Gauge Theory of Composite Fermions: Particle-Flux Separation in Quantum Hall Systems

Fractionalization phenomenon of electrons in quantum Hall states is studied in terms of U(1) gauge theory. We focus on the Chern-Simons(CS) fermion description of the quantum Hall effect(QHE) at the filling factor $\nu=p/(2pq\pm 1)$, and show that the successful composite-fermions(CF) theory of Jain acquires a solid theoretical basis, which we call particle-flux separation(PFS). PFS can be studied efficiently by a gauge theory and characterized as a deconfinement phenomenon in the corresponding gauge dynamics. The PFS takes place at low temperatures, $T \leq T_{\rm PFS}$, where each electron or CS fermion splinters off into two quasiparticles, a fermionic chargeon and a bosonic fluxon. The chargeon is nothing but Jain's CF, and the fluxon carries $2q$ units of CS fluxes. At sufficiently low temperatures $T \leq T_{\rm BC} (< T_{\rm PFS})$, fluxons Bose-condense uniformly and (partly) cancel the external magnetic field, producing the correlation holes. This partial cancellation validates the mean-field theory in Jain's CF approach. FQHE takes place at $T < T_{\rm BC}$ as a joint effect of (i) integer QHE of chargeons under the residual field $\Delta B$ and (ii) Bose condensation of fluxons. We calculate the phase-transition temperature $T_{\rm PFS}$ and the CF mass. PFS is a counterpart of the charge-spin separation in the t-J model of high-$T_{\rm c}$ cuprates in which each electron dissociates into holon and spinon. Quasiexcitations and resistivity in the PFS state are also studied. The resistivity is just the sum of contributions of chargeons and fluxons, and $\rho_{xx}$ changes its behavior at $T = T_{\rm PFS}$, reflecting the change of quasiparticles from chargeons and fluxons at $T < T_{\rm PFS}$ to electrons at $T_{\rm PFS} < T$.Comment: 18 pages, 7 figure

Fluctuation effects of gauge fields in the slave-boson t-J model

We present a quantitative study of the charge-spin separation(CSS) phenomenon in a U(1) gauge theory of the t-J model of high-Tc superconductures. We calculate the critical temperature of confinement-deconfinement phase transition below which the CSS takes place.Comment: Latex, 9 pages, 3 figure

Field Quantization in 5D Space-Time with Z2_2-parity and Position/Momentum Propagator

Field quantization in 5D flat and warped space-times with Z$_2$-parity is comparatively examined. We carefully and closely derive 5D position/momentum(P/M) propagators. Their characteristic behaviours depend on the 4D (real world) momentum in relation to the boundary parameter ($l$) and the bulk curvature (\om). They also depend on whether the 4D momentum is space-like or time-like. Their behaviours are graphically presented and the Z$_2$ symmetry, the "brane" formation and the singularities are examined. It is shown that the use of absolute functions is important for properly treating the singular behaviour. The extra coordinate appears as a {\it directed} one like the temperature. The $\delta(0)$ problem, which is an important consistency check of the bulk-boundary system, is solved {\it without} the use of KK-expansion. The relation between P/M propagator (a closed expression which takes into account {\it all} KK-modes) and the KK-expansion-series propagator is clarified. In this process of comparison, two views on the extra space naturally come up: orbifold picture and interval (boundary) picture. Sturm-Liouville expansion (a generalized Fourier expansion) is essential there. Both 5D flat and warped quantum systems are formulated by the Dirac's bra and ket vector formalism, which shows the warped model can be regarded as a {\it deformation} of the flat one with the {\it deformation parameter} \om. We examine the meaning of the position-dependent cut-off proposed by Randall-Schwartz.Comment: 44 figures, 22(fig.)+41 pages, to be published in Phys.Rev.D, Fig.4 is improve

Wall and Anti-Wall in the Randall-Sundrum Model and A New Infrared Regularization

An approach to find the field equation solution of the Randall-Sundrum model with the $S^1/Z_2$ extra axis is presented. We closely examine the infrared singularity. The vacuum is set by the 5 dimensional Higgs field. Both the domain-wall and the anti-domain-wall naturally appear, at the {\it ends} of the extra compact axis, by taking a {\it new infrared regularization}. The stability is guaranteed from the outset by the kink boundary condition. A {\it continuous} (infrared-)regularized solution, which is a truncated {\it Fourier series} of a {\it discontinuous} solution, is utilized.The ultraviolet-infrared relation appears in the regularized solution.Comment: 36 pages, 29 eps figure file

CP Violation from a Higher Dimensional Model

It is shown that Randall-Sundrum model has the EDM term which violates the CP-symmetry. The comparison with the case of Kaluza-Klein theory is done. The chiral property, localization, anomaly phenomena are examined. We evaluate the bulk quantum effect using the method of the induced effective action. This is a new origin of the CP-violation.Comment: 15pages, Proc. of Int. Workshop on "Neutrino Masses and Mixings"(Dec.17-19,2006,Univ.of Shizuoka,Japan

