Modified density matrix renormalization group algorithm for the zigzag spin-1/2 chain with frustrated antiferromagnetic exchange: Comparison with field theory at large J(2)/J(1)

A modified density matrix renormalization group (DMRG) algorithm is applied to the zigzag spin-1/2 chain with frustrated antiferromagnetic exchange J(1) and J(2) between first and second neighbors. The modified algorithm yields accurate results up to J(2)/J(1) approximate to 4 for the magnetic gap Delta to the lowest triplet state, the amplitude B of the bond order wave phase, the wavelength lambda of the spiral phase, and the spin correlation length xi. The J(2)/J(1) dependences of Delta, B, lambda, and xi provide multiple comparisons to field theories of the zigzag chain. The twist angle of the spiral phase and the spin structure factor yield additional comparisons between DMRG and field theory. Attention is given to the numerical accuracy required to obtain exponentially small gaps or exponentially long correlations near a quantum phase transition.

Noncommutative Quantum Field Theory : Problem of Time and Some Applications

In this thesis the current status and some open problems of noncommutative quantum field theory are reviewed. The introduction aims to put these theories in their proper context as a part of the larger program to model the properties of quantized space-time. Throughout the thesis, special focus is put on the role of noncommutative time and how its nonlocal nature presents us with problems. Applications in scalar field theories as well as in gauge field theories are presented. The infinite nonlocality of space-time introduced by the noncommutative coordinate operators leads to interesting structure and new physics. High energy and low energy scales are mixed, causality and unitarity are threatened and in gauge theory the tools for model building are drastically reduced. As a case study in noncommutative gauge theory, the Dirac quantization condition of magnetic monopoles is examined with the conclusion that, at least in perturbation theory, it cannot be fulfilled in noncommutative space.

Geometric Algebra and Einstein’s Electron

This thesis entitled Geometric algebra and einsteins electron: Deterministic field theories .The work in this thesis clarifies an important part of Koga’s theory.Koga also developed a theory of the electron incorporating its gravitational field, using his substitutes for Einstein’s equation.The third chapter deals with the application of geometric algebra to Koga’s approach of the Dirac equation. In chapter 4 we study some aspects of the work of mendel sachs (35,36,37,).Sachs stated aim is to show how quantum mechanics is a limiting case of a general relativistic unified field theory.Chapter 5 contains a critical study and comparison of the work of Koga and Sachs. In particular, we conclude that the incorporation of Mach’s principle is not necessary in Sachs’s treatment of the Dirac equation.

Studies in quantum field theory at finite temperature

The thesis deals with certain quantum field systems exhibiting spontaneous symmetry breaking and their response to temperature. These models find application in diverse branches such as particle physics, solid state physics and non~linear optics. The nature of phase transition that these systems may undergo is also investigated. The thesis contains seven chapters. The first chapter is introductory and gives a brief account of the various phenomena associated with spontaneous symmetry breaking. The chapter closes with anote on the effect of temperature on quantum field systems. In chapter 2, the spontaneous symmetry breaking phenomena are reviewed in more detail. Chapter 3, deals with the formulation of ordinary and generalised sine-Gordon field theories on a lattice and the study of the nature of phase transition occurring in these systems. In chapter 4, the effect of temperature on these models is studied, using the effective potential method. Chapter 5 is a continuation of this study for another model, viz, the m6 model. The nature of phase transition is also studied. Chapters 5 and 6 constitute a report of the investigations on the behaviour of coupling constants under thermal excitation D1 $4 theory, scalar electrodynamics, abelian and non-abelian gauge theories

Effects of new nonlinear couplings in relativistic effective field theory

We extend the relativistic mean field theory model of Sugahara and Toki by adding new couplings suggested by modern effective field theories. An improved set of parameters is developed with the goal to test the ability of the models based on effective field theory to describe the properties of finite nuclei and, at the same time, to be consistent with the trends of Dirac-Brueckner-Hartree-Fock calculations at densities away from the saturation region. We compare our calculations with other relativistic nuclear force parameters for various nuclear phenomena.

Understanding the effects of anesthetic agents on the EEG through neural field theory

Anesthetic and analgesic agents act through a diverse range of pharmacological mechanisms. Existing empirical data clearly shows that such "microscopic" pharmacological diversity is reflected in their "macroscopic" effects on the human electroencephalogram (EEG). Based on a detailed mesoscopic neural field model we theoretically posit that anesthetic induced EEG activity is due to selective parametric changes in synaptic efficacy and dynamics. Specifically, on the basis of physiologically constrained modeling, it is speculated that the selective modification of inhibitory or excitatory synaptic activity may differentially effect the EEG spectrum. Such results emphasize the importance of neural field theories of brain electrical activity for elucidating the principles whereby pharmacological agents effect the EEG. Such insights will contribute to improved methods for monitoring depth of anesthesia using the EEG.

Neural population models and cortical field theory: overview

The term neural population models (NPMs) is used here as catchall for a wide range of approaches that have been variously called neural mass models, mean field models, neural field models, bulk models, and so forth. All NPMs attempt to describe the collective action of neural assemblies directly. Some NPMs treat the densely populated tissue of cortex as an excitable medium, leading to spatially continuous cortical field theories (CFTs). An indirect approach would start by modelling individual cells and then would explain the collective action of a group of cells by coupling many individual models together. In contrast, NPMs employ collective state variables, typically defined as averages over the group of cells, in order to describe the population activity directly in a single model. The strength and the weakness of his approach are hence one and the same: simplification by bulk. Is this justified and indeed useful, or does it lead to oversimplification which fails to capture the pheno ...

