arXiv subjects
Publications and source records attributed to Jae Hyung Yee.
The differential structure on the kappa-Minkowski spacetime from Jordanian twist of Weyl algebra is constructed, and it is shown to be closed in 4-dimensions in contrast to the conventional formulation. Based on this differential structure, we have formulated a scalar field theory in this kappa-Minkowski spacetime.
Using the twist deformation of $U(igl(4,R))$, the linear part of the diffeomorphism, we define a scalar function and construct a free scalar field theory in four-dimensional $κ$-Minkowski spacetime. The action in momentum space turns out to differ only in integration measure from the commutative theory.
We study the Casimir energy of a spherical shell of radius $a$ in $κ$-Minkowski spacetime for a complex field with an asymmetric ordering and obtain the energy up to $O(1/κ^2)$. We show that the vacuum breaks particle and anti-particle symmetry if one requires the spectra to be consistent with the blackbody radiation at the commutative limit.
We study a novel phenomena of smearing of black hole horizons from the effect of space noncommutativity. We present an explicit example in $AdS_3$ space, using the Chern-Simons formulation of gravity. This produces a smeared BTZ black hole which goes beyond the classical spacetime unexpectedly and there is {\it no} reality problem in our approach with the gauge group $U(1,1) \times U(1,1)$. The horizons are smeared, due to a splitting of the Killing horizon and the apparent horizon, and there is a metric signature change to Euclidean in the smeared region. The inner boundary of the smeared region acts as a trapped surface for timelike particles but the outer as a classical barrier for ingoing particles. The lightlike signals can escape from or reach the smeared region in a {\it finite} time, which indicates that {\it the black hole is not so dark, even classically.} In addition, it is remarked that the Hawking temperature can {\it not} be defined by the regularity in the Euclidean geometry except in the non-rotating case, and the origin can be smeared by a {\it new} (apparent) horizon.
We study four dimensional $κ$-Minkowski spacetime constructed by the twist deformation of $U(igl(4,R))$. We demonstrate that the differential structure of such twist-deformed $κ$-Minkowski spacetime is closed in four dimensions contrary to the construction of $κ$-Poincaré bicovariant calculus which needs an extra fifth dimension. Our construction holds in arbitrary dimensional spacetimes.
We twist the Hopf algebra of igl(n,R) to obtain the kappa-deformed spacetime coordinates. Coproducts of the twisted Hopf algebras are explicitly given. The kappa-deformed spacetime obtained this way satisfies the same commutation relation as that of the conventional kappa-Minkowski spacetime, but its Hopf algebra structure is different from the well known kappa-deformed Poincare algebra in that it has larger symmetry algebra than the kappa-Minkowski case. There are some physical models which consider this symmetry. Incidentally, we obtain the canonical (theta-deformed) non-commutative spacetime from canonically twisted igl(n,R) Hopf algebra.
We present the Casimir energy of spherical shell, for the symmetrically deformed scalar field in $κ$-Minkowski space-time, satisfying Dirichlet boundary condition. The Casimir energy shows the particle anti-particle symmetry contrary to the asymmetrically deformed case. In addition, the deformation effect starts from $O(1/κ)$ term unlike in the parallel plates.
The properties of the uniform Bose gas is studied within the optimized variational perturbation theory (Gaussian approximation) in a self-consistent way. It is shown that the atomic BEC with a repulsive interaction becomes unstable when the gas parameter gamma=rho a^3 exceeds a critical value gamma_{crit} ~ 0.01. The quantum corrections beyond the Bogoliubov-Popov approximation to the energy density, chemical potential and pressure in powers of gamma expansions are presented.
We have computed the black body radiation spectra in $κ-$Minkowski space-time, using the quantum mechanical picture of massless scalar particles as well as effective quantum field theory picture. The black body radiation depends on how the field theory (and thus how the $κ-$Poincaré algebra) handles the ordering effect of the noncommutative space-time. In addition, there exists a natural momentum cut-off of the order $κ$, beyond which a new real mode takes its shape from a complex mode and the old real mode flows out to be a new complex mode. However, the new high momentum real mode should not be physical since its contributions to the black-body radiation spoils the commutative limit.
We propose a variational perturbation method based on the observation that eigenvalues of each parity sector of both the anharmonic and double-well oscillators are approximately equi-distanced. The generalized deformed algebra satisfied by the invariant operators of the systems provides well defined Hilbert spaces to both of the oscillators. There appears a natural expansion parameter defined by the ratios of three distance scales of the trial wavefunctions. The energies of the ground state and the first order excited state, in the $0^{th}$ order variational approximation, are obtained with errors $<10^{-2}$% for vast range of the coupling strength for both oscillators. An iterative formula is presented which perturbatively generates higher order corrections from the lower order invariant operators and the first order correction is explicitly given.
