Geodesic
The quantum theory of the Lorentzian fermionic differential forms
Teoretičeskaâ i matematičeskaâ fizika, Tome 202 (2020) no. 2, pp. 207-242 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider the quantum theory of the Lorentzian fermionic differential forms and the corresponding bispinor quantum fields, which are expansion coefficients of the forms in the bispinor basis of Becher and Joos. We describe the canonical quantization procedure for the bispinor gauge theory in terms of its Dirac spinor constituents in detail and derive the corresponding Feynman rules and also all possible mass terms for massive fermions in the bispinor gauge theory. We classify the solutions by a scalar spin quantum number, a number with no analogue in the standard gauge theory and in the Standard Model. The possible mass terms correspond to combinations of scalar spin-zero singlets and scalar spin-$1/2$ doublets in the generation space. We describe the connection between the Lorentz spin of bispinors and the scalar spin of bispinor constituents.
Keywords: quantum field theory, bispinor gauge theory, perturbation theory, Feynman rules. 
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A. Jourjine. The quantum theory of the Lorentzian fermionic differential forms. Teoretičeskaâ i matematičeskaâ fizika, Tome 202 (2020) no. 2, pp. 207-242. http://geodesic.mathdoc.fr/item/TMF_2020_202_2_a3/

[1] D. Iwanenko, L. Landau, “Zur Theorie des magnetischen Elektrons. I”, Z. Phys., 48:5–6 (1928), 340–348 | DOI

[2] P. A. M. Dirac, “The quantum theory of the electron”, Proc. Roy. Soc. London Ser. A, 117:778 (1928), 610–624 | DOI

[3] E. Kähler, “Der innere Differentialkalkül”, Rend. Mat. Appl., 21 (1962), 425–523 | MR

[4] W. Graf, “Differential forms as spinors”, Ann. Inst. H. Poincaré Sect. A (N. S.), 29:1 (1978), 85–109 | MR

[5] I. M. Benn, R. W. Tucker, “A generation model based on Kähler fermions”, Phys. Lett. B, 119:4–6 (1982), 348–350 | DOI

[6] T. Banks, Y. Dothan, D. Horn, “Geometric fermions”, Phys. Lett. B, 117:6 (1982), 413–417 | DOI | MR

[7] P. Becher, H. Joos, “The Dirac–Kähler equation and fermions on the lattice”, Z. Phys. C, 15:4 (1982), 343–365 | DOI | MR

[8] B. Holdom, “Gauged fermions from tensor fields”, Nucl. Phys. B, 233:3 (1984), 413–432 | DOI | MR

[9] A. N. Jourjine, “Space-time Dirac–Kahler spinors”, Phys. Rev. D, 35:2 (1987), 757–758 | DOI | MR

[10] I. M. Benn, R. W. Tucker, “Fermions without spinors”, Commun. Math. Phys., 89:3 (1983), 341–362 | DOI | MR

[11] D. D. Ivanenko, Yu. N. Obukhov, S. N. Solodukhin, On antisymmetric tensor representation of the Dirac equation, ICTP Preprint IC/85/2, ICTP, Trieste, 1985

[12] J. Kato, N. Kawamoto, A. Miyake, “$N=4$ twisted superspace from Dirac–Kähler twist and off-shell SUSY invariant actions in four dimensions”, Nucl. Phys. B, 721:1–3 (2005), 229–286, arXiv: hep-th/0502119 | DOI | MR

[13] K. Nagata, Y.-S. Wu, “Twisted supersymmetric invariant formulation of Chern–Simons gauge theory on a lattice”, Phys. Rev. D, 78:6 (2008), 065002, 13 pp., arXiv: 0803.4339 | DOI

[14] F. Bruckmann, S. Catterall, M. de Kok, “Critique of the link approach to exact lattice supersymmetry”, Phys. Rev. D, 75:4 (2007), 045016, 8 pp., arXiv: hep-lat/0611001 | DOI

[15] S. Arianos, A. D'Adda, N. Kawamoto, J. Saito, “Lattice supersymmetry in 1D with two supercharges”, PoS (LATTICE 2007), 42 (2007), 259, 14 pp., arXiv: 0710.0487 | DOI

[16] K. Nagata, “On the continuum and lattice formulations of $N=4$ $D=3$ twisted super Yang–Mills”, JHEP, 01 (2008), 041, 29 pp., arXiv: 0710.5689 | DOI | MR

[17] H. Echigoya, T. Miyazaki, De Rham–Kodaira's theorem and dual gauge transformations, arXiv: hep-th/0011263

[18] Y.-G. Miao, R. Manvelyana, H. J. W. Muller-Kirsten, “Self-duality beyond chiral $p$-form actions”, Phys. Lett. B, 482:1–3 (2000), 264–270, arXiv: hep-th/0002060 | DOI | MR

[19] B. de Wit, M. van Zalk, “Supergravity and M-theory”, Gen. Rel. Grav., 41:4 (2009), 757–784, arXiv: 0901.4519 | DOI | MR

[20] T. Kobayashi, S. Yokoyama, “Gravitational waves from $p$-form inflation”, JCAP, 2009:4 (2009), 004, 9 pp., arXiv: 0903.2769 | DOI

[21] A. N. Jourjine, “Mass mixing, the fourth generation, and the kinematic Higgs mechanism”, Phys. Lett. B, 693:2 (2010), 149–154, arXiv: 1005.3593 | DOI

[22] A. N. Jourjine, “The spectrum of the 4-generation Dirac–Kähler extension of the SM”, Phys. Lett. B, 695:5 (2011), 482–488, arXiv: 1011.0382 | DOI | MR

[23] A. N. Jourjine, “Scalar spin of elementary fermions”, Phys. Lett. B, 728 (2014), 347–357, arXiv: 1307.2694 | DOI

[24] P. Salgado, S. Salgado, “Extended gauge theory and gauged free differential algebras”, Nucl. Phys. B, 926 (2018), 179–199, arXiv: 1702.07819 | DOI | MR

[25] A. Jourjine, Extended gauge theory, bi-spinors, and scalar supersymmetry, arXiv: 1706.01269

[26] K. Itsikson, Zh.-B. Zyuber, Kvantovaya teoriya polya, Mir, M., 1984 | MR