Fields and quanta

fields and particles in particle physics

and in the standard model of particle physics:

force field gauge bosons

scalar bosons

matter field fermions (spinors, Dirac fields)

flavors of fundamental fermions in the
standard model of particle physics:
generation of fermions1st generation2nd generation3d generation
quarks (qq)
up-typeup quark (uu)charm quark (cc)top quark (tt)
down-typedown quark (dd)strange quark (ss)bottom quark (bb)
neutralelectron neutrinomuon neutrinotau neutrino
bound states:
mesonslight mesons:
pion (udu d)
ρ-meson (udu d)
ω-meson (udu d)
ϕ-meson (ss¯s \bar s),
kaon, K*-meson (usu s, dsd s)
eta-meson (uu+dd+ssu u + d d + s s)

charmed heavy mesons:
D-meson (uc u c, dcd c, scs c)
J/ψ-meson (cc¯c \bar c)
bottom heavy mesons:
B-meson (qbq b)
ϒ-meson (bb¯b \bar b)
proton (uud)(u u d)
neutron (udd)(u d d)

(also: antiparticles)

effective particles

hadrons (bound states of the above quarks)


in grand unified theory

minimally extended supersymmetric standard model




dark matter candidates


auxiliary fields

Algebraic Quantum Field Theory

algebraic quantum field theory (perturbative, on curved spacetimes, homotopical)



field theory:

Lagrangian field theory


quantum mechanical system, quantum probability

free field quantization

gauge theories

interacting field quantization



States and observables

Operator algebra

Local QFT

Perturbative QFT



In particle physics the letters MSSM are an abbreviation for “minimally supersymmetric standard model”: an extension of the standard model of particle physics to a model (in particle phyiscs) with a minimum amount of extra global supersymmetry.




The original articles are

  • S. Dimopoulos and H. Georgi, Phys. Lett. B 117, 287 (1982).

  • Steven Weinberg, Phys. Rev. D 26, 287 (1982)

Theoretical predictions

  • Stefano Frixione, Benjamin Fuks, Valentin Hirschi, Kentarou Mawatari, Hua-Sheng Shao, Marthijn P. A. Sunder, Marco Zaro, Automated simulations beyond the Standard Model: supersymmetry (arXiv:1907.04898)


  • S. F. King, S. Moretti, R. Nevzorov, A Review of the Exceptional Supersymmetric Standard Model (arXiv:2002.02788)

Relation to flavour anomalies

Suggestion that the MSSM with R-parity violation could explain the flavour anomalies:

  • Dong-Yang Wang, Ya-Dong Yang, Xing-Bo Yuan, bcτν¯b \to c \tau \bar \nu decays in supersymmetry with R-parity violation (arXiv:1905.08784)

  • Quan-Yi Hu, Lin-Lin Huang, Explaining bs + b\to s \ell^+ \ell^- data by sneutrinos in the R-parity violating MSSM (arXiv:1912.03676)

  • Quan-Yi Hu, Ya-Dong Yang, Min-Di Zheng, Revisiting the B-physics anomalies in R-parity violating MSSM (arXiv:2002.09875)

  • Wolfgang Altmannshofer, P. S. Bhupal Dev, Amarjit Soni, Yicong Sui, Addressing R D *R_{D^\ast}, R K *R_{K^\ast}, muon g2g-2 and ANITA anomalies in a minimal R-parity violating supersymmetric framework (arXiv:2002.12910)

In heterotic string theory

The origin of all string phenomenology is the top-down approach in the heterotic string due to (Candelas-Horowitz-Strominger-Witten 85).

A brief review of motivations for GUT models in heterotic string theory is in

The following articles establish the existences of exact realization of the gauge group and matter-content of the MSSM in heterotic string theory (not yet checking Yukawa couplings):

A computer search through the “landscape” of Calabi-Yau varieties showed several hundreds more such exact heterotic standard models (about one billionth of all CYs searched, and most of them arising as SU(5)SU(5)-GUTs)

The resulting database of compactifications is here:

Review includes

Computation of metrics on these Calabi-Yau compactifications (eventually needed for computing their induced Yukawa couplings) is started in

This “heterotic standard model” has a “hidden sector” copy of the actual standard model, more details of which are discussed here:

The issue of moduli stabilization in these kinds of models is discussed in

Principles singling out heterotic models with three generations of fundamental particles are discussed in:

See also

In F-theory

A geometric engineering of the MSSM in F-theory (see at string phenomenology) is claimed in

  • Mirjam Cvetič, Ling Lin, Muyang Liu, Paul-Konstantin Oehlmann, An F-theory Realization of the Chiral MSSM with 2\mathbb{Z}_2-Parity (arXiv:1807.01320)

A large number of realizations of the exact field content of the MSSM in F-theory is claimed to be realized in

Last revised on April 13, 2020 at 20:57:14. See the history of this page for a list of all contributions to it.