Kvantinė laukų teorija ir Standartinis modelis

Quantum field theory and standard model

A modern theory that describes subatomic particles and their inherent interactions

From particles to fields

Early quantum mechanics (1920s) treated particles as wave functions in potential wells, explaining atomic structure well, but mainly delved into systems of one or a few particles. Meanwhile relativistic approaches made it possible to understand that new particles (e.g. electron-positron pairs) can be created or destroyed during high-energy processes, which contradicted the non-relativistic wave formalism. In the 1930s and 1940s, physicists saw the need to unify special relativity and quantum principles into a general system where particles appear as fundamental fields excitations. This was how it was helped Quantum field theories (QFT) foundations.

In the context of KLT, each type of particle is a member of a certain field that permeates space, quantum excited state. Suppose electrons are excitations of the "electron field", photons - of the "electromagnetic field", etc. Particle interactions reflect the interactions of fields, which are usually described by a Lagrangian or Hamiltonian, and their inherent symmetries determine glad (gauge) invariantsThese gradual discoveries eventually formed into Standard model – the crowning theory describing the known fundamental particles (fermions) and forces (except gravity).

2. Fundamentals of quantum field theory

2.1 “Second quantization” and particle formation

In conventional quantum mechanics, the wave function ψ(x, t) describes a system of a fixed number of particles. However, in the realm of relativistic energies, processes occur that create new particles or destroy existing ones (e.g., the production of an electron-positron pair). Quantum Field Theory (QFT) introduces the idea that fields are essential entities, and number of particles is not constant. The fields become quantized:

  • Field operators: φ̂(x) or Ψ̂(x) – they can create/destroy particles at position x.
  • Fock space: A Hilbert space involving states with a variable number of particles.

This allows for systematic calculations of scattering phenomena in high-energy collisions based on perturbation theory, Feynman diagrams and renormalization.

2.2 Gauge invariance

The fundamental principle is – local gauge invariance: certain field transformations that vary in spacetime from point to point do not change physical quantities. For example, electromagnetism follows from the U(1) symmetry of the Gadd, while more complex Gadd groups (e.g., SU(2) or SU(3)) describe the weak and strong interactions. This unifying approach defines the conditions of the interactions (coupling constants), the force carriers, and the structure of the fundamental interactions.

2.3 Renormalization

Early attempts to develop QED (quantum electrodynamics) raised infinite terms in perturbation scatterings. Renormalization developed a systematic way to deal with these divergent expressions so that the final physical quantities (electron mass, charge, etc.) are finite, observable. KED has become one of the most accurate theories in physics, predicting experimentally confirmed values ​​to extremely high accuracy (e.g., the electron magnetic moment) [1,2].

3. Standard Model Overview

3.1 Particles: Fermions and Bosons

Standard model divides subatomic particles into two broad categories:

  1. Fermions (spin ½):
    • Quarks: up, down, charm, strange, top, bottom, each has 3 "colors". Hadrons (e.g. protons, neutrons) are formed from quarks.
    • Leptons: electron, muon, tau (with corresponding neutrino types). Neutrinos are extremely light particles that interact only weakly.
    Fermions obey Pauli's exclusion principle, is the basic building block of matter.
  2. Bosons (spin integer) – carriers of power.
    • Gauge bosons: photon (γ) for electromagnetic force, W± and Z0 for the weak interaction, gluons (eight types) for the strong interaction.
    • Higgs boson: a scalar boson that imparts mass to W and Z bosons and fermions through spontaneous symmetry breaking In the Higgs field.

The Standard Model describes three fundamental interactions: electromagnetic, weak, and strong (gravity is not yet included). The electromagnetic and weak are unified into electroweak theory, which about 100 The GeV energy level spontaneously decays into separate forces, emitting a photon and W/Z bosons [3,4].

3.2 Quarks and confinement

Quarks has a color charge involved in the strong interaction, which is mediated by gluons. Due to colored imprisonment Quarks cannot normally exist alone (one by one) – they are “imprisoned” in hadrons (mesons, baryons). Gluons themselves carry color, which makes the QCD (quantum chromodynamics) equation extremely ambiguous and nonlinear. High-energy collisions or heavy-ion impacts can create quark-gluon plasmas, reminiscent of the conditions of the early Universe.

3.3 Symmetry Breaking: The Higgs Mechanism

Electroweak unity is based on SU(2)L × U(1)Y group. Above ~100 At GeV energies, the weak and electromagnetic interactions merge. Higgs field acquires a non-zero vacuum expectation value, spontaneously destroying this symmetry, so W± and Z0 The bosons become massive, the photon becomes massless. The fermion masses arise from the Yukawa interaction with the Higgs field. Higgs boson The discovery (at the LHC in 2012) confirmed this key element of the Standard Model.

4. Standard Model Predictions and Success

4.1 Precision checks

Quantum electrodynamics (QED) – the electromagnetic part of the Standard Model – perhaps the most accurate theory in physics (the electron's magnetic moment agrees with measurements up to 10-12 part). Meanwhile, the accuracy of the electroweak interaction has been confirmed by the LEP (CERN) and SLC (SLAC) experiments, which have evaluated radiative corrections. QCD (quantum chromodynamics) also agrees with the data from high-energy accelerators, if scale dependence and parton distribution functions are properly handled.

4.2 Particle discoveries

  • W and Z boson discovery (1983 at CERN)
  • Top quark (Fermilab 1995)
  • You are a neutrino. (2000)
  • Higgs boson (LHC 2012)

The masses and interactions of each discovered object, measured experimentally, agreed with SM predictions or free parameters determined from other data. Collectively, this provides a highly reliable experimental justification for SM.