On the generalized eigenvalue method for energies and matrix elements in lattice field theory

We discuss the generalized eigenvalue problem for computing energies and matrix elements in lattice gauge theory, including effective theories such as HQET. It is analyzed how the extracted effective energies and matrix elements converge when the time separations are made large. This suggests a particularly efficient application of the method for which we can prove that corrections vanish asymptotically as exp(-(E(N+1) - E(n))t). The gap E(N+1) - E(n) can be made large by increasing the number N of interpolating fields in the correlation matrix. We also show how excited state matrix elements can be extracted such that contaminations from all other states disappear exponentially in time. As a demonstration we present numerical results for the extraction of ground state and excited B-meson masses and decay constants in static approximation and to order 1/m(b) in HQET.

Structural aspects of the fermion-boson mapping in two-dimensional gauge and anomalous gauge theories with massive fermions

Using a synthesis of the functional integral and operator approaches we discuss the fermion-buson mapping and the role played by the Bose field algebra in the Hilbert space of two-dimensional gauge and anomalous gauge field theories with massive fermions. In QED, with quartic self-interaction among massive fermions, the use of an auxiliary vector field introduces a redundant Bose field algebra that should not be considered as an element of the intrinsic algebraic structure defining the model. In anomalous chiral QED, with massive fermions the effect of the chiral anomaly leads to the appearance in the mass operator of a spurious Bose field combination. This phase factor carries no fermion selection rule and the expected absence of Theta-vacuum in the anomalous model is displayed from the operator solution. Even in the anomalous model with massive Fermi fields, the introduction of the Wess-Zumino field replicates the theory, changing neither its algebraic content nor its physical content. (C) 2002 Elsevier B.V. (USA).

Ghost free dual vector theories in 2+1 dimensions

We explore here the issue of duality versus spectrum equivalence in dual theories generated through the master action approach. Specifically we examine a generalized self-dual (GSD) model where a Maxwell term is added to the self-dual model. A gauge embedding procedure applied to the GSD model leads to a Maxwell-Chern-Simons (MCS) theory with higher derivatives. We show here that the latter contains a ghost mode contrary to the original GSD model. By figuring out the origin of the ghost we are able to suggest a new master action which interpolates between the local GSD model and a nonlocal MCS model. Those models share the same spectrum and are ghost free. Furthermore, there is a dual map between both theories at classical level which survives quantum correlation functions up to contact terms. The remarks made here may be relevant for other applications of the master action approach.

Generalized duality between local vector theories in D=2+1

The existence of an interpolating master action does not guarantee the same spectrum for the interpolated dual theories. In the specific case of a generalized self-dual (GSD) model defined as the addition of the Maxwell term to the self-dual model in D = 2 + 1, previous master actions have furnished a dual gauge theory which is either nonlocal or contains a ghost mode. Here we show that by reducing the Maxwell term to first order by means of an auxiliary field we are able to define a master action which interpolates between the GSD model and a couple of non-interacting Maxwell-Chern-Simons theories of opposite helicities. The presence of an auxiliary field explains the doubling of fields in the dual gauge theory. A generalized duality transformation is defined and both models can be interpreted as self-dual models. Furthermore, it is shown how to obtain the gauge invariant correlators of the non-interacting MCS theories from the correlators of the self-dual field in the GSD model and vice-versa. The derivation of the non-interacting MCS theories from the GSD model, as presented here, works in the opposite direction of the soldering approach.

A new approach to integrable theories in any dimension

The zero curvature representation for two-dimensional integrable models is generalized to spacetimes of dimension d + 1 by the introduction of a d-form connection. The new generalized zero curvature conditions can be used to represent the equations of motion of some relativistic invariant field theories of physical interest in 2 + 1 dimensions (BF theories, Chern-Simons, 2 + 1 gravity and the CP1 model) and 3 + 1 dimensions (self-dual Yang-Mills theory and the Bogomolny equations). Our approach leads to new methods of constructing conserved currents and solutions. In a submodel of the 2 + 1-dimensional CP1 model, we explicitly construct an infinite number of previously unknown non-trivial conserved currents. For each positive integer spin representation of sl(2) we construct 2j + 1 conserved currents leading to 2j + 1 Lorentz scalar charges. (C) 1998 Elsevier B.V. B.V.

The behavior of the sextic coupling for the scalar field at the intermediate and strong coupling regime

We study the behavior of the renormalized sextic coupling at the intermediate and strong coupling regime for the phi(4) theory defined in d = 2 dimensions. We found a good agreement with the results obtained by the field-theoretical renormalization-group in the Ising limit. In this work we use the lattice regularization method.

Field-theory Two-point Functions via Negative Dimension Integration

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Cubic twistorial string field theory

Witten has recently proposed a string theory in twistor space whose D-instanton contributions are conjectured to compute M = 4 super-Yang-Mills scattering amplitudes. An alternative string theory in twistor space was then proposed whose open string tree amplitudes reproduce the D-instanton computations of maximal degree in Witten's model. In this paper, a cubic open string field theory action is constructed for this alternative string in twistor space, and is shown to be invariant under parity transformations which exchange MHV and googly amplitudes. Since the string field theory action is gauge-invariant and reproduces the correct cubic super-Yang-Mills interactions, it provides strong support for the conjecture that the string theory correctly computes N-point super-Yang-Mills tree amplitudes. © SISSA/ISAS 2004.