Quasi-excitations and superconductivity in the t-J model on a ladder

We study the t-J model on a ladder by using slave-fermion-CP^1 formalism which is quite useful for study of lightly-doped high-T_c cuprates. By integrating half of spin variables, we obtain a low-energy effective field theory whose spin part is nothing but CP^1 sigma model. We especially focus on dynamics of composite gauge field which determines properties of quasi-excitations. Value of the coefficient of the topological term strongly influences gauge dynamics and explaines why properties of quasi-excitations depend on the number of legs of ladder. We also show that superconductivity appears as a result of short-range antiferromagnetism and order parameter has d-wave type symmetry.Comment: Latex, 28 pages and 1 figur

Effective gauge field theory of the t-J model in the charge-spin separated state and its transport properties

We study the slave-boson t-J model of cuprates with high superconducting transition temperatures, and derive its low-energy effective field theory for the charge-spin separated state in a self-consistent manner. The phase degrees of freedom of the mean field for hoppings of holons and spinons can be regarded as a U(1) gauge field, $A_i$. The charge-spin separation occurs below certain temperature, $T_{\rm CSS}$, as a deconfinement phenomenon of the dynamics of $A_i$. Below certain temperature $T_{\rm SG} (< T_{\rm CSS})$, the spin-gap phase develops as the Higgs phase of the gauge-field dynamics, and $A_i$ acquires a mass $m_A$. The effective field theory near $T_{\rm SG}$ takes the form of Ginzburg-Landau theory of a complex scalar field $\lambda$ coupled with $A_i$, where $\lambda$ represents d-wave pairings of spinons. Three dimensionality of the system is crucial to realize a phase transition at $T_{\rm SG}$. By using this field theory, we calculate the dc resistivity $\rho$. At $T > T_{\rm SG}$, $\rho$ is proportional to $T$. At $T < T_{\rm SG}$, it deviates downward from the $T$-linear behavior as $\rho \propto T \{1 -c(T_{\rm SG}-T)^d \}$. When the system is near (but not) two dimensional, due to the compactness of the phase of the field $\lambda$, the exponent $d$ deviates from its mean-field value 1/2 and becomes a nonuniversal quantity which depends on temperature and doping. This significantly improves the comparison with the experimental data

Quarks, Gluons and Frustrated Antiferromagnets

The Contractor Renormalization Group method (CORE) is used to establish the equivalence of various Hamiltonian free fermion theories and a class of generalized frustrated antiferromagnets. In particular, after a detailed discussion of a simple example, it is argued that a generalized frustrated SU(3) antiferromagnet whose single-site states have the quantum numbers of mesons and baryons is equivalent to a theory of free massless quarks. Furthermore, it is argued that for slight modification of the couplings which define the frustrated antiferromagnet Hamiltonian, the theory becomes a theory of quarks interacting with color gauge-fields.Comment: 21 pages, Late

Bad expression influences time to androgen escape in prostate cancer

&lt;b&gt;OBJECTIVE&lt;/b&gt;: To assess the role of selected downstream Bcl-2 family members (Bad, Bax, Bcl-2 and Bcl-xL) in the development of androgen-independent prostate cancer (AIPC), as androgen-deprivation therapy is the treatment of choice in advanced prostate cancer, yet patients generally relapse and progress to an AI state within 18–24 months. &lt;b&gt;PATIENTS, MATERIALS AND METHODS&lt;/b&gt;: The patient cohort was established by retrospectively selecting patients with prostate cancer who had an initial response to androgen-deprivation therapy, but subsequently relapsed with AIPC. In all, 58 patients with prostate cancer were included with matched androgen-dependent (AD) and AI prostate tumours available for immunohistochemical analysis; two independent observers using a weighted-histoscore method scored the staining. Changes in Bad, Bax, Bcl-2 and Bcl-xL expression during transition to AIPC were evaluated and then correlated to known clinical variables. &lt;b&gt;RESULTS&lt;/b&gt;: High Bad expression in AD tumours was associated with an increased time to biochemical relapse (&lt;i&gt;P&lt;/i&gt; = 0.007) and a trend towards improved overall survival (&lt;i&gt;P&lt;/i&gt; = 0.053). There were also trends towards a decrease in Bad (&lt;i&gt;P&lt;/i&gt; = 0.068) and Bax (&lt;i&gt;P&lt;/i&gt; = 0.055) expression with progression to AIPC. There were no significant results for Bcl-2 or Bcl-xL. &lt;b&gt;CONCLUSION&lt;/b&gt;: There is evidence to suggest that Bad expression levels at diagnosis influence time to biochemical relapse and overall survival, and that levels of pro-apoptotic proteins Bad and Bax fall during AIPC development. Bad might therefore represent a possible positive prognostic marker and potential therapeutic target for AIPC in the future