Related papers: Schrodinger's Cataplex
The massive, real scalar field described by the Klein-Gordon equation in one spatial dimension is the most elementary example of a bosonic quantum field theory. It has been investigated for many decades either as a simple academic theory or…
In this paper, we discuss the dynamics of two- scalar-field cosmological models. Unlike in the situation of exponential potential, we find that there are late-time attractors in which one scalar field dominates the energy density of…
This paper will describe how combinatorial interpretations can help us understand the algebraic structure of two aspects of perturbative quantum field theory, namely analytic Dyson-Schwinger equations and periods of scalar Feynman graphs.…
In this paper, we propose a new representation of the minimal form factors in integrable quantum field theories. These are solutions of the two-particle form factor equations, which have no poles on the physical sheet. Their expression…
We emphasize that the group-theoretical considerations leading to SO(10) unification of electro-weak and strong matter field components naturally extend to space-time components, providing a truly unified description of all generation…
We obtain a generalization of the relativistic diffusion of Schay and Dudley for particles with spin. The diffusion equation is a classical version of an equation for the Wigner function of an elementary particle. The elementary particle is…
Deterministic dynamical models are discussed which can be described in quantum mechanical terms. In particular, a local quantum field theory is presented which is a supersymmetric classical model. -- The Hilbert space approach of Koopman…
Any local field theory can be equivalently reformulated in the so-called unfolded form. General unfolded equations are non-Lagrangian even though the original theory is Lagrangian. Using the theory of a scalar field as a basic example, the…
We study the quantum field theory (QFT) of a scalar field in the Schr\"odinger picture in the functional formulation. We derive a formula for the evolution kernel in a flat expanding metric. We discuss a transition between Riemannian and…
In this paper, we have made the attempt to classify the integrand basis of all two-loop diagrams in pure four-dimension space-time. Our classification includes the topology of two-loop diagrams which determines the structure of…
By extending the quantum evolution of a scalar field in time-dependent backgrounds to the complex-time plane and transporting the in-vacuum along a closed path, we argue that the geometric transition from the simple pole at infinity…
It is shown, that by means of a special projection operator, the Liouville equation for an N-particle distribution function of classical particles, driven from an equilibrium state by an external field, can be exactly converted into a…
The propagators of the elementary degrees of freedom of (minimal-)Landau-gauge Yang-Mills theory have been a useful tool in various investigations. However, in lattice calculations they show severe dependencies on lattice artifacts. This…
We study the electron propagator in quantum electrodynamics in lower dimensions. In the case of free electrons, it is well known that the propagator in momentum space takes the simple form $S_F(p)=1/(\gamma\cdot p-m)$. In the presence of…
In this paper, we use four-dimensional quaternionic algebra to describing space-time field equations in curvature form. The transformation relations of a quaternionic variable are established with the help of basis transformations of…
The theme of doing quantum mechanics on all abelian groups goes back to Schwinger and Weyl. If the group is a vector space of finite dimension over a non-archimedean locally compact division ring, it is of interest to examine the structure…
We consider a class of linear Schroedinger equations in R^d, with analytic symbols. We prove a global-in-time integral representation for the corresponding propagator as a generalized Gabor multiplier with a window analytic and decaying…
Some aspects of integrable field theories possessing purely transmitting defects are described. The main example is the sine-Gordon model and several striking features of a classical field theory containing one or more defects are pointed…
Many candidate fundamental theories contain scalar fields that can acquire spacetime-varying expectation values in a cosmological context. Such scalars typically obey Lorentz-violating effective dispersion relations. We illustrate this fact…
Bound and scattering state Schr\"odinger functions of nonrelativistic quantum mechanics as representation matrix elements of space and time are embedded into residual representations of spacetime as generalizations of Feynman propagators.…