Related papers: Choosing a basis that eliminates spurious solution…
Let $\mathfrak q$ be a Lie algebra over a field $\mathbb K$ and $p,\tilde p\in\mathbb K[t]$ two different normalised polynomials of degree at least 2. As vector spaces both quotient Lie algebras $\mathfrak q[t]/(p)$ and $\mathfrak…
This series of papers is devoted to an open-ended project aimed at the solution of Hilbert's sixth problem (concerning joint axiomatization of physics and probability theory) proposed to be constructed in the framework of an all-embracing…
We introduce a Hamiltonian for fermions on a lattice and prove a theorem regarding its topological properties. We identify the topological criterion as a $\mathbb{Z}_2-$ topological invariant $p(\textbf{k})$ (the Pfaffian polynomial). The…
We provide a general algorithm to construct a Hamiltonian, such that its dynamical flow covariantly defines any given spherically symmetric and static metric. This Hamiltonian is defined as a linear combination of the standard (general…
We show that a large class of Euclidean extended supersymmetric lattice gauge theories constructed in [hep-lat/0302017 - hep-lat/0503039] can be regarded as compact formulations by using the polar decomposition of the complex link fields.…
In this paper we discuss physical derivations of the quantum K theory rings of symplectic Grassmannians. We compare to standard presentations in terms of Schubert cycles, but most of our work revolves around a proposed description in terms…
We discuss an alternative version of non- relativistic Newtonian mechanics in terms of a real Hilbert space mathematical framework. It is demonstrated that the physics of this scheme correspondent with the standard formulation.…
A Symplectic Effective Field Theory that unveils the observed emergence of symplectic symmetry in atomic nuclei is advanced. Specifically, starting from a simple extension of the harmonic-oscillator Lagrangian, an effective field theory…
We study the problem of Hamiltonian sparsification: given a parameter $\varepsilon \in (0,1)$ and an $n$-qubit Hamiltonian $H$ which is the sum of $r$-local positive semi-definite (PSD) terms $H_1, \dots H_m$, our goal is to compute a…
The Hamiltonian formalism is extremely elegant and convenient to mechanics problems. However, its application to the classical field theories is a difficult task. In fact, you can set one to one correspondence between the Lagrangian and…
To reduce general relativity to the canonical Hamiltonian formalism and construct the path (functional) integral in a simpler and, especially in the discrete case, less singular way, one extends the configuration superspace, as in the…
We give a Hamiltonian analysis of the asymptotically flat spherically symmetric system of gravity coupled to a scalar field. This 1+1 dimensional field theory may be viewed as the "standard model" for studying black hole physics. Our…
We formulate singular classical theories without involving constraints. Applying the action principle for the action (27) we develop a partial (in the sense that not all velocities are transformed to momenta) Hamiltonian formalism in the…
We describe a multi-scale resolution approach to analyzing problems in Quantum Mechanics using Daubechies wavelet basis. The expansion of the wavefunction of the quantum system in this basis allows a natural interpretation of each basis…
We develop the topological band theory for systems described by non-Hermitian Hamiltonians, whose energy spectra are generally complex. After generalizing the notion of gapped band structures to the non-Hermitian case, we classify "gapped"…
We present a review of our recent works directed towards discovery of a periodic, kink-like and soliton-like travelling wave solutions within the models of transport phenomena and the mathematical biology. Analytical description of these…
We develop an efficient $hp$-finite element method for piecewise-smooth differential equations with periodic boundary conditions, using orthogonal polynomials defined on circular arcs. The operators derived from this basis are banded and…
As another evidence for the matrix Discrete Light Cone formulation of M theory, we show how general integrable Hamiltonian systems emerge from BPS bound states of k longitudinal fivebranes. Such configurations preserve eight supercharges…
In this chapter we present a general method of constructing the effective equation which describes the behaviour of small-amplitude solutions for a nonlinear PDE in finite volume, provided that the linear part of the equation is a…
We present a family of exactly solvable models at arbitrary filling in any dimensions which exhibit novel superconductivity with interband pairing. By the use of the hidden $SU(2)$ algebra the Hamiltonians were diagonalized explicitly. The…