相关论文: Algebraic Structure of Classical Field Theory: Kin…

The first part of this work deals with the development of a natural differential calculus on non-commutative manifolds. The second part extends the covariance and equivalence principle as well studies its kinematical consequences such as…

The classical fields with fractional derivatives are investigated by using the fractional Lagrangian formulation.The fractional Euler-Lagrange equations were obtained and two examples were studied.

We explore a framework for complex classical fields, appropriate for describing quantum field theories. Our fields are linear transformations on a Hilbert space, so they are more general than random variables for a probability measure. Our…

Classical nonlinear theories are highly successful in describing far-from-equilibrium dynamics of magnets, encompassing phenomena such as parametric resonance, ultrafast switching, and even chaos. However, at ultrashort length and time…

We consider the coupling of quantum fields to classical gravity in the formalism of ensembles on configuration space, a model that allows a consistent formulation of interacting classical and quantum systems. Explicit calculations show that…

Classical mechanics is presented here in a unary operator form, constructed using the binary multiplication and Poisson bracket operations that are given in a phase space formalism, then a Gibbs equilibrium state over this unary operator…

In this thesis we study classical aspects of superconformal field theory via symmetry principles. Specifically, by employing the powerful setup of conformal superspace, we obtain a plethora of new results in the fields of geometric and…

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…

In earlier work, we have developed a nonequilibrium statistical field theory description of cosmic structure formation, dubbed Kinetic Field Theory (KFT), which is based on the Hamiltonian phase-space dynamics of classical particles and…

We consider the spectral correlations of clean globally hyperbolic (chaotic) quantum systems. Field theoretical methods are applied to compute quantum corrections to the leading (`diagonal') contribution to the spectral form factor.…

The ordinary formalism for classical field theory is applied to dynamical group field theories. Focusing first on a local group field theory over one copy of SU(2) and, then, on more involved nonlocal theories (colored and non colored)…

The long-standing problem of time in canonical quantum gravity is the source of several conceptual and technical issues. Here, recent mathematical results are used to provide a consistent algebraic formulation of dynamical symplectic…

In this Thesis we develop the geometric formulations for higher-order autonomous and non-autonomous dynamical systems, and second-order field theories. In all cases, the physical information of the system is given in terms of a Lagrangian…

Lecture notes for a one-semester master-level course on analytical mechanics and classical field theory, covering: 0 Mathematical Introduction, 1 Lagrangian Mechanics, 2 Application: Motion in Central Fields, 3 Hamiltonian Mechanics, 4…

Spherical field theory is a new non-perturbative method for studying quantum field theories. It uses the spherical partial wave expansion to reduce a general d-dimensional Euclidean field theory into a set of coupled one-dimensional…

The goal of this article is to investigate the dynamics of semi-relativistic or non-relativistic charged particles in interaction with a scalar meson field. Our main contribution is the derivation of the classical dynamics of a…

We develop a systematic procedure for constructing quantum many-body problems whose spectrum can be partially or totally computed by purely algebraic means. The exactly-solvable models include rational and hyperbolic potentials related to…

The relationship between classical and quantum mechanics is usually understood via the limit $\hbar \rightarrow 0$. This is the underlying idea behind the quantization of classical objects. The apparent incompatibility of general relativity…

The challenges posed by the development of field theories, both classical and quantum, force us to question their most basic and foundational ideas like the role and origin of space-time, the meaning of physical states, etc. Among them the…

Our aim is to introduce a category-theoretic framework sufficiently general to describe a wide variety of open kinematic systems in classical mechanics while uniquely characterizing systems with specified simplest components. The framework…