Harmonic BRST quantization of systems with irreducible holomorphic bosonic and fermionic constraints

Abstract

We consider systems with second-class constraints or, equivalently, first-class holomorphic constraints. We show that the harmonic Becchi-Rouet-Stora-Tyutin method of quantizing systems with bosonic holomorphic constraints extends to systems having both bosonic and fermionic holomorphic constraints. The ghosts for bosonic holomorphic constraints in the harmonic BRST method have a Poisson brackets structure different from that of the ghosts in the usual BRST method, which applies to systems with real first-class constraints. Apart from this exotic ghost structure for bosonic constraints, the new feature of the harmonic BRST method is the introduction of two new holomorphic BRST charges 8 and 8 and the addition of an extra term -/3(8,8] to the BRST-invariant Hamiltonian. We apply the Fradkin-Vilkovisky theorem to general systems with mixed bosonic and fermionic holomorphic constraints and show that, taking an appropriate limit, the extra term in the harmonic BRST-modified path integral reproduces the correct Senjanovic measure.PACS number(s1: 03.65. Ca,

Neutrino physics at meson factories and spallation neutron sources

“…The good angular resolution allowed a clean separation of νe − elastic scattering events from other neutrino reactions and cosmic-ray backgrounds, as shown in figure 3, where a well-defined forward peak is clearly visible in the data. The measured [19] ν e e − → ν e e − elastic scattering rate of 236 ± 35 events yields the total elastic scattering cross section [10.0 ± 1.5 (stat) ± 0.9 (syst)] × 10 −45 cm 2 × (E ν (MeV)), and a model independent measurement of the strength of the destructive interference between the charged and neutral currents, I = −1.07 ± 0.21, that agrees well with the SM prediction I = −1.08. The model independent measurement of the ν e e − cross section was also interpreted in terms of limits against non-standard electroweak couplings, allowing very stringent limits on electromagnetic interactions of neutrinos (both electron-and muon-type), and on the existence of new gauge bosons.…”

Measurements of neutrino electron scattering

“…A viable alternative would be to use a detector with good tracking capability. This approach was taken by E225 at Los Alamos [16,22]. A tracking detector at an SNS would probably cost more per unit target mass and thus we do not consider it further here.…”

“…Some astrophysical limits are stronger than laboratory experiments but are more model dependent [14,15]. Limits on muon neutrino magnetic moments have been obtained from neutrino electron elastic scattering [1,16,17]. The best current limit, 6.8 × 10 −10 µ B , was obtained by LSND using ν µ and νµ from a decay-at-rest neutrino source [17].…”

“…Two experiments using DAR ν e beams at Los Alamos National Laboratory obtained samples of several hundred events from the reaction ν e + e → ν e + e. LSND measured I = −1.01 ± 0.13(stat) ± 0.12(syst) and 1 − f ee < 0.32 at 90% confidence level [17]. E225 measured I = −1.07 ± 0.17(stat) ± 0.11(syst) and 1 − f ee < 0.35 at 90% confidence level [16,22]. An experiment at an SNS could measure I with a statistical uncertainty of 0.03 and a systematic uncertainty of 0.01.…”

Reality conditions, reducibility, and ghosts

“…The standard inner product for the ghosts is given by the integral over Fermi variables, in analogy with commuting variables For bosonic functions f (q) = fo + f17) and s ( q ) = go + glq, the standard inner product with a real ghost, (f Is) = / dv f*(n)g(r)) = f:sof;91. (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18) is replaced by when the ghosts are complex. We emphasize that q* and q are not both dynamical variables.…”