We analyze the response of a detector with a uniform acceleration $α$ in $κ-$Minkowski spacetime using the first order perturbation theory. The monopole detector is coupled to a massless complex scalar field in such a way that it is sensitive to the Lorentz violation due to the noncommutativity of spacetime present in the $κ-$deformation. The response function deviates from the thermal distribution of Unruh temperature at the order of $1/κ$ and vanishes exponentially as the proper time of the detector exceeds a certain critical time, a logarithmic function of $κ$. This suggests that the Unruh temperature becomes not only fuzzy but also eventually decreases to zero in this model.
We construct a quantum field theory in noncommutative spacetime by twisting the algebra of quantum operators (especially, creation and annihilation operators) of the corresponding quantum field theory in commutative spacetime. The twisted Fock space and S-matrix consistent with this algebra have been constructed. The resultant S-matrix is consistent with that of Filk\cite{Filk}. We find from this formulation that the spin-statistics relation is not violated in the canonical noncommutative field theories.
We study the spectrum of metric fluctuation in $κ$-deformed inflationary universe. We write the theory of scalar metric fluctuations in the $κ-$deformed Robertson-Walker space, which is represented as a non-local theory in the conventional Robertson-Walker space. One important consequence of the deformation is that the mode generation time is naturally determined by the structure of the $κ-$deformation. We expand the non-local action in $H^2/κ^2$, with $H$ being the Hubble parameter and $κ$ the deformation parameter, and then compute the power spectra of scalar metric fluctuations both for the cases of exponential and power law inflations up to the first order in $H^2/κ^2$. We show that the power spectra of the metric fluctuation have non-trivial corrections on the time dependence and on the momentum dependence compared to the commutative space results. Especially for the power law inflation case, the power spectrum for UV modes is weakly blue shifted early in the inflation and its strength decreases in time. The power spectrum of far-IR modes has cutoff proportional to $k^3$ which may explain the low CMB quadrupole moment.
A new variational perturbation theory is developed based on the $q-$deformed oscillator. It is shown that the new variational perturbation method provides 200 or 10 times better accuracy for the ground state energy of anharmonic oscillator than the Gaussian and the improved Gaussian approximation, respectively.
In an attempt to clarify what is the velocity of a particle in doubly special relativity, we solve Maxwell's equations invariant under the position-space nonlinear Lorentz transformation proposed by Kimberly, Magueijo, and Medeiros. We show that only the amplitude of the Maxwell wave, not the phase, is affected by the nonlinearity of the transformation. Thus, although the Maxwell wave appears to have infinitely large energy near the Planck time, the wave velocity is the same as the conventional light velocity. Surprisingly, the velocity of the Maxwell wave is not the same as the maximum signal velocity determined by the null geodesic condition, which is infinitely large near the Planck time and monotonically decreases in time to the conventional light velocity when time approaches infinity. This implies that, depending on the position of the particle in question, the light cone determined by Maxwell's equations may be inside or outside the null cone determined by the null geodesic equation, which may lead to the causality problem.
The post Gaussian effective potential in $D=2+2\veps$ dimensions is evaluated for the Ginzburg-Landau theory of superconductivity. Two and three loop integrals for the post Gaussian correction terms in $D=2+2\veps$ dimensions are calculated and $\veps$-expansion for these integrals are constructed. In $D=2+2\veps$ fractal dimensions Ginzburg Landau parameter turned out to be sensitive to $\veps$ and the contribution of the post Gaussian term is larger than that for D=3. Adjusting $\veps$ to the recent experimental data on $κ(T)$ for high -$T_c$ cuprate superconductor $Tl_2Ca_2Ba_2Cu_3O_{10} (T\cl-2223)$, we found that $\veps=0.21$ is the best choice for this material. The result clearly shows that, in order to understand high - $T_c$ superconductivity, it is necessary to include the fluctuation contribution as well as the contribution from the dimensionality of the sample. The method gives a theoretical tool to estimate the effective dimensionality of the samples.
The post Gaussian effective potential in D=3 dimensions and the Gaussian effective potential in D=2+epsilon are evaluated for the Ginzburg-Landau theory of superconductivity. It is shown that, the next order correction to the Gaussian approximation of the Ginzburg-Landau parameter (kappa) is significant, whereas contribution from the two dimensionality is rather small. This strongly indicates that strong correlation plays a more dominant role than the two dimensionality does in high T_c superconductivity.
The perturbative framework of the space-time non-commutative real scalar field theory is formulated, based on the unitary S-matrix. Unitarity of the S-matrix is explicitly checked order by order using the Heisenberg picture of Lagrangian formalism of the second quantized operators, with the emphasis of the so-called minimal realization of the time-ordering step function and of the importance of the $\star$-time ordering. The Feynman rule is established and is presented using $ϕ^4$ scalar field theory. It is shown that the divergence structure of space-time non-commutative theory is the same as the one of space-space non-commutative theory, while there is no UV-IR mixing problem in this space-time non-commutative theory.