Aspectos básicos del método de amplitudes I: caso sin masa
DOI:
https://doi.org/10.31349/RevMexFisE.22.010203Keywords:
Amplitudes, little group, helicity, Weyl spinorsAbstract
En este trabajo se revisa el formalismo de los espinores de helicidad o el método de amplitudes en el espacio de cuatro dimensiones (D=4), en el contexto de la Electrodinámica Cuántica (QED, por sus siglas en inglés). Se muestran los cálculos explícitos de la amplitud del proceso físico e+ e- ---> mu+ mu- a nivel árbol como un ejemplo de motivación a este método en el límite de altas energías o ultra-relativista. El objetivo es introducir a estudiantes de física en las nuevas técnicas de cálculo que se desarrollan a partir del formalismo de amplitudes.
In this work, the helicity spinors formalism or just amplitudes is reviewed in four-dimensional space (D = 4), in the context of Quantum Electrodynamics (QED). Explicit calculations for the amplitude of the physical process e +e − → µ +µ − at the tree level in the high energy or ultra-relativistic limit are shown as an example of motivation for study this method. The objective is to introduce particle physics students to the new calculation techniques that are developed from the amplitude program.
References
L. H. Ryder, Quantum Field Theory, Cambridge University Press, 1996, https://doi.org/10.1017/CBO9780511813900
A. M. Steane, An introduction to spinors, [arXiv:1312.3824 [math-ph]]
E. Cartan, Bull. Math. France 41 (1913) 53. Lectures on the theory of spinors. I: Spinors of three-dimensional space, Actual. Sci. Ind. 643 (1938) 1-98
P. A. M. Dirac, The quantum theory of the electron, Proc. Roy. Soc. Lond. A 117 (1928) 610-624 https://doi.org/10.1098/rspa.1928.0023
E. Majorana, Teoria simmetrica dell’elettrone e del positrone, Nuovo Cim. 14 (1937) 171-184 https://doi.org/10.1007/BF02961314
B. L. Van Der Waerden, Nachrichten Akad. Wiss. Gottingen, Math.-Physik- K1- (1929) 100
H. Weyl, Quantenmechanik und Gruppentheorie, Zeitschrift für Physik 46 (1927) 1, https://doi.org/10.1007/BF02055756
M. E. Peskin and D. V. Schroeder, An Introduction to quantum field theory (Addison-Wesley, USA, 1995)
G. Kane, Modern elementary particle physics, (Cambridge University Press, second edition)
M. Thomson, Modern Particle Physics, (Cambridge University Press, Cambridge, 2013), https://doi.org/10.1017/CBO9781139525367
H. Elvang and Y.-T. Huang, Scattering Amplitudes in Gauge Theory and Gravity, (Cambridge University Press, 2015). https://doi.org/10.1017/CBO9781107706620
F. Berends et al., Single bremsstrahlung processes in gauge theories, Phys. Lett. B 103 (1981) 124, https://doi.org/10.1016/0370-2693(81)90685-7
K. Hagiwara and D. Zeppenfeld, Helicity amplitudes for heavy lepton production in e +e − annihilation, Nucl. Phys. B 274 (1986) 1, https://doi.org/10.1016/0550-3213(86)90615-2
S. J. Parke and T. R. Taylor, An Amplitude for n Gluon Scattering, Phys. Rev. Lett. 56 (1986) 2459, https://doi.org/10.1103/PhysRevLett.56.2459
M. D. Schwartz, Quantum Field Theory and the Standard Model, Cambridge University Press, 2014)
H. K. Dreiner, H. E. Haber and S. P. Martin, Two-component spinor techniques and Feynman rules for quantum field theory and supersymmetry, Phys. Rept. 494 (2010) 1, https://doi.org/10.1016/j.physrep.2010.05.002
N. Arkani-Hamed, T. C. Huang and Y. t. Huang, Scattering amplitudes for all masses and spins, JHEP 2021 (2021) 70, https://doi.org/10.1007/JHEP11(2021)070
R. K. Ellis, Z. Kunszt, K. Melnikov and G. Zanderighi, One-loop calculations in quantum field theory: from Feynman diagrams to unitarity cuts, Phys. Rept. 518 (2012) 141- 250 https://doi.org/10.1016/j.physrep.2012.01.008
W. J. Torres Bobadilla et al. May the four be with you: Novel IR-subtraction methods to tackle NNLO calculations, Eur. Phys. J. C 81 (2021) 250 https://doi.org/10.1140/epjc/s10052-021-08996-y
V. Radovanovic, Problem book in Quantum Field Theory, (Springer, 2006), pp. 74-75
M. Robinson, Symmetry and the Standard Model, (Springer, 2011), pp. 116- 136
P. Langacker, The standard model and beyond, 2nd ed. (CRC Press, 2017). https://doi.org/10.1201/b22175
J. Díaz Cruz, B. Larios, O. Meza Aldama, and J. Reyes Pérez, Espinores de Weyl y el formalismo de helicidad, Rev. Mex. Fis. E, 61 (2015) 104-112
D. Bailin and A. Love, Supersymmetric Gauge Field Theory and String Theory (CRC Press, 1994), https://doi.org/10.1201/9780367805807
E. P. Wigner, On Unitary Representations of the Inhomogeneous Lorentz Group Ann. Math. 40 (1939) 149, https://doi.org/10.2307/1968551
Y. S. Kim and E. P. Wigner, Space-time Geometry of Relativistic Particles, J. Math. Phys. 31 (1990) 55, https://doi.org/10.1063/1.528827
S. Weinberg, The Quantum Theory of Fields, vol. I, (Cambridge University Press, 2005) pp. 609
F. A. Berends and W. T. Giele, Recursive Calculations for Processes with n Gluons, Nucl. Phys. B 306 (1988) 759, https://doi.org/10.1016/0550-3213(88)90442-7
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2025 Jonathan Reyes Pérez
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Authors retain copyright and grant the Revista Mexicana de Física E right of first publication with the work simultaneously licensed under a CC BY-NC-ND 4.0 that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
