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In an N-body quantum system with a constant electric field, by inverse scattering, we uniquely reconstruct pair potentials, belonging to the optimal class of short-range potentials and long-range potentials, from the high-velocity limit of…
We discuss the effects of a (possibly) negative $(1+z)^6$ type contribution to the Friedmann equation. No definite answer can be given as to the presence and magnitude of a particular mechanism, because any test using the general relation…
In this paper certain classes of infinite sums involving special functions are evaluated analytically by application of basic quantum mechanical principles to simple models of half harmonic oscillator and a particle trapped inside an…
In this paper, we investigate an example of summation of non-logarithmic singularities of a specific type in a two-dimensional non-linear sigma model. As a result of the study, we obtained an explicit formula, which, upon formal expansion…
Consequences of new quantum spin perspective in quantum gravity are far-reaching. Results of this novel perspective in loop quantum gravity, i.e., the modification of the equation of geometrical operators such as the area and the volume…
The energy loss due to a quadratic velocity dependent force on a quantum particle bouncing on a perfectly reflecting surface is obtained for a full cycle of motion. We approach this problem by means of a new effective phenomenological…
Using a regularization by putting the system in finite volume, we develop a novel approach to form factor perturbation theory for nonintegrable models described as perturbations of integrable ones. This permits to go beyond first order in…
The scheme of using the Chern-Simons action to regularize the gravitational Hamiltonian constraint is extended to including the Lorentzian term in the $k=0$ cosmological model. The Euclidean term and the Lorenzian term are thus regularized…
A boundary-state computation is performed to obtain derivative corrections to the Chern-Simons coupling between a p-brane and the RR gauge potential C(p-3). We work to quadratic order in the gauge field strength F, but all orders in…
Quantum forces are long-range interactions originating from vacuum fluctuations of mediator fields. Such forces inevitably arise between ordinary matter particles whenever they couple to light mediator species. Conventional computations of…
We obtain exact for order estimates of best uniform approximations and uniform approximations by Fourier sums of classes of convolutions the periodic functions belong to unit balls of spaces $L_{p}, \ {1\leq p<\infty}$, with generating…
Integrable boundary Toda theories are considered. We use boundary one-point functions and boundary scattering theory to construct the explicit solutions corresponding to classical vacuum configurations. The boundary ground state energies…
We provide a reformulation of finite dimensional quantum theory in the circuit framework in terms of mathematical axioms, and a reconstruction of quantum theory from operational postulates. The mathematical axioms for quantum theory are the…
Let $\mu_1, \ldots, \mu_s$ be real numbers, with $\mu_1$ irrational. We investigate sums of shifted $k$th powers $\mathfrak{F}(x_1, \ldots, x_s) = (x_1 - \mu_1)^k + \ldots + (x_s - \mu_s)^k$. For $k \ge 4$, we bound the number of variables…
The problem of bound states in effective field theories is studied. A rescaled version of nonrelativistic effective field theory is formulated which makes the velocity power counting of operators manifest. Results obtained using the…
In this paper, we establish some reciprocity formulas for certain generalized Hardy-Berndt sums by using the Fourier series technique and some properties of the periodic zeta function and the Lerch zeta function. It turns out that one of…
In quantum cosmology, one has to select a specific wave function solution of the quantum state equations under consideration in order to obtain concrete results. The simplest choices have been already explored, in different frameworks,…
We consider the possible quantum effect for infinite systems produced by variations of the Planck's constant. Using the algebraic formulation of quantum theory we study behaviour of states $\omega$ defined as positive, normalized…
Some 67 years ago (1951) Wolfgang Pauli mooted the three sum rules: \[ \sum_n (-1)^{2S_n} g_n = 0; \qquad \sum_n (-1)^{2S_n} g_n \; m_n^2 =0; \qquad \sum_n (-1)^{2S_n} g_n \; m_n^4=0. \] These three sum rules are intimately related to both…
We calculate the perturbative corrections to order \alpha_s^2\beta_0 to the sum rule derived from the second moment of the time-ordered product of b \to c currents near zero recoil. This sum rule yields a bound on \lambda_1, the expectation…