Related papers: Random Polynomials and the Friendly Landscape
We discuss some applications of the effective quantum field theory to the description of the physics beyond the Standard Model. We consider two different examples. In the first one we derive, at the one-loop level, an effective lagrangian…
The application of the Legendre transformation to a hyperregular Lagrangian system results in a Hamiltonian vector field generated by a Hamiltonian defined on the phase space of the mechanical system. The Legendre transformation in its…
Nonrelativstic effective field theories have shown to be a useful framework to describe systems of weakly bound particles. This work focuses on the matching procedure to the underlying relativistic theory. The concept of a physical mass in…
Action-dependent field theories are systems where the Lagrangian or Hamiltonian depends on new variables that encode the action. They model a larger class of field theories, including non-conservative behavior, while maintaining a…
Despite widespread interest and practical use, the theoretical properties of random forests are still not well understood. In this paper we contribute to this understanding in two ways. We present a new theoretically tractable variant of…
This is a brief review, in relatively non-technical terms, of recent advances in the theory of random field geometry. These advances have provided a collection of explicit new formulae describing mean values of a variety of geometric…
In light of recent discussions of the string landscape, it is essential to understand the degree to which string theory is predictive. We argue that it is unlikely that the landscape as a whole will exhibit unique correlations amongst…
A new approach to model the biomatter dynamics based on the field theory is presented. It is shown that some well known tools in field theory can be utilized to describe the physical phenomena in life matters, in particular at elementary…
In this paper and in the companion one we address the problem of identifying the effective theory that describes the statistics of the fluctuations of what is thought to be the relevant order parameter for glassy systems---the overlap field…
The string landscape accommodates a broad range of possible effective field theories. This poses a challenge for extracting verifiable predictions as well as falsifiable signatures of string theory. Motivated by these considerations, in…
In lattice QCD and other field theories with a mass gap, the field variables in distant regions of a physically large lattice are only weakly correlated. Accurate stochastic estimates of the expectation values of local observables may…
Persistent homology computes the multiscale topology of a data set by using a sequence of discrete complexes. In this paper, we propose that persistent homology may be a useful tool for studying the structure of the landscape of string…
This is the first paper of a five part work in which we study the Lagrangian and Hamiltonian structure of classical field theories with constraints. Our goal is to explore some of the connections between initial value constraints and gauge…
We discuss the approach of effective field theory on a d-dimensional Euclidean space in a scalar theory with two different mass scales in the presence of flat surfaces. Then considering Dirichlet and Neumann boundary conditions, we…
We review results about entanglement (or modular) Hamiltonians of quantum many-body systems in field theory and statistical mechanics models, as well as recent applications in the context of quantum information and quantum simulation.
Many complex systems are characterized by intriguing spatio-temporal structures. Their mathematical description relies on the analysis of appropriate correlation functions. Functional integral techniques provide a unifying formalism that…
In the recent times a lot of effort has been devoted to improve our knowledge about the space of string theory vacua (``the landscape'') to find statistical grounds to justify how and why the theory selects its vacuum. Particularly…
The goal of this paper is to present the way to define fermionic fields and their Lagrangians in terms of three orthogonal vector fields of norm 1 together with two real valued scalar fields. This paper is based on a toy model where there…
The paper investigates random fields in the ball. It studies three types of such fields: restrictions of scalar random fields in the ball to the sphere, spin, and vector random fields. The review of the existing results and new spectral…
Field theoretical models with first order Lagrangean can be formulated in a covariant Hamiltonian formalism. In this article, the geometrical construction of the Gerstenhaber structure that encodes the equations of motion is explained for…