%0 Journal Article %1 Acosta2015Bosonic %A Acosta, E. G. Delgado %A Guzman, V. M. Banda %A Kirchbach, M. %D 2015 %J The European Physical Journal A %K groups %N 3 %R 10.1140/epja/i2015-15035-x %T Bosonic and fermionic Weinberg-Joos (j,0)+ (0,j) states of arbitrary spins as Lorentz-tensors or tensor-spinors and second order theory %U http://dx.doi.org/10.1140/epja/i2015-15035-x %V 51 %X We propose a general method for the description of arbitrary single spin-j states transforming according to (j,0)+(0,j) carrier spaces of the Lorentz algebra in terms of Lorentz-tensors for bosons, and tensor-spinors for fermions, and by means of second order Lagrangians. The method allows to avoid the cumbersome matrix calculus and higher \partial^2j order wave equations inherent to the Weinberg-Joos approach. We start with reducible Lorentz-tensor (tensor-spinor) representation spaces hosting one sole (j,0)+(0,j) irreducible sector and design there a representation reduction algorithm based on one of the Casimir invariants of the Lorentz algebra. This algorithm allows us to separate neatly the pure spin-j sector of interest from the rest, while preserving the separate Lorentz- and Dirac indexes. However, the Lorentz invariants are momentum independent and do not provide wave equations. Genuine wave equations are obtained by conditioning the Lorentz-tensors under consideration to satisfy the Klein-Gordon equation. In so doing, one always ends up with wave equations and associated Lagrangians that are second order in the momenta. Specifically, a spin-3/2 particle transforming as (3/2,0)+ (0,3/2) is comfortably described by a second order Lagrangian in the basis of the totally antisymmetric Lorentz tensor-spinor of second rank, \Psi\_ \mu\nu. Moreover, the particle is shown to propagate causally within an electromagnetic background. In our study of (3/2,0)+(0,3/2) as part of \Psi\_\mu\nu we reproduce the electromagnetic multipole moments known from the Weinberg-Joos theory. We also find a Compton differential cross section that satisfies unitarity in forward direction. The suggested tensor calculus presents itself very computer friendly with respect to the symbolic software FeynCalc.

@article{Acosta2015Bosonic, abstract = {We propose a general method for the description of arbitrary single spin-j states transforming according to (j,0)+(0,j) carrier spaces of the Lorentz algebra in terms of Lorentz-tensors for bosons, and tensor-spinors for fermions, and by means of second order Lagrangians. The method allows to avoid the cumbersome matrix calculus and higher \partial^{2j} order wave equations inherent to the Weinberg-Joos approach. We start with reducible Lorentz-tensor (tensor-spinor) representation spaces hosting one sole (j,0)+(0,j) irreducible sector and design there a representation reduction algorithm based on one of the Casimir invariants of the Lorentz algebra. This algorithm allows us to separate neatly the pure spin-j sector of interest from the rest, while preserving the separate Lorentz- and Dirac indexes. However, the Lorentz invariants are momentum independent and do not provide wave equations. Genuine wave equations are obtained by conditioning the Lorentz-tensors under consideration to satisfy the Klein-Gordon equation. In so doing, one always ends up with wave equations and associated Lagrangians that are second order in the momenta. Specifically, a spin-3/2 particle transforming as (3/2,0)+ (0,3/2) is comfortably described by a second order Lagrangian in the basis of the totally antisymmetric Lorentz tensor-spinor of second rank, \Psi\_[ \mu\nu]. Moreover, the particle is shown to propagate causally within an electromagnetic background. In our study of (3/2,0)+(0,3/2) as part of \Psi\_[\mu\nu] we reproduce the electromagnetic multipole moments known from the Weinberg-Joos theory. We also find a Compton differential cross section that satisfies unitarity in forward direction. The suggested tensor calculus presents itself very computer friendly with respect to the symbolic software FeynCalc.}, added-at = {2019-02-23T22:09:48.000+0100}, archiveprefix = {arXiv}, author = {Acosta, E. G. Delgado and Guzman, V. M. Banda and Kirchbach, M.}, biburl = {https://www.bibsonomy.org/bibtex/240a736d2fa7c2a2b484e5afbf10a7eec/cmcneile}, citeulike-article-id = {13562578}, citeulike-linkout-0 = {http://arxiv.org/abs/1503.07230}, citeulike-linkout-1 = {http://arxiv.org/pdf/1503.07230}, citeulike-linkout-2 = {http://dx.doi.org/10.1140/epja/i2015-15035-x}, day = 24, doi = {10.1140/epja/i2015-15035-x}, eprint = {1503.07230}, interhash = {7c383b6928399aca0482083641439fa3}, intrahash = {40a736d2fa7c2a2b484e5afbf10a7eec}, issn = {1434-6001}, journal = {The European Physical Journal A}, keywords = {groups}, month = mar, number = 3, posted-at = {2015-03-26 10:34:38}, priority = {2}, timestamp = {2019-02-23T22:15:27.000+0100}, title = {{Bosonic and fermionic Weinberg-Joos (j,0)+ (0,j) states of arbitrary spins as Lorentz-tensors or tensor-spinors and second order theory}}, url = {http://dx.doi.org/10.1140/epja/i2015-15035-x}, volume = 51, year = 2015 }