Related papers: A note on Gaussian integrals over paragrassmann va…
Recently, we presented a new class of quantum-mechanical Hamiltonians which can be written as the $F^{th}$ power of a conserved charge: $H=Q^F$ with $F=2,3,...\,.$ This construction, called fractional supersymmetric quantum mechanics, was…
By using the quasi-determinant the construction of Gel'fand et al. leads to the inverse of a matrix with noncommuting entries. In this work we offer a new method that is more suitable for physical purposes and motivated by deformation…
An outline of a proof of the local decomposition of linear metric perturbations into gauge-invariant and gauge-variant parts on an arbitrary background spacetime is briefly explained. We explicitly construct the gauge-invariant and…
Perturbing resonant systems causes shifts in their associated scattering poles in the complex plane. In a previous study [arXiv: 2408.11360], we demonstrated that these shifts can be calculated numerically by analyzing the residue of a…
Within the framework of the q-deformed Heisenberg algebra a dynamical equation of q-deformed quantum mechanics is discussed. The perturbative aspects of the q-deformed Schr\"odinger equation are analyzed. General representations of the…
Starting with a four-dimensional gauge theory approach to rational, elliptic, and trigonometric solutions of the Yang-Baxter equation, we determine the corresponding quantum group deformations to all orders in $\hbar$ by deducing their RTT…
We analyze qubit channels by exploiting the possibility of representing two-level quantum systems in terms of characteristic functions. To do so, we use functions of non-commuting variables (Grassmann variables), defined in terms of…
We define $\Gamma_q(B,S \otimes H)$, the generalized $q$-gaussian von Neumann algebras associated to a sequence of symmetric independent copies $(\pi_j,B,A,D)$ and to a subset $1 \in S = S^* \subset A$ and, under certain assumptions, prove…
We study the effect of noncommutativity of space on the physics of a quantum interferometer located in a rotating disk in a gauge field background. To this end, we develop a path-integral approach which allows defining an effective action…
In this paper, we propose a full characterization of a generalized $q-$deformed Tamm-Dancoff oscillator algebra and investigate its main mathematical and physical properties. Specifically, we study its various representations and find the…
In this paper we review the recently proposed path-integral counterpart of the Koopman-von Neumann operatorial approach to classical Hamiltonian mechanics. We identify in particular the geometrical variables entering this formulation and…
Path integrals play a crucial role in describing the dynamics of physical systems subject to classical or quantum noise. In fact, when correctly normalized, they express the probability of transition between two states of the system. In…
We use a probabilistic approach to describe the behavior as $n -> \infty$ of the Laplace transforms of $P^n$, where $P$ a fixed complex polynomial. As a consequence we obtain a new elementary proof of an result of Gillis-Ismail-Offer in the…
We study a pathwise integral with respect to paths of finite quadratic variation, defined as the limit of non-anticipative Riemann sums for gradient-type integrands. We show that the integral satisfies a pathwise isometry property,…
We construct a family of metric-deformed gauge theories based on a recently introduced $q$-Dirac operator $D_q = \gamma^\mu \sqrt{|g^{\mu\mu}|}\partial_\mu$, which arises from a deformed D'Alembertian $\Box_q = |g^{00}|\partial_t^2 - \sum_i…
In recent years enormous progress has been made in perturbative quantum field theory by applying methods of algebraic geometry to parametric Feynman integrals for scalar theories. The transition to gauge theories is complicated not only by…
We compute explicitly the equations of motion of the Hamiltonian formulation of quadratic gravity. This is the theory with the most general Lagrangian with terms of quadratic order in the curvature tensor. We employ the symbolic…
We show that the method of separation of variables gives a natural generalisation of integral relations for classical special functions of one variable. The approach is illustrated by giving a new proof of the ``quadratic'' integral…
Completely integrable Hamiltonians defining classical mechanical systems of $N$ coupled oscillators are obtained from Poisson realizations of Heisenberg--Weyl, harmonic oscillator and $sl(2,\R)$ coalgebras. Various completely integrable…
The paper considers the problem of estimating a $p\geq2$\ dimensional mean vector of a multivariate conditionally normal distribution under quadratic loss. The problem of this type arises when estimating the parameters in a continuous time…