Related papers: Euclidean field theory and singular classical fiel…
We discuss the continuum field theory limit of the physical scenario described in Ref. [1], the universe arising from the interpretation of the most general collection of logical codes in terms of distributions of units of energy along…
We study the formation of structure in the Universe assuming that dark matter can be described by a scalar field $\tilde{\Phi}$ with a potential $V(\Phi)=-\mathfrak{m}^{2}\tilde{\Phi}^{2}/2+\lambda\tilde{\Phi}^4/4$. We derive the evolution…
The Clifford action on superspaces is analyzed with a view on generalized Dirac fields taking values in some Clifford supermodule. the stress is here on two principles: complexification and polarisation. For applications in field theory,…
We study the spectrum of quasiparticles in a scalar quantum field theory at high temperature. Our results indicate the existence of novel quasiparticles with purely collective origin at low momenta for some choices of the masses and…
It is shown that the classical field equations pertaining to gravity coupled to other bosonic fields are equivalent to a single geodesic equation, describing the free fall of a point particle in superspace. Some implications for quantum…
In Coupled-Cluster (CC) theory, unphysical complex energies may arise in the presence of strong magnetic fields, near conical intersections, or in systems exhibiting complex Abelian point group symmetries. This issue originates from the…
The physical fields (electromagnetic and electron fields) considered in the framework of Clifford algebras $\C_2$ and $\C_4$. The electron field described by the algebra $\C_4$ which in spinor representation is realized by well-known Dirac…
Standard two-dimensional orientation-field based phase-field models rely on a continuous scalar field to represent crystallographic orientation. The corresponding order parameter space is the unit circle, which is not simply-connected. This…
We discuss the possible applications supersymmetric theories might find in the field of elementary particle physics. The supersymmetric generalization of the $SU(3)\times SU(2)\times U(1)$ standard model is discussed in detail. Special…
A mathematically rigorous Hamiltonian formulation for classical and quantum field theories is given. New results include clarifications of the structure of linear fields, and a plausible formulation for nonlinear fields. Many mathematical…
A pure Yang-Mills theory extended by addition of a quartic term is considered in order to study the transition from the quantum tunneling regime to that of classical, i.e. thermal, behaviour. The periodic field configurations are found,…
Split-complex fields usually appear in the context of Euclidean supersymmetry. In this paper, we propose that this can be generalized to the non-Euclidean case and that, in fact, the split-complex representation may be the most natural way…
We solve numerically for periodic, spherically symmetric, classical solutions of SU(2)-Higgs theory in four-dimensional Euclidean space. In the limit of short periods the solutions approach tiny instanton-anti-instanton superpositions…
The infinite dimensional generalization of the quantum mechanics of extended objects, namely, the quantum field theory of extended objects is presented. The paradigm example studied in this paper is the Euclidean scalar field with a…
We consider theories for scalar and vector fields coupled to the energy-momentum tensor. Since these fields also carry a non-trivial energy-momentum tensor, the coupling prescription generates self-interactions. In analogy with gravity…
Extra dimensions can be utilized to simplify problems in classical mechanics, offering new insights. Here we show a simple example of how the motion of a test particle under the influence of an inverse-quadratic potential in 1D is…
The field theory with high space-time symmetry is considered with the aim to examine the mass-shell particles production processes. The general conclusion is following: no real particle production exists if the space-time symmetry…
This paper initiates the systematic study of thermal field theory for generic equilibrium density matrices, which feature arbitrary values not only of temperature and chemical potentials, but also of average angular momentum. The focus here…
QED_2 with mass and flavor has in common many features with QCD, and thus is an interesting toy model relevant for four dimensional physics. The model is constructed using Euclidean path integrals and mass perturbation series. The vacuum…
A new classical solution for the Yang-Mills theory in which the Euclidean energy plays a role of a parameter is discussed. The instanton and sphaleron are shown to be particular examples of this more general solution. The energy parameter…