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Author: James Brian Silk Publisher: ISBN: Category : Languages : en Pages :
Book Description
The aim of this thesis is to explore correlation functions in two dimensional quantum field theories in two distinct ways. In part I a new method for calculating the differential equations parametrising the correlation functions of twist fields associated with the U (1) symmetry of the Dirac model is presented. While developing this method a new family of descendent twist fields are identified and their form factors calculated. This provides a novel way of calculating the vacuum expectation values of the primary twist fields and is shown to be entirely consistent with known results. The method of calculating the correlation functions of twist fields provides a parametrisation of several other correlation functions for various quantum states. Since this method relies on the Ward identities found in a double copy model it is hoped to have wider applications in other free fermion models. Part II concerns the truncated conformal space approach which has been developed to approximate perturbed conformal field theories. In this part the theory underpinning the approach is discussed and a working algorithm is developed for both bulk and boundary perturbed minimal models. The energy levels, mass gaps and one point functions of various models are computed using the truncated conformal space approach and are shown to be in good agreement with previous calculations. A possible method for using this approach to approximate two point functions in perturbed conformal field theories is discussed.
Author: James Brian Silk Publisher: ISBN: Category : Languages : en Pages :
Book Description
The aim of this thesis is to explore correlation functions in two dimensional quantum field theories in two distinct ways. In part I a new method for calculating the differential equations parametrising the correlation functions of twist fields associated with the U (1) symmetry of the Dirac model is presented. While developing this method a new family of descendent twist fields are identified and their form factors calculated. This provides a novel way of calculating the vacuum expectation values of the primary twist fields and is shown to be entirely consistent with known results. The method of calculating the correlation functions of twist fields provides a parametrisation of several other correlation functions for various quantum states. Since this method relies on the Ward identities found in a double copy model it is hoped to have wider applications in other free fermion models. Part II concerns the truncated conformal space approach which has been developed to approximate perturbed conformal field theories. In this part the theory underpinning the approach is discussed and a working algorithm is developed for both bulk and boundary perturbed minimal models. The energy levels, mass gaps and one point functions of various models are computed using the truncated conformal space approach and are shown to be in good agreement with previous calculations. A possible method for using this approach to approximate two point functions in perturbed conformal field theories is discussed.
Author: Stefano Evangelisti Publisher: Minkowski Institute Press ISBN: 1927763096 Category : Science Languages : en Pages : 213
Book Description
This doctoral thesis analytically and numerically examines some of the most important concepts in quantum correlations in low-dimensional physics: entanglement and out-of-equilibrium dynamics. As John Bell once said: "Entanglement expresses the spooky nonlocality inherent to quantum mechanics", and its study not only concerns the foundations of any quantum theory, but also has important applications in quantum information and condensed matter theory, amongst others. The first chapters are devoted to the study of "entanglement entropies", a popular measure of the "quantumness" of a physical system. The main focus of the analysis is the one-dimensional XYZ spin-1/2 chain in equilibrium, an interacting theory which in addition to being integrable also has interesting scaling limits, such as the sine-Gordon field theory. Moving away from equilibrium the subsequent chapters deal with the dynamics of quantum correlators after an instantaneous quantum quench. The emphasis is on two different models and techniques; the transverse field Ising chain is studied using the form-factor approach and the O(3) non-linear sigma model is studied by means of the semi-classical theory. In the final chapter the author highlights an important general result: in the absence of long-range interactions in the final Hamiltonian the dynamics of a quantum system are determined by the same statistical ensemble that describes static correlations.
Author: H Saleur Publisher: World Scientific ISBN: 9814549991 Category : Science Languages : en Pages : 346
Book Description
The following topics were covered: the study of renormalization group flows between field theories using the methods of quantum integrability, S-matrix theory and the thermodynamic Bethe Ansatz; impurity problems approached both from the point of view of conformal field theory and quantum integrability. This includes the Kondo effect and quantum wires; solvable models with 1/r² interactions (Haldane-Shastri models). Yangian symmetries in 1/r² models and in conformal field theories; correlation functions in integrable 1+1 field theories; integrability in three dimensions; conformal invariance and the quantum hall effect; supersymmetry in statistical mechanics; and relations to two-dimensional Yang-Mills and QCD.
