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The classical multidimensional resultant can be defined as the, suitably normalized, generator of a projective elimination ideal in the ring of universal coefficients. This is the approach via the so-called inertia forms or…
In this note we define geometric classical r-matrices and quantum R-matrices, and show how any geometric classical r-matrix can be quantized to a geometric quantum R-matrix. This is one of the simplest nontrivial examples of quantization of…
The familiar generating functionals in quantum field theory fail to be true measures and, so they make the sense only in the framework of the perturbation theory. In our approach, generating functionals are defined strictly as the Fourier…
A general scheme for construction of flat pencils of contravariant metrics and Frobenius manifolds as well as related solutions to WDVV associativity equations is formulated. The advantage is taken from the Rota-Baxter identity and some…
We derive equations for the source terms appearing in structure function equations for the fourth and sixth order under the assumption of homogeneity and isotropy. The source terms can be divided into two classes, namely those stemming from…
The new classes of homogeneous cosmological models for the scalar fields are build in the context of Lyra's geometry. The different types of exact solution for the model are obtained by applying two procedures, viz the generating function…
In this work we deform the phi^4 model with distinct deformation functions, to propose a diversity of sine-Gordon-like models. We investigate the proposed models and we obtain all the topological solutions they engender. In particular, we…
Framework for constructing Fock spaces associated either with certain solutions of the quantum Yang-Baxter equation or with infinite dimensional Hecke algebra is presented. For the former case, the quantum deformed oscillator algebra…
Exploiting the quantum integrability condition we construct an ancestor model associated with a new underlying quadratic algebra. This ancestor model represents an exactly integrable quantum lattice inhomogeneous anisotropic model and at…
We continue the study of form factors of descendant operators in the sinh- and sine-Gordon models in the framework of the algebraic construction proposed in [arXiv:0812.4776]. We find the algebraic construction to be related to a particular…
The relation between four-dimensional $SO(4)$ pure Yang-Mills theory and the gravity is discussed. The functional integral for Yang-Mills theory is rewritten in terms of the gravity metric and Riemann tensors. This relation is shown to also…
Using the recently introduced boundary form factor bootstrap equations, the form factors of boundary exponential operators in the sinh-Gordon model are constructed. The ultraviolet scaling dimension and the normalization of these operators…
This work develops a procedure to find classes of Lagrangian densities that describe generalizations of the Abelian Maxwell-Higgs, the Chern-Simons-Higgs and the Maxwell-Chern-Simons-Higgs models. The investigation focuses on the…
Classical three dimensional Yang-Mills is seen to be related to the topological Chern-Simons term through a nonlinear but fully local and covariant gauge field redefinition. A classical recursive cohomological argument is provided.
We have constructed a nonlinear multi-graviton theory. An application of this theory to cosmology is discussed. We found that scale factors in a solution for this theory repeat acceleration and deceleration.
The classical Yang-Mills equations are solved perturbatively in covariant gauge for a collision of two ultrarelativistic nuclei. The nuclei are taken as ensembles of classical color charges on eikonal trajectories. The classical gluon field…
It was proposed in hep-th/0403047 that all tree amplitudes in pure Yang-Mills theory can be constructed from known MHV amplitudes. We apply this approach for calculating tree amplitudes of gauge fields and fermions and find agreement with…
In this paper we obtain a set of meta-functional equations as new species of formulas in classical mathematical analysis. Mentioned species are generated by crossbreeding complete hybrid formula as a mother formula. Namely, they are…
Soft and collinear factorisations can be used to construct expressions for amplitudes in theories of gravity. We generalise the "half-soft" functions used previously to "soft-lifting" functions and use these to generate tree and one-loop…
We consider an extended version of the Kerr theorem incorporated in the Kerr-Schild formalism. It allows one to construct the series of exact solutions of the Einstein-Maxwell field equations from a holomorphic generating function $F$ of…