Mu-In Park

BRST Quantization of the Proca Model Based on the BFT and the BFV Formalism

The BRST quantization of the Abelian Proca model is performed using the Batalin–Fradkin–Tyutin and the Batalin-Fradkin-Vilkovisky formalism. First, the BFT Hamiltonian method is applied in order to systematically convert a second class constraint system of the model into an effectively first class one by introducing new fields. In finding the involutive Hamiltonian we adopt a new approach which is simpler than the usual one. We also show that in our model the Dirac brackets of the phase space variables in the original second class constraint system are exactly the same as the Poisson brackets of the corresponding modified fields in the extended phase space due to the linear character of the constraints comparing the Dirac or Faddeev–Jackiw formalisms. Then, according to the BFV formalism we obtain that the desired resulting Lagrangian preserving BRST symmetry in the standard local gauge fixing procedure naturally includes the Stuckelberg scalar related to the explicit gauge symmetry breaking effect due to the presence of the mass term. We also analyze the nonstandard nonlocal gauge fixing procedure.

NON-ABELIAN PROCA MODEL BASED ON THE IMPROVED BFT FORMALISM

We present the newly improved Batalin–Fradkin–Tyutin (BFT) Hamiltonian formalism and the generalization to the Lagrangian formulation, which provide a much more simple and transparent insight into the usual BFT method, with application to the non-Abelian Proca model, which has been a difficult problem in the usual BFT method. The infinite terms of the effectively first class contraints can be made to be the regular power series forms by an ingenious choice of Xαβ and ωαβ matrices. In this new method, the first class Hamiltonian, which also needs infinite correction terms, is obtained simply by replacing the original variables in the original Hamiltonian with the BFT physical variables. Remarkably, all the infinite correction terms can be expressed in the compact exponential form. We also show that in our model the Poisson brackets of the BFT physical variables in the extended phase space have the same structure as the Dirac brackets of the original phase space variables. With the help of both our newly developed Lagrangian formulation and Hamiltons equations of motion, we obtain the desired classical Lagrangian corresponding to the first class Hamiltonian which can be reduced to the generalized Stuckelberg Lagrangian which is a nontrivial conjecture in our infinitely many terms involved in the Hamiltonian and the Lagrangian.

On the foundation of the relativistic dynamics with the tachyon

SummaryThe theoretical foundation of an object moving faster than light in vacuum (tachyon) is still missing or incomplete. Here we present the classical foundation of the relativistic dynamics including the tachyon. An anomalous sign-factor extracted from the transformation of √1 -u2/c2 under the Lorentz transformation, which has always been missed in the usual formulation of the tachyon, has a crucial role in the dynamics of the tachyon. Due to this factor the mass of the tachyon transforms in an unusual way although the energy and momentum, which are defined as the conserved quantities in all uniformly moving systems, trasform in the usual way as in the case of an object moving slower than light (bradyon). We show that this result can also be obtained from the least-action approach. On the other hand, we show that the ambiguities in the description of the dynamics for an object moving with the velocity of light (luxon) can be consistently removed only by introducing a new dynamical variable. Furthermore, by using the fundamental definition of the momentum and energy, we show that the zero-point energy for any kind of objects,i.e. the tachyon, bradyon, and luxon, which has been known as the undetermined constant, should satisfy some constraints for consistency, and we note that this is essentially another novel relativistic effect. Finally, we remark about the several unsolved problems.

Investigation on the tachyonic neutrino

According to the experimental data, it is still controversial whether the neutrinos, especially the electron–neutrino and muon–neutrino, can be considered as the fermionic spinorial tachyons, and there is still no reliable report on the existence of the right-handed neutrinos. In this letter, we show that only the neutrinos with both handedness can be the tachyons, while the single handedness neutrinos are impossible to be the tachyons. Several implications of this result are discussed.

The quantization of the chiral Schwinger model based on the BFT-BFV formalism II

We apply the newly improved Batalin - Fradkin - Tyutin (BFT) Hamiltonian method to the chiral Schwinger model in the case of the regularization ambiguity a>1. We show that one can systematically construct the first class constraints by the BFT Hamiltonian method, and also show that the well-known Dirac brackets of the original phase space variables are exactly the Poisson brackets of the corresponding modified fields in the extended phase space. Furthermore, we show that the first class Hamiltonian is simply obtained by replacing the original fields in the canonical Hamiltonian by these modified fields. Performing the momentum integrations, we obtain the corresponding first class Lagrangian in the configuration space.

Operator ordering problem of the nonrelativistic Chern-Simons theory.

The operator ordering problem due to the quantization or regularization ambiguity in the Chern-Simons theory exists. However, we show that this can be avoided if we require Galilei covariance of the nonrelativistic Abelian Chern-Simons theory even at the quantum level for the extended sources. The covariance can be recovered only by choosing some particular operator orderings for the generators of the Galilei group depending on the quantization ambiguities of the gauge-matter commutation relation. We show that the desired ordering for the unusual prescription is not the same as the well-known normal ordering but still satisfies all the necessary conditions. Furthermore we show that the equations of motion can be expressed in a similar form regardles of the regularization ambiguity. This suggests that the different regularization prescriptions do not change the physics. On the other hand, for the case of point sources the regularization prescription is uniquely determined, and only the orderings, which are equivalent to the usual one, are allowed.

New gauge invariant formulation of the Chern-Simons gauge theory: Classical and quantal analysis

A recently proposed new gauge invariant formulation of the Chern–Simons gauge theory is considered in detail. This formulation is consistent with the gauge fixed formulation. Furthermore, it is found that the canonical (Noether) Poincare generators are not gauge invariant even on the constraints surface and do not satisfy the Poincare algebra contrast to usual case. It is the improved generators, constructed from the symmetric energy–momentum tensor, which are (manifestly) gauge invariant and obey the quantum as well as classical Poincare algebra. The physical states are constructed and it is found in the Schrodinger picture that unusual gauge invariant longitudinal mode of the gauge field is crucial for constructing the physical wave-functional which is genuine to (pure) Chern–Simons theory. In matching to the gauge fixed formulation, we consider three typical gauges, Coulomb, axial and Weyl gauges as explicit examples. Furthermore, recent several confusions about the effect of Diracs dressing function and the gauge fixings are clarified. The analysis according to old gauge independent formulation a la Dirac is summarized in an appendix.

NOTE ON SELF-DUALITY CONDITION IN THE CHIRAL BOSON THEORY

We demonstrate that the self-duality condition for the field itself can naturally be obtained without requiring any boundary condition in Floreanini and Jackiw’s chiral boson theory if we treat carefully the quantum theoretical equation of motion for the theory.