Related papers: Systematic study of the completeness of two-dimens…
This work is a natural continuation of our recent study in quantizing relativistic particles. There it was demonstrated that, by applying a consistent quantization scheme to a classical model of a spinless relativistic particle as well as…
This paper is devoted to constructing and studying exactly solvable dynamical systems in discrete time obtained from some algebraic operations on matrices, to reductions of such systems leading to classical field theory models in…
We study a model of fully-packed dimer configurations (or perfect matchings) on a bipartite periodic graph that is two-dimensional but not planar. The graph is obtained from $\mathbb Z^2$ via the addition of an extensive number of extra…
A physically more adequate definition of a quaternionic holomorphic (H-holomorphic) function of one quaternionic variable compared to known ones and a quaternionic generalization of Cauchy-Riemann's equations are presented. At that a class…
Classical field theory is considered as a theory of unparametrized surfaces embedded in a configuration space, which accommodates, in a symmetric way, spacetime positions and field values. Dynamics is defined by a (Hamiltonian) constraint…
The path-integral quantization of thermal scalar, vector and spinor fields is performed newly in the coherent-state representation. In doing this, we choose the thermal electrodynamics and $\phi ^4$ theory as examples. By this quantization,…
It is shown that the Foldy-Wouthuysen transformation for relativistic particles in strong external fields provides the possibility of obtaining a meaningful classical limit of the relativistic quantum mechanics. The full agreement between…
Constructing a classical mechanical system associated with a given quantum mechanical one, entails construction of a classical phase space and a corresponding Hamiltonian function from the available quantum structures and a notion of…
The aim of this short note is to draw attention to a method by which the partition function and marginal probabilities for a certain class of random fields on complete graphs can be computed in polynomial time. This class includes Ising…
These lectures are an introduction to formal semiclassical quantization of classical field theory. First we develop the Hamiltonian formalism for classical field theories on space time with boundary. It does not have to be a cylinder as in…
Two different families of abelian chiral gauge theories on the torus are investigated: the aim is to test the consistency of two-dimensional anomalous gauge theories in the presence of global degrees of freedom for the gauge field. An…
We characterize the entire functions $P$ of $d$ variables, $d\ge 2,$ for which the $\mzd$-translates of $P\chi_{[0,N]^d}$ satisfy the partition of unity for some $N\in \mn.$ In contrast to the one-dimensional case, these entire functions…
The quantum no cloning theorem is an essential result in quantum information theory. Following this idea, we give a physically natural definition of cloning in the context of classical mechanics using symplectic geometry, building on work…
We study the integrability of two-dimensional theories that are obtained by a dimensional reduction of certain four-dimensional gravitational theories describing the coupling of Maxwell fields and neutral scalar fields to gravity in the…
The transition from a classical to quantum theory is investigated within the context of orthogonal and symplectic Clifford algebras, first for particles, and then for fields. It is shown that the generators of Clifford algebras have the…
We investigate an integrable property and observables of 2 dimensional N=(4,4) topological field theory defined on a discrete lattice by using the "orbifolding" and "deconstruction" methods. We show that our lattice model possesses the…
Jerrum, Sinclair and Vigoda (2004) showed that the permanent of any square matrix can be estimated in polynomial time. This computation can be viewed as approximating the partition function of edge-weighted matchings in a bipartite graph.…
Given a bipartite graph that has a perfect matching, a prefect proportional allocation is an assignment of positive weights to the nodes of the right partition so that every left node is fractionally assigned to its neighbors in proportion…
If the diffeomorphism symmetry of general relativity is fully implemented into a path integral quantum theory, the path integral leads to a partition function which is an invariant of smooth manifolds. We comment on the physical…
In this work several techniques to treat the partition function of the real scalar quartic quantum field theory on the Moyal plane is discussed. A factorisation approach requires the polytope volume for the diagonal subpolytope of symmetric…