4.3 Neutrino transformations

The original version of the Standard Model considered neutrinos to be massless, but neutrino transformation (oscillation) experiments (Super-Kamiokande, SNO) have shown that they have a small mass and can change flavors. This suggests new physics beyond the simple SM. The most commonly proposed solutions are right-handed polarization neutrinos or the "seesaw" mechanism. However, this does not change the essence of the SM, it only shows that it is not complete in terms of neutrino mass.

5.Limits and unresolved issues

5.1 Without gravity

The standard model does not include gravity. Attempts to quantize gravity or unify it with other forces run into difficulties. Research in string theory, in loop quantum gravity etc. are trying to integrate the concept of spin-2 graviton or derived spacetime, but so far there is no unified theory that combines SM with gravity.

5.2 Dark matter and dark energy

Space analysis shows that ~85 % of matter is "dark matter", an unknown particle not predicted by the current SM: WIMPs, axons or other hypothetical fields. In addition, the Universe is expanding with I accelerate., showing "dark energy" - perhaps a cosmological constant or a dynamical field that is not included in the SM. These phenomena show that although the SM is comprehensive, it does not complete the explanation of "everything".

5.3 Hierarchy and fine-tuning problems

Questions arise as to why the Higgs mass is so small compared to higher energies. hierarchy problem), where the structure of three-particle families comes from, why CP-breaking is so fragile, what determines the CP problem of the strong interaction, etc. In the formal SM, these questions are in the realm of free parameters, but many theoretical physicists see that this implies a deeper reason. Grand unified theories (GUT), supersymmetry, or other models have tried to solve them, but have not yet been confirmed by experiments.

6. Modern accelerator experiments and future directions

6.1 Large Hadron Collider (LHC)

CERN has been operating since 2008 LHC collides protons up to 13–14 TeV, testing the Standard Model at high energies, searching for new particles (SUSY, additional measurements), investigating the properties of the Higgs, and refining the limits of QCD/electroweak interaction. The discovery of the Higgs boson at the LHC (2012) was a huge step, but no clear "beyond the SM" signals have been found yet.

6.2 Future devices

Next-generation accelerators available:

  • High lumen LHC (HL-LHC) – more data for rare reactions.
  • Future Circular Collider (FCC) whether CEPC, possibly reaching 100 TeV energy or a separate lepton accelerator for Higgs research.
  • Neutrino projects (DUNE, Hyper-Kamiokande) – precise transformation/scale studies.

They could show whether there really is a "desert" behind the SM energy, or whether there are still undiscovered phenomena.

6.3 Non-accelerator searches

Direct detection experiments of dark matter (XENONnT, LZ, SuperCDMS), cosmic ray/gamma ray observations, ultra-precise measurements of fundamental constants or gravitational wave detections may also lead to breakthroughs in science. The combination of collider and astrophysical data will be crucial in understanding the frontiers of particle physics.

7. Philosophical and conceptual significance

7.1 Field-centric worldview

Quantum field theory goes beyond the old "particle in empty space" notion - here fields is the fundamental reality, and particles are just excitations of those fields, also composed of vacuum vibrations, virtual processes, etc. Even vacuum is not empty, but full of zero energy and possible processes.

7.2 Reductionism and unity

The Standard Model unifies the electromagnetic and weak forces into the electroweak theory, taking a step toward a universal unity of forces. Many speculate that at even higher energies, grand unified theories (GUT), which can unify both the strong and electroweak interactions (e.g., SU(5), SO(10) or E6).Experimental confirmation of these theories has not yet been achieved, but the dream of a deeper unity of nature persists.

7.3 Continuous searches

Although the Standard Model is successful in describing known phenomena, it still has "gaps" in it, such as neutrinos, dark matter, and gravity. Is there a more convenient explanation, for example, why such mass hierarchies exist, or what symmetry could unify even more interactions? Theoretical speculation, new experiments, and cosmic observations are developing in parallel, so the coming decades may reveal a new phase of physics and expand or rewrite the mosaic of fields of the Standard Model.

8. Conclusion

Quantum field theory and the Standard Model – this is an astonishing achievement of 20th century physicists, which connected quantum and relativistic principles into a coherent system capable of accurately describing subatomic particles and fundamental forces (strong, weak, electromagnetic). The concept of particles here arises from field excitations, so particle creation, antiparticles, quark confinement and Higgs mechanism becomes a natural conclusion.

Despite the fact that questions have arisen regarding gravity, dark matter, dark energy, neutrino masses and hierarchies – showing that the Standard Model is not “final” – ongoing LHCs, neutrino research centers, space observatories and (perhaps) future accelerators should help us to go beyond the “Standard Model”. For now, the CLT remains the foundation of our understanding of the microworld – a testament to our ability to reveal the subtle structure of fields, matter and forces that determine the observable structure of the Universe.

References and further reading

  1. Peskin, ME, & Schroeder, DV (1995). An Introduction to Quantum Field Theory. Westview Press.
  2. Weinberg, S. (1995). The Quantum Theory of Fields (3 volumes). Cambridge University Press.
  3. Glashow, SL, Iliopoulos, J., & Maiani, L. (1970). "Weak interactions with lepton–hadron symmetry." Physical Review D, 2, 1285.
  4. 't Hooft, G. (1971). "Renormalizable Lagrangians for Massive Yang–Mills Fields." Nuclear Physics B, 35, 167–188.
  5. Zee, A. (2010). Quantum Field Theory in a Nutshell, 2nd ed. Princeton University Press.
  6. Patrignani, C., & Particle Data Group (2017). "Review of Particle Physics." Chinese Physics C, 40, 100001.
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