Related papers: Field theory with the Maxima computer algebra syst…

We show that on three-dimensional Riemannian manifolds without boundaries and with trivial first real de Rham cohomology group (and in no other dimensions) scalar field theory and Maxwell theory are equivalent: the ratio of the partition…

We propose a gravitational theory in which the effective Lagrangian of the gravitational field is given by an arbitrary function of the Ricci scalar, the trace of the matter energy-momentum tensor, and the contraction of the Ricci tensor…

A new approach to model the biomatter dynamics based on the field theory is presented. It is shown that some well known tools in field theory can be utilized to describe the physical phenomena in life matters, in particular at elementary…

This paper presents the XAMG library for solving large sparse systems of linear algebraic equations with multiple right-hand side vectors. The library specializes but is not limited to the solution of linear systems obtained from the…

Maxwell's vacuum equations are integrated for admissible electromagnetic fields in homogeneous spaces. Admissible electromagnetic fields are those for which the space group generates an algebra of symmetry operators ( integrals of motion )…

Cosmological scaling solutions, which give rise to a scalar-field density proportional to a background fluid density during radiation and matter eras, are attractive to alleviate the energy scale problem of dark energy. In the presence of…

Background fields of electromagnetic and gravitational type emerge in the low kinetic energy limit of any regular Lagrangian system and, in particular, in the corresponding limit of any spacetime theory in which the free motion of test…

MaxCal is a variational principle that can be used to infer distributions of paths in the phase space of dynamical systems. It has been successfully applied to different areas of classical physics, in particular statistical mechanics in and…

This article summarizes new features and enhancements of the first major update of Package-X. Package-X 2.0 can now generate analytic expressions for arbitrarily high rank dimensionally regulated tensor integrals with up to four distinct…

Theorema 2.0 stands for a re-design including a complete re-implementation of the Theorema system, which was originally designed, developed, and implemented by Bruno Buchberger and his Theorema group at RISC. In this paper, we present the…

A theorem prover without an extensive library is much less useful to its potential users. Algebra, the study of algebraic structures, is a core component of such libraries. Algebraic theories also are themselves structured, the study of…

In this paper, the notion of strongly typed language will be borrowed from the field of computer programming to introduce a calculational framework for linear algebra and tensor calculus for the purpose of detecting errors resulting from…

MFGSB, a computer code for self-consistent mean-field calculations of atomic nuclei using the Gaussian expansion method, is now accessible at Chiba University Repository.

In this paper we complete our construction of frame-like gauge invariant description for massive mixed symmetry tensor fields corresponding to arbitrary Young tableau with two rows started in [1]. We consider general massive theory in (A)dS…

This paper shows how to write Maxwell's Equations in Hamilton's Quaternions. The fact that the quaternion product is non-commuting leads to distinct left and right derivatives which must both be included in the theory. A new field component…

The paper contains a differential-geometric foundations for an attempt to formulate Lagrangian (canonical) quantum field theory on fibre bundles. In it the standard Hilbert space of quantum field theory is replace with a Hilbert bundle; the…

We explore a comprehensive analysis of the formalism governing the gravitational field equations in degenerate higher-order scalar-tensor theories. The propagation of these theories in the vacuum has a maximum of three degrees of freedom…

This note is based on the plenary talk given by the second author at MACIS 2015, the Sixth International Conference on Mathematical Aspects of Computer and Information Sciences. Motivated by some of the work done within the Priority…

In this work, we develop a space--time Chebyshev spectral collocation method for three-dimensional Maxwell's equations and combine it with tensor-network techniques in Tensor-Train (TT) format. Under constant material parameters, the…

In this chapter of the book entitled, "Extending the Theory of Composites to Other Areas of Science" [edited by Graeme W. Milton, 2016] we give a rigorous derivation of the field equation recursion method in the abstract theory of…