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We discuss the possibility of a laboratory search for light minicharged particles carrying electric charge, which is a small fraction ϵ of that of electron. We point out that the production of pairs of such particles in an electric field would result in a measurable discharge in vacuum of electrically charged objects. A realistic experiment may be sensitive to such particles at least down to ϵ~10^-8, if their mass is below ~10^-4eV.

Systems of strongly correlated fermions on certain geometrically frustrated lattices at particular filling factors support excitations with fractional charges ±e/2. We calculate quantum mechanical ground states, low–lying excitations and spectral functions of finite lattices by means of numerical diagonalization. The ground state of the most thorough-fully studied case, the criss-crossed checkerboard lattice, is degenerate and shows long–range order. Static fractional charges are confined by a weak linear force, most probably leading to bound states of large spatial extent. Consequently, the quasi-particle weight is reduced, which reflects the internal dynamics of the fractionally charged excitations. By using an additional parameter, we fine–tune the system to a special point at which fractional charges are manifestly deconfined—the so–called Rokhsar–Kivelson point. For a deeper understanding of the low–energy physics of these models and for numerical advantages, several conserved quantum numbers are identified.

This article was mainly written by a team of high school students that have won the CERN Beamline for Schools (BL4S) competition in 2017. They had some help from professional scientists, in particular Branislav Ristic. The team had proposed to set up an experiment to search for elementary particles with a fractional electric charge. This paper describes the preparation of their proposal, experimental setup, detectors and data analysis throughout the search for such particles using a 10GeV$c^{-1}$ proton beam with a fixed iron target. It was clear to the team that the chance for finding such particles in a relatively simple experiment was minimal but that by doing this experiment they would learn a lot about experimental physics. Due to large amounts of noise, the result of the experiment is inconclusive. Further experimentation to search for these hypothesized particle is encouraged.

Systems of strongly correlated fermions on certain geometrically frustrated lattices at particular filling factors support excitations with fractional charges ±e/2. We calculate quantum mechanical ground states, low–lying excitations and spectral functions of finite lattices by means of numerical diagonalization. The ground state of the most thoroughfully studied case, the criss-crossed checkerboard lattice, is degenerate and shows long–range order. Static fractional charges are confined by a weak linear force, most probably leading to bound states of large spatial extent. Consequently, the quasi-particle weight is reduced, which reflects the internal dynamics of the fractionally charged excitations. By using an additional parameter, we fine–tune the system to a special point at which fractional charges are manifestly deconfined—the so–called Rokhsar–Kivelson point. For a deeper understanding of the low–energy physics of these models and for numerical advantages, several conserved quantum numbers are identified.

In 1965, Gell-Mann has shown that the magnetic moments of the neutron and the proton are related to the linear combinations of vectors and the axial vector, and which obey the same commutation relations as and . These currents are also expressed as products of Dirac γ_αλ_i and γ_αγ₅λ_i matrices. The index i varies from 0 to 8 with λ_o = (2/3)^1/21. This explains that μ_n/μ_p = −2/3. It is possible to express the magnetic moments in terms of g values, g_n and g_p. The ratio of the magnetic moments can be treated as the ratio of g values. We find that g = 2j+1=2l+1 gives the effective charge of a particle in a given state. Although the charge of a particle in high energy physics depends on isospin, baryon number, etc, it does not depend on spin. We show that the charge of the electron in different states is derivable from the spin. For spin 1/2, the effective charge of the electron in a magnetic field becomes (1/2)ge = [(l + (1/2) ± s)/(2l + 1)]e which for positive sign gives (l + 1)/(2l + 1) which is 2/3 for l = 1 and for the negative sign, l/2l+1 gives 0 for l = 0 and 1/3 for l = 1. Using the helicity, which changes the sign of s, we can obtain the charges of 0, ±1 from the spin and further values can be developed by changing the orbital angular momentum quantum number. Hence, fractional charge of the electron can be explained by the angular momentum.