/2 particles described in terms of Lagrangians designed to reproduce representation specific wave equations which are second order in the momenta and which emerge within the recently elaborated Poincaré covariant projector method. We calculate the electric multipoles of the above spins for the spinor, the four-vector, and the four-vector--spinor representations, attend to the most general non-Lagrangian spin-3/2 currents which are allowed by Lorentz invariance to be of third order in the momenta and construct the linear current equivalent of identical multipole moments of one of them. We conclude that such non-Lagrangian currents are not necessarily more general than the two-term currents emerging within the covariant projector method. We compare our results with those of the conventional Proca-, and Rarita-Schwinger frameworks. Finally, we test the representation dependence of the multipoles by placing spin-1 and spin-3/2 in the respective (1,0)$\oplus$(0,1), and (3/2,0)$\oplus$(0,3/2) single-spin representations. We observe representation independence of the charge monopoles and the magnetic dipoles, in contrast to the higher multipoles, which turn out to be representation dependent. In particular, we find the bi-vector $(1,0)\oplus (0,1)$ to be characterized by an electric quadrupole moment of opposite sign to the one found in $(1/2,1/2)$, and consequently, to the $W$ boson. Our finding points toward the possibility that the $ρ$ meson could transform as part of an antisymmetric tensor with an $a_{1}$ meson-like state as its representation companion.

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arXiv2010

Second order formalism for spin 1/2 fermions and Compton scattering

We develop a second order formalism for spin 1/2 fermions based on the projection over Poincaré invariant subspaces in the $(1/2,0)\oplus(0,1/2)$ representation of the homogeneous Lorentz group. Using $U(1)_{em}$ gauge principle we obtain second order description for the electromagnetic interactions of a spin 1/2 fermion with two free parameters, the gyromagnetic factor $g$ and a parameter $ξ$ related to odd-parity Lorentz structures. We calculate Compton scattering in this formalism. In the particular case $g=2, ξ=0$ and for states with well defined parity we recover Dirac results. In general, we find the correct classical limit and a finite value $r_{c}^{2}$ for the forward differential cross section, independent of the photon energy and of the value of the parameters $g$ and $ξ$. The differential cross section vanishes at high energies for all $g, ξ$ except in the forward direction. The total cross section at high energies vanishes only for $g=2, ξ=0$. We argue that this formalism is more convenient than Dirac theory in the description of low energy electromagnetic properties of baryons and illustrate the point with the proton case.

hep-ph↗

arXiv2009

Compton scattering off elementary spin 3/2 particles

We calculate Compton scattering off an elementary spin 3/2 particle in a recently proposed framework for the description of elementary high spin fields based on the projection onto eigen-subspaces of the Casimir operators of the Poincare group. We also calculate this process in the conventional Rarita-Schwinger formalism. Both formalisms yield the correct Thomson limit but the predictions for the angular distribution and total cross section differ beyond this point. We point out that the average squared amplitudes in the forward direction for Compton scattering off targets with spin s = 0, 1/2, 1 are energy-independent and have the common value 4e^4. As a consequence, in the rest frame of the particle the differential cross section for Compton scattering in the forward direction is energy independent and coincides with the classical squared radius. We show that these properties are also satisfied by a spin 3/2 target in the Poincare projector formalism but not by the Rarita-Schwinger spin 3/2 particle.

hep-th↗

arXiv2007

Electromagnetic couplings of elementary vector particles

On the basis of the three fundamental principles of (i) Poincaré symmetry of space time, (ii) electromagnetic gauge symmetry, and (iii) unitarity, we construct an universal Lagrangian for the electromagnetic interactions of elementary vector particles, i.e., massive spin-1 particles transforming in the /1/2,1/2) representation space of the Homogeneous Lorentz Group (HLG). We make the point that the first two symmetries alone do not fix the electromagnetic couplings uniquely but solely prescribe a general Lagrangian depending on two free parameters, here denoted by ξand g. The first one defines the electric-dipole and the magnetic-quadrupole moments of the vector particle, while the second determines its magnetic-dipole and electric-quadrupole moments. In order to fix the parameters one needs an additional physical input suited for the implementation of the third principle. As such, one chooses Compton scattering off a vector target and requires the cross section to respect the unitarity bounds in the high energy limit. In result, we obtain the universal g=2, and ξ=0 values which completely characterize the electromagnetic couplings of the considered elementary vector field at tree level. The nature of this vector particle, Abelian versus non-Abelian, does not affect this structure. Merely, a partition of the g=2 value into non-Abelian, g_{na}, and Abelian, g_{a}=2-g_{na}, contributions occurs for non-Abelian fields with the size of g_{na} being determined by the specific non-Abelian group appearing in the theory of interest, be it the Standard Model or any other theory.

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