Author: Yixiong Chen Publisher: ISBN: Category : Languages : en Pages : 350
Book Description
The aim of this thesis is to evaluate correlation functions of twist fields in mixed states in two-dimensional integrable models of quantum field theory (QFT). We construct the "Liouville space" for general models of QFT in general mixed states associated to diagonal density matrices, and define mixed-state form factors in Liouville space. We then specialize to two concrete models: the Ising model and U(l) Dirac model. Using a novel method based on deriving and solving a system of nonlinear functional differential equations, we • obtain exact mixed-state form factors of twist fields, in both models. These form factors are in agreement with finite-temperature form factors which correspond to the thermal Gibbs state. We then write down mixed-state correlation functions for these fields in terms of the full form factor expansions with respect to the vacuum in Liouville space. Under weak analytic conditions on the eigenvalues of the density matrix, they are exact large-distance expansions. We apply the results in the Ising model to analyze large-distance behaviours of two-point functions of order and disorder fields in generalized Gibbs ensembles and nonequilibrium steady states. In particular, we find non-equilibrium form factors have branch cuts in rapidity space and the leading large-distance behaviour of two-point functions admit oscillations in the log of the distance between fields. Using the results in the Dirac model and the relation between the Ising and Dirac models, we deduce the Reyi entropy for even integer n. Finally, as an extra work, we deduce the high- and low-temperature limit of the exact current at non-equilibrium steady states in general integrable models of quantum field theory with diagonal scatterings.
Author: Michio Jimbo Publisher: American Mathematical Soc. ISBN: 1470465523 Category : Education Languages : en Pages : 192
Book Description
Integrable models in statistical mechanics and quantum field theory constitute a rich research field at the crossroads of modern mathematics and theoretical physics. An important issue to understand is the space of local operators in the system and, ultimately, their correlation functions and form factors. This book is the first published monograph on this subject. It treats integrable lattice models, notably the six-vertex model and the XXZ Heisenberg spin chain. A pair of fermions is introduced and used to create a basis of the space of local operators, leading to the result that all correlation functions at finite distances are expressible in terms of two transcendental functions with rational coefficients. Step-by-step explanations are given for all materials necessary for this construction, ranging from algebraic Bethe ansatz, representations of quantum groups, and the Bazhanov-Lukyanov-Zamolodchikov construction in conformal field theory to Riemann surfaces and their Jacobians. Several examples and applications are given along with numerical results. Going through the book, readers will find themselves at the forefront of this rapidly developing research field.
Author: Changrim Ahn Publisher: World Scientific ISBN: 9810247370 Category : Science Languages : en Pages : 354
Book Description
This volume includes several lecture notes on the fundamentals and elementary techniques of integrable field theories and on their applications to low-dimensional physics systems contributed by leading scientists in the respective fields. The main topics covered are various aspects of the thermodynamic Bethe ansatz, form factors, Calogero (and related) models, sigma models, conformal boundary conditions, etc. The volume presents both pedagogical material and a current research trend in the field.The proceedings have been selected for coverage in: ? Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings)
Author: Changrim Ahn Publisher: World Scientific ISBN: 9814490180 Category : Science Languages : en Pages : 354
Book Description
This volume includes several lecture notes on the fundamentals and elementary techniques of integrable field theories and on their applications to low-dimensional physics systems contributed by leading scientists in the respective fields. The main topics covered are various aspects of the thermodynamic Bethe ansatz, form factors, Calogero (and related) models, sigma models, conformal boundary conditions, etc. The volume presents both pedagogical material and a current research trend in the field.The proceedings have been selected for coverage in:• Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings)
Author: V.N. Popov Publisher: Springer Science & Business Media ISBN: 9781402003073 Category : Science Languages : en Pages : 316
Book Description
Functional integration is one of the most powerful methods of contempo rary theoretical physics, enabling us to simplify, accelerate, and make clearer the process of the theoretician's analytical work. Interest in this method and the endeavour to master it creatively grows incessantly. This book presents a study of the application of functional integration methods to a wide range of contemporary theoretical physics problems. The concept of a functional integral is introduced as a method of quantizing finite-dimensional mechanical systems, as an alternative to ordinary quantum mechanics. The problems of systems quantization with constraints and the manifolds quantization are presented here for the first time in a monograph. The application of the functional integration methods to systems with an infinite number of degrees of freedom allows one to uniquely introduce and formulate the diagram perturbation theory in quantum field theory and statistical physics. This approach is significantly simpler than the widely accepted method using an operator approach.
Author: James Brian Silk
Author: James Brian Silk
Author: Benjamin Doyon
Author: Stefano Evangelisti
Author: H Saleur
Author: Yixiong Chen
Author: Michio Jimbo
Author: Changrim Ahn
Author: Changrim Ahn
Author: V.N. Popov
Author: M. Jimbo