Related papers: Euclidean Quantum Field Theory from Variational Dy…
Theory of electromagnetic field, specified by an effective action functional, is considered. The causality condition is imposed in the form of a requirement that the group velocities of propagation of small and soft disturbances over the…
The Wigner function, which provides a phase-space description of quantum systems, has various applications in quantum mechanics, quantum kinetic theory, quantum optics, radiation transport and others. The concept of Wigner function has been…
We introduce techniques to analyze unitary operations in terms of quadratic form expansions, a form similar to a sum over paths in the computational basis when the phase contributed by each path is described by a quadratic form over…
We determine the form of the Wigner functional for several types of quantum free field theories in order to analyze the representation of QFT in phase space, as well as to compare it to other mainstream formulations. We use Jackiw's…
The variational formalism for classical field theories is extended to the setting of Lie algebroids. Given a Lagrangian function we study the problem of finding critical points of the action functional when we restrict the fields to be…
Phase spaces with nontrivial geometry appear in different approaches to quantum gravity and can also play a role in e.g. condensed matter physics. However, so far such phase spaces have only been considered for particles or strings. We…
Integrable quantum mechanical systems with magnetic fields are constructed in two-dimensional Euclidean space. The integral of motion is assumed to be a first or second order Hermitian operator. Contrary to the case of purely scalar…
Boundary conditions play a crucial role in the path-integral approach to quantum gravity and quantum cosmology, as well as in the current attempts to understand the one-loop semiclassical properties of quantum field theories. Within this…
This paper expands on previous work to derive and motivate the Lagrangian formulation of field theories. In the process, we take three deliberate steps. First, we give the definition of the action and derive Euler-Lagrange equations for…
We present a variational approach which shows that the wave functions belonging to quantum systems in different potential landscapes, are pairwise linked to each other through a generalized continuity equation. This equation contains a…
The Euclidean quantum field theory for the fields $\phi_{\Delta x}(x)$, which depend on both the position $x$ and the resolution $\Delta x$, constructed in SIGMA 2 (2006), 046, hep-th/0604170, on the base of the continuous wavelet…
Inspired by various quantum gravity approaches, we explore quantum field theory where spacetime exhibits scaling properties and dimensional reduction with changing energy scales, effectively behaving as a multifractal manifold. Working…
The ideal incompressible fluid in two dimensions (Euler fluid) evolves at relaxation from turbulent states to highly coherent states of flow. For the case of double spatial periodicity and zero total vorticity it is known that the…
The path integral by which quantum field theories are defined is a particular solution of a set of functional differential equations arising from the Schwinger action principle. In fact these equations have a multitude of additional…
It is shown that the nature of physical time requires the extended phase-space in mechanics to have a bundle structure with time as the 1-dimensional base manifold and the phase space as the fiber. This bundle picture of the extended phase…
We study the phase diagram of scalar field theory on a three dimensional Euclidean spacetime whose spatial component is a fuzzy sphere. The corresponding model is an ordinary one-dimensional matrix model deformed by terms involving fixed…
On the basis of the gauge principle of field theory, a new variational formulation is presented for flows of an ideal fluid. The fluid is defined thermodynamically by mass density and entropy density, and its flow fields are characterized…
An electric-field-induced phase transition and pattern formation in a binary dielectric fluid layer are studied using a coarse-grained free energy functional. The electrostatic part of the free energy is a nonlinear functional of the…
The quantum correlations of scalar fields are examined as a power series in derivatives. Recursive algebraic equations are derived and determine the amplitudes; all loop integrations are performed. This recursion contains the same…
The 1--loop effective Lagrangian for a massive scalar field on an arbitrary causality violating spacetime is calculated using the methods of Euclidean quantum field theory in curved spacetime. Fields of spin 1/2, spin 1 and twisted field…