Equivalence of many-photon Green's functions in the Duffin-Kemmer-Petiau and Klein-Gordon-Fock statistical quantum field theories

Using the functional integral formalism for the statistical generating functional in the statistical (finite temperature) quantum field theory, we prove the equivalence of many-photon Greens functions in the Duffin-Kennner-Petiau and Klein-Gordon-Fock statistical quantum field theories. As an illustration, we calculate the one-loop polarization operators in both theories and demonstrate their coincidence.

Integrable field theories with defects

The structure of integrable field theories in the presence of defects is discussed in terms of boundary functions under the Lagrangian formalism. Explicit examples of bosonic and fermionic theories are considered. In particular, the boundary functions for the super sinh-Gordon model is constructed and shown to generate the Backlund transformations for its soliton solutions.

Noncommutative integrable field theories in 2d

We study the noncommutative generalization of (Euclidean) integrable models in two dimensions, specifically the sine- and sinh-Gordon and the U(N) principal chiral models. By looking at tree-level amplitudes for the sinh-Gordon model we show that its naive noncommutative generalization is not integrable. on the other hand, the addition of extra constraints, obtained through the generalization of the zero-curvature method, renders the model integrable. We construct explicit nonlocal nontrivial conserved charges for the U(N) principal chiral model using the Brezin-Itzykson-Zinn-Justin-Zuber method. (C) 2003 Elsevier B.V. All rights reserved.

Equivalence of many-gluon Green's functions in the Duffin-Kemmer-Petieu and Klein-Gordon-Fock statistical quantum field theories

We prove the equivalence of many-gluon Green's functions in the Duffin-Kemmer-Petieu and Klein-Gordon-Fock statistical quantum field theories. The proof is based on the functional integral formulation for the statistical generating functional in a finite-temperature quantum field theory. As an illustration, we calculate one-loop polarization operators in both theories and show that their expressions indeed coincide.

Kac-Moody construction of Toda type field theories

Using the coadjoint orbit method we derive a geometric WZWN action based on the extended two-loop Kac-Moody algebra. We show that under a hamiltonian reduction procedure, which respects conformal invariance, we obtain a hierarchy of Toda type field theories, which contain as submodels the Toda molecule and periodic Toda lattice theories. We also discuss the classical r-matrix and integrability properties.

Toda lattice field theories, discrete W algebras, Toda lattice hierarchies and quantum groups

In analogy with the Liouville case we study the sl3 Toda theory on the lattice and define the relevant quadratic algebra and out of it we recover the discrete W3 algebra. We define an integrable system with respect to the latter and establish the relation with the Toda lattice hierarchy. We compute the relevant continuum limits. Finally we find the quantum version of the quadratic algebra.

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.

Type-II defects in integrable classical field theories

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

Higher spatial derivative field theories

In this work, we employ renormalization group methods to study the general behavior of field theories possessing anisotropic scaling in the spacetime variables. The Lorentz symmetry breaking that accompanies these models are either soft, if no higher spatial derivative is present, or it may have a more complex structure if higher spatial derivatives are also included. Both situations are discussed in models with only scalar fields and also in models with fermions as a Yukawa-like model.

Ward identities in Lifshitz-like field theories

In this work, we develop a normal product algorithm suitable to the study of anisotropic field theories in flat space, apply it to construct the symmetries generators and describe how their possible anomalies may be found. In particular, we discuss the dilatation anomaly in a scalar model with critical exponent z = 2 in six spatial dimensions.

Tensorial group field theories

In questa tesi il Gruppo di Rinormalizzazione non-perturbativo (FRG) viene applicato ad una particolare classe di modelli rilevanti in Gravit`a quantistica, conosciuti come Tensorial Group Field Theories (TGFT). Le TGFT sono teorie di campo quantistiche definite sulla variet`a di un gruppo G. In ogni dimensione esse possono essere espanse in grafici di Feynman duali a com- plessi simpliciali casuali e sono caratterizzate da interazioni che implementano una non-localit`a combinatoriale. Le TGFT aspirano a generare uno spaziotempo in un contesto background independent e precisamente ad ottenere una descrizione con- tinua della sua geometria attraverso meccanismi fisici come le transizioni di fase. Tra i metodi che meglio affrontano il problema di estrarre le transizioni di fase e un associato limite del continuo, uno dei pi` u efficaci `e il Gruppo di Rinormalizzazione non-perturbativo. In questo elaborato ci concentriamo su TGFT definite sulla variet`a di un gruppo non-compatto (G = R) e studiamo il loro flusso di Rinormalizzazione. Identifichiamo con successo punti fissi del flusso di tipo IR, e una superficie critica che suggerisce la presenza di transizioni di fase in regime Infrarosso. Ci`o spinge ad uno stu- dio per approfondire la comprensione di queste transizioni di fase e della fisica continua che vi `e associata. Affrontiamo inoltre il problema delle divergenze Infrarosse, tramite un processo di regolarizzazione che definisce il limite termodinamico appropriato per le TGFT. Infine, applichiamo i metodi precedentementi sviluppati ad un modello dotato di proiezione sull’insieme dei campi gauge invarianti. L’analisi, simile a quella applicata al modello precedente, conduce nuovamente all’identificazione di punti fissi (sia IR che UV) e di una superficie critica. La presenza di transizioni di fasi `e, dunque, evidente ancora una volta ed `e possibile confrontare il risultato col modello senza proiezione sulla dinamica gauge invariante.

Bayesian Approach to Spectral Function Reconstruction for Euclidean Quantum Field Theories

We present a novel approach to the inference of spectral functions from Euclidean time correlator data that makes close contact with modern Bayesian concepts. Our method differs significantly from the maximum entropy method (MEM). A new set of axioms is postulated for the prior probability, leading to an improved expression, which is devoid of the asymptotically flat directions present in the Shanon-Jaynes entropy. Hyperparameters are integrated out explicitly, liberating us from the Gaussian approximations underlying the evidence approach of the maximum entropy method. We present a realistic test of our method in the context of the nonperturbative extraction of the heavy quark potential. Based on hard-thermal-loop correlator mock data, we establish firm requirements in the number of data points and their accuracy for a successful extraction of the potential from lattice QCD. Finally we reinvestigate quenched lattice QCD correlators from a previous study and provide an improved potential estimation at T2.33TC.