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Sze-Shiang Feng

Publications and source records attributed to Sze-Shiang Feng.

At least 19 recordsLinked to original sources
arXiv2021

A Generally Covariant Theory of Quantized Dirac Field in de Sitter Spacetime

As a sequel to our previous work\cite{Feng2020}, we propose in this paper a quantization scheme for Dirac field in de Sitter spacetime. Our scheme is covariant under both general transformations and Lorentz transformations. We first present a Hamiltonian structure, then quantize the field following the standard approach of constrained systems. For the free field, the time-dependent quantized Hamiltonian is diagonalized by Bogliubov transformation and the eigen-states at each instant are interpreted as the observed particle states at that instant. The measurable energy-momentum of observed particle/antiparticles are the same as obtained for Klein-Gordon field. Moreover, the energy-momentum also satisfies geodesic equation, a feature justifying its measurability. As in \cite{Feng2020}, though the mathematics is carried out in terms of conformal coordinates for the sake of convenience, the whole theory can be transformed into any other coordinates based on general covariance. It is concluded that particle/antiparticle states, such as vacuum states in particular are time-dependent and vacuum states at one time evolves into non-vacuum states at later times. Formalism of perturbational calculation is provided with an extended Dirac picture.

hep-th↗
arXiv2020

A Generally Covariant Theory of Quantized Real Klein-Gordon Field in de Sitter Spacetime

We propose in this paper a quantization scheme for real Klein-Gordon field in de Sitter spacetime. Our scheme is generally covariant with the help of vierbein, which is necessary usually for spinor field in curved spacetime. We first present a Hamiltonian structure, then quantize the field following the standard approach. For the free field, the time-dependent quantized Hamiltonian is diagonalized by Bogliubov transformation and the eigen-states at each instant are interpreted as the observed particle states at that instant. The interpretation is supported by the known cosmological red-shift formula and the on-shell condition of 4-momentum for a free field. Though the mathematics is carried out in term of conformal coordinates for the sake of convenience, the whole theory can be transformed into any other coordinates based on general covariance. It is concluded that particle states, such as vacuum states in particular are time-dependent and vacuum states at one time evolves into non-vacuum states at later times. Formalism of perturbational is provided with an extended Dirac picture.

hep-th↗
arXiv2015

Implication of Spatial and Temporal Variations of the Fine-Structure Constant

Temporal and spatial variation of fine-structure constant $α\equiv e^2/\hbar c$ in cosmology has been reported in analysis of combination Keck and VLT data. This paper studies this variation based on consideration of basic spacetime symmetry in physics. Both laboratory $α_0$ and distant $α_z$ are deduced from relativistic spectrum equations of atoms (e.g.,hydrogen atom) defined in inertial reference system. When Einstein's $Λ\neq 0$, the metric of local inertial reference systems in SM of cosmology is Beltrami metric instead of Minkowski, and the basic spacetime symmetry has to be de Sitter (dS) group. The corresponding special relativity (SR) is dS-SR. A model based on dS-SR is suggested. Comparing the predictions on $α$-varying with the data, the parameters are determined. The best-fit dipole mode in $α$'s spatial varying is reproduced by this dS-SR model. $α$-varyings in whole sky is also studied. The results are generally in agreement with the estimations of observations. The main conclusion is that the phenomenon of $α$-varying cosmologically with dipole mode dominating is due to the de Sitter (or anti de Sitter) spacetime symmetry with a Minkowski point in an extended special relativity called de Sitter invariant special relativity (dS-SR) developed by Dirac-Inönü-Wigner-Gürsey-Lee-Lu-Zou-Guo.

gr-qc↗
arXiv2006

Ferromagnetism of Ga$_{1-x}$Mn$_x$As and Weiss theory of Curie temperature in the coherent potential approximation

The zinc-blende GaAs-based III-V diluted magnetic semiconductors (DMS)are studied in the coherent potential approximation(CPA). In this work, we use the exact Hilbert transformation of the face-centered cubic(fcc) density of states (DOS), which is different from the usual semi-circle density of states employed in our previous work. Our calculated relation of ground-state energy and impurity magnetization shows that ferromagnetism is always favorable at low temperatures. For very weak Kondo coupling, the density of states (DOS) of the host semiconductor is modified slightly. Impurity band can be generated at the host band bottom only when Kondo coupling is strong enough. Using Weiss molecular theory, we predict a nonlinear relation of Curie temperature with respect to Kondo coupling, as is different from the conclusion of our previous calculations based on semicircle DOS. The agreement of our calculated $T_{\rm C}$ with measured values is convincing.

cond-mat.dis-nn↗
arXiv2005

Ground-state properties and molecular theory of Curie temperature in the coherent potential approximation of diluted magnetic semiconductors

Using spin-1/2 description of valence holes and Kondo coupling between local spins and carriers, GaAs-based III-V diluted magnetic semiconductors (DMS)are studied in the coherent potential approximation(CPA). Our calculated relation of ground-state energy and impurity magnetization shows that ferromagnetism is always favorable at low temperatures. For very weak Kondo coupling, the density of states (DOS) of the host semiconductor is not modified much. Impurity band can be generated at the host band bottom only when Kondo coupling is strong enough. Using Weiss molecular theory, we predict a linear relation of Curie temperature with respect to Kondo coupling and doping concentration $x$ if the hole density is proportional to $x$.

