Related papers: A quantum Mermin--Wagner theorem for a generalized…
By using the Hamiltonian formulation, we demonstrate that the Merton-Garman equation emerges naturally from the Black-Scholes equation after imposing invariance (symmetry) under local (gauge) transformations over changes in the stock price.…
We consider the manifold of all quantum many-body states that can be generated by arbitrary time-dependent local Hamiltonians in a time that scales polynomially in the system size, and show that it occupies an exponentially small volume in…
Let $M$ be a closed and connected manifold, $H:T^*M\times \mathbb{R} / \mathbb{Z} \to \mathbb{R}$ a Tonelli $1$-periodic Hamiltonian and $\mathcal{L} \subset T^*M$ a Lagrangian submanifold Hamiltonianly isotopic to the zero section. We…
We present an operational procedure to transform global symmetries into local symmetries at the level of individual quantum states, as opposed to typical gauging prescriptions for Hamiltonians or Lagrangians. We then construct a compatible…
Incompressible, inviscid, irrotational, and unsteady flows with circulation $\Gamma$ around a distorted toroidal bubble are considered. A general variational principle that determines the evolution of the bubble shape is formulated. For a…
New symmetry properties are found for pointlike scalar and Dirac particles (Higgs boson and all leptons) in Riemannian and Riemann-Cartan spacetimes in the presence of electromagnetic interactions. A Hermitian form of the Klein-Gordon…
Different ways to incorporate two-dimensional systems, which are not amenable to separation of variables, into the framework of Supersymmetrical Quantum Mechanics (SUSY QM) are analyzed. In particular, the direct generalization of…
We analyze the fermion density of the one-dimensional Hubbard model using bosonization and numerical DMRG calculations. For finite systems we find a relatively sharp crossover even for moderate short range interactions into a region with…
The theory of geometric quantum mechanics describes a quantum system as a Hamiltonian dynamical system with a complex projective Hilbert space as its phase space, thus equipped with a Riemannian metric in addition to a symplectic structure.…
We analyse a two-particle quantum system in $\R^d$ with interaction and in presence of a random external potential field with a continuous argument (an Anderson model in a continuous space). Our aim is to establish the so-called Wegner-type…
We consider the created entities (events) in the first moments of universe creation. It is assumed that there exists a causal energetic relationship between all events (nodes) such that all nodes are placed on a world line and each node…
Complex techniques of general relativity are used to determine \emph{all} the states in the two and three dimensional momentum spaces in which the equality holds in the uncertainty relations for the non-commuting basic observables of…
We study the electrodynamics of generic charged particles (bosons, fermions, relativistic or not) constrained to move on an infinite plane. An effective gauge theory in 2+1 dimensional spacetime which describes the real electromagnetic…
We give a simple proof of Kolmogorov's theorem on the persistence of a quasiperiodic invariant torus in Hamiltonian systems. The theorem is first reduced to a well-posed inversion problem (Herman's normal form) by switching the frequency…
We consider small systems of bosonic atoms rotating in a toroidal trap. Using the method of exact numerical diagonalization of the many-body Hamiltonian, we examine the transition from the Bose-Einstein condensed state to the…
Quantum field theory on the noncommutative two-dimensional Minkowski space with Grosse-Wulkenhaar potential is discussed in two ways: In terms of a continuous set of generalised eigenfunctions of the wave operator, and directly in position…
Three geometric formulations of the Hamiltonian structure of the macroscopic Maxwell equations are given: one in terms of the double de Rham complex, one in terms of L2 duality, and one utilizing an abstract notion of duality. The final of…
We construct a well-defined lattice-regularized quantum theory formulated in terms of fundamental fermion and gauge fields, the same type of degrees of freedom as in the Standard Model. The theory is explicitly invariant under local Lorentz…
We show that the supersymmetric algebra of Witten's quantum mechanics is invariant under a given point canonical transformation. It is shown that Witten's supersymmetric quantum mechanics can be isospectral or not to the seed Hamiltonian…
We discuss the dynamical quantum systems which turn out to be bi-unitary with respect to the same alternative Hermitian structures in a infinite-dimensional complex Hilbert space. We give a necessary and sufficient condition so that the…