相关论文: Quantum corrections to static solutions of phi-in-…
We investigate and solve a special class of integrals involving associated Legendre functions, which can be regarded as generalized Mehler-Fock transformations. Some of the integrals appear naturally when dealing with the heat or resolvent…
We introduce a classical fractional particle model in $\mathbb{R}^{n}$, extending the Newtonian particle concept with the incorporation of the fractional Laplacian. A comprehensive discussion on kinetic properties, including linear momentum…
A new approach to generalised Casimir type of problems is derived within the context of renormalisable quantum field theory (QFT). We study the simplest case of a massive fluctuating boson field coupled to a time-independent background…
We consider pure three-dimensional quantum gravity with a negative cosmological constant. The sum of known contributions to the partition function from classical geometries can be computed exactly, including quantum corrections. However,…
We investigate symmetric oscillators, and in particular their quantization, by employing semiclassical and quantum phase functions introduced in the context of Liouville-Green transformations of the Schr\"{o}dinger equation. For anharmonic…
A Green's function approach is presented for the D-dimensional inverse square potential in quantum mechanics. This approach is implemented by the introduction of hyperspherical coordinates and the use of a real-space regulator in the…
The infinite dimensional generalization of the quantum mechanics of extended objects, namely, the quantum field theory of extended objects is employed to address the hitherto nonrenormalizable gravitational interaction following which the…
Previous work in the literature has studied gravitational radiation in black-hole collisions at the speed of light. In particular, it had been proved that the perturbative field equations may all be reduced to equations in only two…
A generalization of Jacobi's elliptic functions is introduced as inversions of hyperelliptic integrals. We discuss the special properties of these functions, present addition theorems and give a list of indefinite integrals. As a physical…
Analytical solutions of the Klein-Gordon equation are obtained by reducing the radial part of the wave equation to a standard form of a second order differential equation. Differential equations of this standard form are solvable in terms…
Using the Cartan formulation of General Relativity, we construct a well defined lattice-regularized theory capable to describe large non-perturbative quantum fluctuations of the frame field (or the metric) and of the spin connection. To…
New formulas for approximation of zeta-constants were derived on the basis of a number-theoretic approach constructed for the irrationality proof of certain classical constants. Using these formulas it's possible to approximate certain…
A $q$-analogue of the Hurwitz zeta-function is introduced through considerations on the spectral zeta-function of quantum group $SU_{q}(2)$, and its analytic aspects are studied via the Euler-MacLaurin summation formula. Asymptotic formulas…
In this paper, we present a quantum computational method to calculate the many-body Green's function matrix in a spin orbital basis. We apply our approach to finite-sized fermionic Hubbard models and related impurity models within Dynamical…
We calculate in a general background gauge, to one-loop order, the leading logarithmic contribution from the graviton self-energy at finite temperature $T$, extending a previous analysis done at $T=0$. The result, which has a transverse…
Quantum mechanics in a noncommutative plane is considered. For a general two dimensional central field, we find that the theory can be perturbatively solved for large values of the noncommutative parameter ($\theta$) and explicit…
We consider the effective theory of perturbative quantum gravity coupled to a point particle, quantizing fluctuations of both the gravitational field and the particle's position around flat space. Using a recent relational approach to…
Quantum corrections to the classical pressure are obtained for Lennard-Jones models of argon, neon, and helium using classical Metropolis algorithm computer simulations. The corrections for non-commutativity are obtained to fourth order in…
New quantum modes of the free scalar field are derived in a special time-evolution picture that may be introduced in moving charts of de Sitter backgrounds. The wave functions of these new modes are solutions of the Klein-Gordon equation…
A careful study of the classical/quantum connection with the aid of coherent states offers new insights into various technical problems. This analysis includes both canonical as well as closely related affine quantization procedures. The…