cond-mat.mtrl-sci↗
arXiv2005

A low temperature derivation of spin-spin exchange in Kondo lattice model

Using Hubbard-Stratonovich transformation and drone-fermion representations for spin-1/2 and for spin-3/2, which is presented for the first time, we make a path-integral formulation of the Kondo lattice model. In the case of weak coupling and low temperature, the functional integral over conduction fermions can be approximated to the quadratic order and this gives the well-known RKKY interaction. In the case of strong coupling, the same quadratic approximation leads to an effective local spin-spin interaction linear in hopping energy $t$

cond-mat.str-el↗
arXiv2005

Spin-wave softening and Hund's coupling in ferromagnetic manganites

Using one-orbital model of hole-doped manganites, we show with the help of Holstein-Primakov transformation that finite Hund's coupling is responsible for the spin-wave softening in the ferromagnetic $B$-phase manganites. We obtain an analytical result for the spin-wave spectrum for $\JH\gg t$. In the limit of infinte Hund's coupling, the spectrum is the conventional nearest-neighbor Heisenberg ferromagnetic spin-wave. The $o(t/\JH)$-order correction is negative and thus accounts for the softening near the zone boundary.

cond-mat.str-el↗
arXiv2001

The shortest cut in brane cosmology

We consider brane cosmology studying the shortest null path on the brane for photons, and in the bulk for gravitons. We derive the differential equation for the shortest path in the bulk for a 1+4 cosmological metric. The time cost and the redshifts for photons and gravitons after traveling their respective path are compared. We consider some numerical solutions of the shortest path equation, and show that there is no shortest path in the bulk for the Randall-Sundrum vacuum brane solution, the linear cosmological solution of Binétruy, et al for $ω= -1, -{2/3}$, and for some expanding brane universes.

hep-th↗
arXiv2001

New superconducting states in the Hubbard model

By acting on the excited states at half-filling in the positive-$U$ Hubbard model with the $η$-pairing operators, we found some new superconducting states in the Hubbard model away from half-filling. Such eigenstates are different from the zero-pair and one-pair states introduced by Yang. It is shown that the one-pair states are not the ground-states and possess ODLRO.

cond-mat↗
arXiv2000

Local observed time and redshift in curved spacetime

Using the observed time and spatial intervals defined originally by Einstein and the observation frame in the vierbein formalism, we propose that in curved spacetime, for a wave received in laboratories, the observed frequency is the changing rate of the phase of the wave relative to the local observable time scale and the momentum the changing rate of the phase relative to the local observable spatial length scale. The case of Robertson-Walker universe is especially considered.

hep-th↗
arXiv1999

Two Theorems on Pseudo-spin in the Hubbard Model

An inequality of the eigenvalues of the reduced density matrix $ρ_2$ at finite temperature in the Hubbard model is obtained by means of the Bogolyubov inequality. The quasi-average of $\tilde{S}^{+}$ in a simple symmetry-breaking perturbation of the Hamiltonian for a bipartite lattice is shown to be zero.

cond-mat.str-el↗
arXiv1999

(2+1)-Dimensional Fermion Determinant in a Constant Background Field at Finite Temperature and Density

We evaluate exactly both the non-relativistic and relativistic fermion determinant in 2+1 dimensions in a constant background field at finite temperature. The effect of finite chemical potential is also considered. In both cases, the systems are decoupled into an infinite number of 1+1 fermions by Fourier transformation in the $β$-variable. The total effective actions demonstrate non-extensiveness in the $β$ dimension.

hep-th↗
arXiv1999

Gaussian Effective Potential Analysis of Sinh(Sine)-Gordon Models by New Regularization-Renormalization Scheme

Using the new regularization and renormalization scheme recently proposed by Yang and used by Ni et al, we analyse the sine-Gordon and sinh-Gordon models within the framework of Gaussian effective potential in D+1 dimensions. Our analysis suffers no divergence and so does not suffer from the manipulational obscurities in the conventional analysis of divergent integrals. Our main conclusions agree exactly with those of Ingermanson for D=1,2 but disagree for D=3: the D=3 sinh(sine)-Gordon model is non-trivial. Furthermore, our analysis shows that for D=1,2, the running coupling constant (RCC)has poles for sine-Gordon model($γ^2<0$) and the sinh-Gordon model ($γ^2>0$) has a possible critical point $γ^2_c$ while for D=3, the RCC has poles for both $γ^2>0$ and $γ^2<0$.

hep-th↗
arXiv1999

Exact Results of Strongly Correlated Systems at Finite Temperature

Some rigorous conclusions of the Hubbard model, Kondo lattice model and periodic Anderson model at finite temperature are acquired employing the fluctuation-dissipation theorem and particle-hole transform. The main conclusion states that for the three models, the expectation value of ${\bf \tilde{S}}^2-{\bf \tilde{S}}^2_z$ will be of order $N_Λ$ at any finite temperature.

cond-mat.str-el↗
arXiv1999

Induced Parity-Breaking Term at Finite Chemical Potential and Temparature

We exactly calculated the parity-odd term of the effective action induced by the fermions in 2+1 dimensions at finite chemical potential and finite temperature. It shows that gauge invariance is still respected. A more gerneral class of background configurations is considered. The knowledge of the reduced 1+1 determinant is required in order to draw exact conclusions about the gauge invariance of the parity-odd term in this latter case.

hep-th↗
arXiv1999

Conservative Currents of Boundary Charges in $AdS_{2+1}$ Gravity

The boundary charges which constitute the Virasoro algebra in 2+1 dimensional anti-de Sitter gravity are derived by way of Noether theorem and diffeomorphic invariance. It shows that the boundary charges under discussion recently exhaust all the independent nontrivial charges available. Therefore, the state counting via the Virasoro algebra is complete.

hep-th↗