Related papers: Finite VEVs from a Large Distance Vacuum Wave Func…
We obtain exactly the vacuum expectation values $<(\partial\phi)^2 ({\bar\partial}\phi) e^{i\alpha\phi}>$ in the sine-Gordon model and $<L_{-2}{\bar L}_{-2} \Phi_{l,k}>$ in $\Phi_{1,3}$ perturbed minimal CFT. We discuss applications of…
We prove extension-dimensional versions of finite dimensional selection and approximation theorems. As applications, we obtain several results on extension dimension.
In this paper approximation methods for infinite-dimensional Levy processes, also called (time-dependent) Levy fields, are introduced. For square integrable fields beyond the Gaussian case, it is no longer given that the one-dimensional…
First, a misconception about the spectrum of a confined particle is evidentiated. Then, the results are shown to be incorrect by means of a counter-example, an explicit preparation for the probe is given that yields an arbitrary…
Extended shallow water wave equations are derived, using the method of asymptotic expansions, from the Euler (or water wave) equations. These extended models are valid one order beyond the usual weakly nonlinear, long wave approximation,…
Take a random variable X with some finite exponential moments. Define an exponentially weighted expectation by E^t(f) = E(e^{tX}f)/E(e^{tX}) for admissible values of the parameter t. Denote the weighted expectation of X itself by r(t) =…
We consider the low-energy effective field theory describing the infrared dynamics of non-dissipative fluids. We extend previous work to accommodate conserved charges, and we clarify the matching between field theory variables and…
We present an approximation scheme for functions in three dimensions, that requires only their samples on the Cartesian grid, under the assumption that the functions are sufficiently concentrated in both space and frequency. The scheme is…
In finite volume the partition function of QCD with a given $\theta$ is a sum of different topological sectors with a weight primarily determined by the topological susceptibility. If a physical observable is evaluated only in a fixed…
Motivated by extending the functional stochastic calculus, to important functionals to which it does not apply, a notion of functional derivative along a curve is introduced. This new setting is developed by incorporating path-dependent…
A general formula is derived for the finite volume dependence of vacuum expectation values analogous to Luscher's formula for the masses. The result involves no integrals over kinematic quantities and depends only on the matrix element…
We show that the main results of the expected utility and dual utility theories can be derived in a unified way from two fundamental mathematical ideas: the separation principle of convex analysis, and integral representations of continuous…
We set up a method for a recursive calculation of the effective potential which is applied to a cubic potential with imaginary coupling. The result is resummed using variational perturbation theory (VPT), yielding an exponentially fast…
A formula for calculating Extensions of (mainly integral) Polynomial Functors is established, based upon projective resolutions. Sample computations are performed, which, in particular, exhibit a surprising non-trivial extension of Divided…
Wigner functions generically attain negative values and hence are not probability densities. We prove an asymptotic expansion of Wigner functions in terms of Hermite spectrograms, which are probability densities. The expansion provides…
Use of non one-dimensional distributed feedback in VFEL gives possibility of frequency tuning in wide range. In present work dependence of lasing process on the angle between resonant diffraction grating grooves and direction of electron…
Path dependence is omnipresent in many disciplines such as engineering, system theory and finance. It reflects the influence of the past on the future, often expressed through functionals. However, non-Markovian problems are often…
This is a companion to our previous paper. Here, we derive local dimension-free estimates for volumes of sub- and super-level sets of analytic functions of several variables.
It has been shown that an improved estimation of quantum vacuum energy can yield not only acceptable but also experimentally sensible results. The very idea consists in a straightforward extraction of gravitationally interacting part of the…
In this short note, we propose an unified method to derive formulas for derivations conjugated by exponential functions on an almost complex manifold. In v3, we corrected some mistakes in previous versions.