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Mu-In Park

Publications and source records attributed to Mu-In Park.

47 records · Page 3Linked to original sources
arXiv1998

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

We apply an improved version of Batalin-Fradkin-Tyutin (BFT) Hamiltonian method to the a=1 chiral Schwinger Model, which is much more nontrivial than the a>1.$ one. Furthermore, through the path integral quantization, we newly resolve the problem of the non-trivial $δ$ function as well as that of the unwanted Fourier parameter $ξ$ in the measure. As a result, we explicitly obtain the fully gauge invariant partition function, which includes a new type of Wess-Zumino (WZ) term irrelevant to the gauge symmetry as well as usual WZ action.

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arXiv1998

New Gauge Invariant Formulation of the Chern-Simons Gauge Theory

A new gauge invariant formulation of the relativistic scalar field interacting with Chern-Simons gauge fields is considered. This formulation is consistent with the gauge fixed formulation. Furthermore we find that canonical (Noether) Poincaré generators are not gauge invariant even on the constraints surface and do not satisfy the (classical) Poincaré algebra. It is the improved generators, constructed from the symmetric energy-momentum tensor, which are (manifestly) gauge invariant and obey the classical Poincaré algebra.

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arXiv1998

Statistical Entropy of Three-dimensional Kerr-De Sitter Space

I consider the (2+1)-dimensional Kerr-De Sitter space and its statistical entropy computation. It is shown that this space has only one (cosmological) event horizon and there is a phase transition between the stable horizon and the evaporating horizon at a point $M^2={1/3}J^2/l^2$ together with a lower bound of the horizon temperature. Then, I compute the statistical entropy of the space by using a recently developed formulation of Chern-Simons theory with boundaries, and extended Cardy's formula. This is in agreement with the thermodynamics formula.

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arXiv1998

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 the much more simple and transparent insight to the usual BFT method, with application to the non-Abelian Proca model which has been an difficult problem in the usual BFT method. The infinite terms of the effectively first class constraints can be made to be the regular power series forms by ingenious choice of $X_{αβ}$ and $ω^{αβ}$-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 are the same structure as the Dirac brackets of the original phase space variables. With the help of both our newly developed Lagrangian formulation and Hamilton's equations of motion, we obtain the desired classical Lagrangian corresponding to the first class Hamiltonian which can be reduced to the generalized Stückelberg Lagrangian which is non-trivial conjecture in our infinitely many terms involved in Hamiltonian and Lagrangian.

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arXiv1997

Note on the Abelian Pure CS Theory Based on the Improved BFT Method

We reconsider the Abelian pure Chern-Simons theory in three dimensions by using our improved Batalin-Fradkin-Tyutin Hamiltonian formalism. As a result, we show several novel features, including the connection of the Dirac brackets. In particular, through the path integral quantization, we obtain the desired new type of the Wess-Zumino action.

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arXiv1997

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 more 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 Stückelberg 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.

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arXiv1997

The Quantization of the Chiral Schwinger Model based on the BFT-BFV formalism

We apply newly improved Batalin-Fradkin-Tyutin 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.

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arXiv1995

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 the neutrinos with the single handedness can not be the tachyons, but only those of the both handedness can be. Several implications of this result are discussed.

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arXiv1995

On the Foundation of the Relativistic Dynamics with the Tachyon

The theoretical foundation of the object moving faster than light in vacuum ({\it 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 ${ \sqrt{1-u^{2}/c^{2} } }$ under the Lorentz transformation, which has been always 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 the unusual way although the energy and momentum, which are defined as the conserved quantities in all uniformly moving systems, transform in the usual way as in the case of the object moving slower than light ({\it bradyon}). We show that this result can be also obtained from the least action approach. On the other hand, we show that the ambiguities for the description of the dynamics for the object moving with the velocity of light ({\it 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 the objects, {\it 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.

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arXiv1994

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 regardless 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.

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