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In this paper, a generalization of a quadratic manifold approach for the reduction of geometrically nonlinear structural dynamics problems is presented. This generalization is constructed by a linearization of the static force with respect…
We consider a complex singlet scalar in the spectral action approach to the standard model. It is shown that there is a range of initial values at the unification scale which is able to produce Higgs and top quark masses at low energies.…
Dualities between quantum field theories have proven to be a powerful tool in various areas of physics. In this paper, we introduce a new perspective for obtaining strong coupling expansions based on a well-known technique -- the…
Ultralight scalar dark matter may couple to the Standard Model through dimension-five operators that contain the field-strength tensors of the gauge interactions. Recent progress in nuclear clocks is projected to increase the sensitivity to…
We propose a new non-perturbative method to search for marginal deformations in level truncated open string field theory. Instead of studying the flatness of the effective potential for the marginal field (which is not expected to give a…
Quantum gravity can determine the dependence of gauge couplings in a scalar field, which is related to possible fifth forces and time varying fundamental "constants". This prediction is based on the scaling solution of functional flow…
We study global scale invariance along with the unimodular gravity in the vacuum. The global scale invariant gravitational action which follows the unimodular general coordinate transformations is considered without invoking any scalar…
We describe the fully gauge invariant cosmological perturbation equations in teleparallel gravity by using the gauge covariant version of the Stewart lemma for obtaining the variations in tetrad perturbations. In teleparallel theory,…
It is a well-known result of T.\,Kato that given a continuous path of square matrices of a fixed dimension, the eigenvalues of the path can be chosen continuously. In this paper, we give an infinite-dimensional analogue of this result,…
Over the last two years, the canonical approach to quantum gravity based on connections and triads has been put on a firm mathematical footing through the development and application of a new functional calculus on the space of gauge…
We study a set of scattering matrices of quantum graphs containing minimal number of passbands, i.e., maximal number of zero elements. The cases of even and odd vertex degree are considered. Using a solution of inverse scattering problem,…
In a four-dimensional space I shall construct all of the conformally invariant, scalar-vector-tensor field theories that are consistent with conservation of charge, and flat space compatible. By the last assumption I mean that the…
A family of cosmological solutions with $(n+1)$ Ricci-flat spaces in the theory with several scalar fields and multiple exponential potential is obtained when coupling vectors in exponents obey certain relations. Two subclasses of solutions…
We give in this paper which is the fifth in a series of eight a theory of covariant derivatives of multivector and extensor fields based on the geometric calculus of an arbitrary smooth manifold M, and the notion of a connection extensor…
We present a model of vacuum tunneling through a classically forbidden region where a scalar field changes its value simultaneously over the entire volume of a (meta)stable ancestor vacuum with spherical curvature. The tunneling leaves the…
Cubic invariants for two-dimensional Hamiltonian systems are investigated using the Jacobi geometrization procedure. This approach allows for a unified treatment of invariants at both fixed and arbitrary energy. In the geometric picture the…
It is known that besides the usual unitary mappings $\Omega = 1/\Omega^\dagger$ between the equivalent representations of the physical Hilbert space of Quantum Mechanics (often, Fourier transformations), the generalized non-unitary maps…
Multiple scalar fields appear in vast modern particle physics and gravity models. When they couple to gravity non-minimally, conformal transformation is utilized to bring the theory into Einstein frame. However, the kinetic terms of scalar…
There is a classical geometric construction which uses a binary quadratic form to define an involution on the space of binary d-ics. We give a complete characterization of a general class of such involutions which are definable using…
Results of a general study on the dynamics of cosmological scalar fields with arbitrary potentials are presented. Exact and approximate attractor solutions are found, with applications to quintessence, moduli stabilization and inflation.