Various topological excitations in the SO(4) gauge field in higher dimensions

Following the original analysis Of Zhang and Hu for the 4-dimensional generalization of Quantum Hall effect, there has been much work from different viewpoints on the higher dimensional condensed matter systems. In this paper, we discuss three kinds of topological excitations in the SO(4) gauge field of condensed matter systems in 4-dimension-the instantons and anti-instantons, the 't Hooft-Polyakov monopoles, and the 2-membranes. Using the phi-mapping topological theory, it is revealed that there are 4-, 3-, and 2-dimensional topological currents inhering in the SO (4) gauge field, and the above three kinds of excitations can be directly and explicitly derived from these three kinds of currents, respectively. Moreover, it is shown that the topological charges of these excitations are characterized by the Hopf indices and Brouwer degrees of phi-mapping. (c) 2005 Elsevier Inc. All rights reserved.

Gauge Field Theories, Quantum Space-Time and Some Applications

In this thesis, the possibility of extending the Quantization Condition of Dirac for Magnetic Monopoles to noncommutative space-time is investigated. The three publications that this thesis is based on are all in direct link to this investigation. Noncommutative solitons have been found within certain noncommutative field theories, but it is not known whether they possesses only topological charge or also magnetic charge. This is a consequence of that the noncommutative topological charge need not coincide with the noncommutative magnetic charge, although they are equivalent in the commutative context. The aim of this work is to begin to fill this gap of knowledge. The method of investigation is perturbative and leaves open the question of whether a nonperturbative source for the magnetic monopole can be constructed, although some aspects of such a generalization are indicated. The main result is that while the noncommutative Aharonov-Bohm effect can be formulated in a gauge invariant way, the quantization condition of Dirac is not satisfied in the case of a perturbative source for the point-like magnetic monopole.

BCS-BEC crossover induced by a synthetic non-Abelian gauge field

We investigate the ground state of interacting spin-1/2 fermions in three dimensions at a finite density (rho similar to k(F)(3)) in the presence of a uniform non-Abelian gauge field. The gauge-field configuration (GFC) described by a vector lambda equivalent to (lambda(x),lambda(y),lambda(z)), whose magnitude lambda determines the gauge coupling strength, generates a generalized Rashba spin-orbit interaction. For a weak attractive interaction in the singlet channel described by a small negative scattering length (k(F)vertical bar a(s)vertical bar less than or similar to 1), the ground state in the absence of the gauge field (lambda = 0) is a BCS (Bardeen-Cooper-Schrieffer) superfluid with large overlapping pairs. With increasing gauge-coupling strength, a non-Abelian gauge field engenders a crossover of this BCS ground state to a BEC (Bose-Einstein condensate) of bosons even with a weak attractive interaction that fails to produce a two-body bound state in free vacuum (lambda = 0). For large gauge couplings (lambda/k(F) >> 1), the BEC attained is a condensate of bosons whose properties are solely determined by the Rashba gauge field (and not by the scattering length so long as it is nonzero)-we call these bosons ``rashbons.'' In the absence of interactions (a(s) = 0(-)), the shape of the Fermi surface of the system undergoes a topological transition at a critical gauge coupling lambda(T). For high-symmetry GFCs we show that the crossover from the BCS superfluid to the rashbon BEC occurs in the regime of lambda near lambda(T). In the context of cold atomic systems, these results make an interesting suggestion of obtaining BCS-BEC crossover through a route other than tuning the interaction between the fermions.

Feshbach resonance in a synthetic non-Abelian gauge field

We study the Feshbach resonance of spin-1/2 particles in a uniform synthetic non-Abelian gauge field that produces spin-orbit coupling and constant spin potentials. We develop a renormalizable quantum field theory including the closed-channel boson which engenders the resonance. We show that the gauge field shifts the Feshbach field where the low-energy scattering length diverges. In addition the Feshbach field is shown to depend on the center-of-mass momentum of the particles. For high-symmetry gauge fields which produce a Rashba spin coupling, we show that the system supports two bound states over a regime of magnetic fields when the background scattering length is negative and the resonance width is comparable to the energy scale of the spin-orbit coupling. We discuss interesting consequences useful for future theoretical and experimental studies, even while our predictions are in agreement with recent experiments.

Inner structure of Spin(c)(4) gauge potential on 4-dimensional manifolds

The decomposition of Spin(c)(4) gauge potential in terms of the Dirac 4-spinor is investigated, where an important characterizing equation Delta A(mu) = -lambda A(mu) has been discovered. Here, lambda is the vacuum expectation value of the spinor field, lambda = parallel to Phi parallel to(2), and A(mu) the twisting U(1) potential. It is found that when), takes constant values, the characterizing equation becomes an eigenvalue problem of the Laplacian operator. It provides a revenue to determine the modulus of the spinor field by using the Laplacian spectral theory. The above study could be useful in determining the spinor field and twisting potential in the Seiberg-Witten equations. Moreover, topological characteristic numbers of instantons in the self-dual sub-space are also discussed.

