Related papers: Paths with singularities in functional integrals o…
We describe the self-interacting scalar field on the truncated sphere and we perform the quantization using the functional (path) integral approach. The theory posseses a full symmetry with respect to the isometries of the sphere. We…
We discuss the time-continuous path integration in the coherent states basis in a way that is free from inconsistencies. Employing this notion we reproduce known and exact results working directly in the continuum. Such a formalism can set…
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…
We give an indication that gravity coupled to an infinite number of fields might be a renormalizable theory. A toy model with an infinite number of interacting fermions in four-dimentional space-time is analyzed. The model is finite at any…
Scalar field systems containing higher derivatives are studied and quantized by Hamiltonian path integral formalism. A new point to previous quantization methods is that field functions and their derivatives with time are considered as…
We review a recently-discovered link between the functional relations approach to integrable quantum field theories and the properties of certain ordinary differential equations in the complex domain.
An analysis of classical mechanics in a complex extension of phase space shows that a particle in such a space can behave in a way redolant of quantum mechanics; additional degrees of freedom permit 'tunnelling' without recourse to…
We formulate a quantum formalism for the statistical mechanical models of discretized field theories on lattices and then show that the discrete version of $\phi^4$ theory on 2D square lattice is complete in the sense that the partition…
We develop a reformulation of the functional integral for bosons in terms of bilocal fields. Correlation functions correspond to quantum probabilities instead of probability amplitudes. Discrete and continuous global symmetries can be…
The equations for topological fields in the $4d$ higher spin theory are considered. It is shown that these fields contain a finite number of degrees of freedom that justifies their naming. The issue of construction of gauge invariant…
Quantum field theory in curved spacetime may be defined either through a manifestly unitary canonical approach or via the manifestly covariant path integral formalism. For gauge theories, these two approaches have produced conflicting…
We show how to transform a $d$-dimensional Euclidean path integral in terms of two (Cartesian) fields to a path integral in terms of polar field variables. First we present a conjecture that states how this transformation should be done.…
We consider an atomistic model defined through an interaction field satisfying a variational principle, and can therefore be considered a toy model of (orbital free) density functional theory. We investigate atomistic-to-continuum coupling…
We propose a construction of actions of a quantum gauge field theory on a noncommutative space-time, based on a Fourier transform on the Doplicher-Fredenhagen-Roberts group. This approach leads to a functional integral representation of the…
By demanding that the path integral measure of topological field theories be metric independent, we can derive powerful constraints on the particle content of a topological field theory as well as on the dimensionality of space-time.
A novel geometric model of a noncommutative plane has been constructed. We demonstrate that it can be construed as a toy model for describing and explaining the basic features of physics in a noncommutative spacetime from a field theory…
We study space-time symmetries in scalar quantum field theory (including interacting theories) on static space-times. We first consider Euclidean quantum field theory on a static Riemannian manifold, and show that the isometry group is…
The real-time operator formalism for thermal quantum field theories, thermofield dynamics, is formulated in terms of a path-integral approach in non-commutative spaces. As an application, the two-point function for a thermal non-commutative…
A detailed analysis of the phase trajectories of cosmological models based on classical and scalar fields near surfaces of zero effective energy has been carried out. A study of the differential parameters of the convergence of phase…
The general boundary formulation of quantum field theory is applied to a massive scalar field in two dimensional Rindler space. The field is quantized according to both the Schr\"odinger-Feynman quantization prescription and the holomorphic…