Electromagnetic gauge field interpolation between the instant form and the front form of the Hamiltonian dynamics

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Quantum Space-Time and Noncommutative Gauge Field Theories

Arguments arising from quantum mechanics and gravitation theory as well as from string theory, indicate that the description of space-time as a continuous manifold is not adequate at very short distances. An important candidate for the description of space-time at such scales is provided by noncommutative space-time where the coordinates are promoted to noncommuting operators. Thus, the study of quantum field theory in noncommutative space-time provides an interesting interface where ordinary field theoretic tools can be used to study the properties of quantum spacetime. The three original publications in this thesis encompass various aspects in the still developing area of noncommutative quantum field theory, ranging from fundamental concepts to model building. One of the key features of noncommutative space-time is the apparent loss of Lorentz invariance that has been addressed in different ways in the literature. One recently developed approach is to eliminate the Lorentz violating effects by integrating over the parameter of noncommutativity. Fundamental properties of such theories are investigated in this thesis. Another issue addressed is model building, which is difficult in the noncommutative setting due to severe restrictions on the possible gauge symmetries imposed by the noncommutativity of the space-time. Possible ways to relieve these restrictions are investigated and applied and a noncommutative version of the Minimal Supersymmetric Standard Model is presented. While putting the results obtained in the three original publications into their proper context, the introductory part of this thesis aims to provide an overview of the present situation in the field.

Synthesis and electrical properties of the (PVA)(0.7)(Kl)(0.3)center dot xH(2)SO(4) (0 <= x <= 5) polymer electrolytes and their performance in a primary Zn/MnO2 battery

Solid acid polymer electrolytes (SAPE) were synthesised using polyvinyl alcohol, potassium iodide and sulphuric acid in different molar ratios by solution cast technique. The temperature dependent nature of electrical conductivity and the impedance of the polymer electrolytes were determined along with the associated activation energy. The electrical conductivity at room temperature was found to be strongly depended on the amorphous nature of the polymers and H2SO4 concentration. The ac (100 Hz to 10 MHz) and dc conductivities of the polymer electrolytes with different H2SO4 concentrations were analyzed. A maximum dc conductivity of 1.05 x 10(-3) S cm(-1) has been achieved at ambient temperature for electrolytes containing 5 M H2SO4. The frequency and temperature dependent dielectric and electrical modulus properties of the SAPE were studied. The charge transport in the present polymer electrolyte was obtained using Wagner's polarization technique, which demonstrated the charge transport to be mainly due to ions. Using these solid acid polymer electrolytes novel Zn/SAPE/MnO2 solid state batteries were fabricated and their discharge capacity was calculated. An open circuit voltage of 1.758V was obtained for 5 M H2SO4 based Zn/SAPE/MnO2 battery. (C) 2010 Elsevier Ltd. All rights reserved.

Bound states of two spin-1/2 fermions in a synthetic non-Abelian gauge field

We study the bound states of two spin-1/2 fermions interacting via a contact attraction (characterized by a scattering length) in the singlet channel in three-dimensional space in presence of a uniform non-Abelian gauge field. The configuration of the gauge field that generates a Rashba-type spin-orbit interaction is described by three coupling parameters (lambda(x),lambda(y),lambda(z)). For a generic gauge field configuration, the critical scattering length required for the formation of a bound state is negative, i.e., shifts to the ``BCS side'' of the resonance. Interestingly, we find that there are special high-symmetry configurations (e.g., lambda(x) = lambda(y) = lambda(z)) for which there is a two-body bound state for any scattering length however small and negative. Remarkably, the bound-state wave functions obtained for such configurations have nematic spin structure similar to those found in liquid He-3. Our results show that the BCS-BEC (Bose-Einstein condensation) crossover is drastically affected by the presence of a non-Abelian gauge field. We discuss possible experimental signatures of our findings both at high and low temperatures.

Trapped fermions in a synthetic non-Abelian gauge field

On increasing the coupling strength (lambda) of a non-Abelian gauge field that induces a generalized Rashba spin-orbit interaction, the topology of the Fermi surface of a homogeneous gas of noninteracting fermions of density rho similar to k(F)(3) undergoes a change at a critical value, lambda(T) approximate to k(F) [Phys. Rev. B 84, 014512 ( 2011)]. In this paper we analyze how this phenomenon affects the size and shape of a cloud of spin-1/2 fermions trapped in a harmonic potential such as those used in cold atom experiments. We develop an adiabatic formulation, including the concomitant Pancharatnam-Berry phase effects, for the one-particle states in the presence of a trapping potential and the gauge field, obtaining approximate analytical formulas for the energy levels for some high symmetry gauge field configurations of interest. An analysis based on the local density approximation reveals that, for a given number of particles, the cloud shrinks in a characteristic fashion with increasing.. We explain the physical origins of this effect by a study of the stress tensor of the system. For an isotropic harmonic trap, the local density approximation predicts a spherical cloud even for anisotropic gauge field configurations. We show, via a calculation of the cloud shape using exact eigenstates, that for certain gauge field configurations there is a systematic and observable anisotropy in the cloud shape that increases with increasing gauge coupling lambda. The reasons for this anisotropy are explained using the analytical energy levels obtained via the adiabatic approximation. These results should be useful in the design of cold atom experiments with fermions in non-Abelian gauge fields. An important spin-off of our adiabatic formulation is that it reveals exciting possibilities for the cold-atom realization of interesting condensed matter Hamiltonians by using a non-Abelian gauge field in conjunction with another potential. In particular, we show that the use of a spherical non-Abelian gauge field with a harmonic trapping potential produces a monopole field giving rise to a spherical geometry quantum Hall-like Hamiltonian in the momentum representation.

Consistent deformations of [p,p]-type gauge field theories

Using BRST-cohomological techniques, we analyze the consistent deformations of theories describing free tensor gauge fields whose symmetries are represented by Young tableaux made of two columns of equal length p, p > 1. Under the assumptions of locality and Poincaré invariance, we find that there is no consistent deformation of these theories that non-trivially modifies the gauge algebra and/or the gauge transformations. Adding the requirement that the deformation contains no more than two derivatives, the only possible deformation is a cosmological-constant-like term. © SISSA/ISAS 2004.