Modern Physics Letters A

Light-front (LF) quantization of massless fields in two spacetime dimensions is a long-standing and much debated problem. Even though the classical wave-equation is well-documented for almost two centuries, either as problems with initial values in spacetime variables or with initial data on characteristics in light-cone variables, the way to a consistent quantization in both types of frames is still a puzzle in many respects. This is in contrast to the most successful Conformal Field Theoretic (CFT) approach in terms of complex variables $z$, $\bar{z}$ pioneered by Belavin, Polyakov and Zamolodchikov in the ’80s. It is shown here that the 2D-massless canonical quantization in both reference frames is completely consistent provided that quantum fields are treated as Operator-Valued Distributions (OPVD) with Partition of Unity (PU) test functions. We recall first that classical fields have to be considered as distributions (e.g. generalized functions in the Russian literature). Then, a necessary condition on the PU test function follows from the required matching of the classical solutions of the massless differential equations in both types of reference frame. Next we use a mathematical formulation for OPVD, developed in the recent past. Specifically, smooth ${{𝒞}}^{\infty }$ fields are introduced through the convolution operation in the distributional context. Due to the specific behavior of the Fourier-transform of the initial test function, this convolution transform has a well-defined integral in the dual space, whatever the initial choice of the reference frame. The relation to the conformal fields method follows immediately from the transition to Euclidean time and leads directly to explicit calculations of a few correlation functions of the scalar field and its energy–momentum tensor. The LF derivation of the Virasoro algebra is then obtained from the $z$ and $\bar{z}$ expansions of the canonical fields as distributional Laplace-transform in these variables. Finally, the popular and problematic Discretized Light Cone Quantization (DLCQ) method is scrutinized with respect to its zero mode and ultraviolet content as encompassed in the continuum OPVD formulation.

We discuss a special type of Skyrmion spacetime-defect solution, which has a positive energy density of the matter fields but a vanishing asymptotic gravitational mass. With a mass term for the matter field added to the action (corresponding to massive “pions” in the Skyrme model), this particular soliton-type solution has no long-range fields and can appropriately be called a “stealth defect”.

The aim of this work is to introduce a new family of potentials with inverse square singularity which we called the Pöschl–Teller family of potentials. We enforced the matrix representation of the wave operator to be symmetric and (2k+1) band-diagonal with respect to a square integrable basis set. This, in principle, is only satisfied for specific potential functions within the used basis set. The basis functions we used here are written in terms of Jacobi polynomials, which is the same basis used in the Tridiagonal Representation Approach (TRA). This yield a more general form of Pöschl–Teller potential that can have many terms which could be beneficial for modeling different physical systems where this potential applies. As an illustration, we have studied a specific new five-parameter potential that belongs to this new family and calculated the bound states for both s-wave and l-wave cases using the Asymptotic Iteration Method (AIM). Along the way, we have introduced new approximation schemes to deal with the l-wave centrifugal potential within the AIM at different approximation orders.

We propose a procedure for the renormalization of Casimir energy that is based on the implicit versions of standard steps of renormalization procedure — regularization, subtraction and removing the regularization. The proposed procedure is based on the calculation of a set of convergent sums, which are related to the original divergent sum for the non-renormalized Casimir energy. Then, we construct a linear equation system that connects this set of convergent sums with the renormalized Casimir energy, which is a solution to this system of equations. This procedure slightly reduces the indeterminacy that arises in the standard procedure when we choose the particular regularization and the explicit form of the counterterm. The proposed procedure can be applied not only to systems with the explicit transcendental equation for the spectrum but also to systems with the spectrum that can be obtained only numerically. However, to perform the proposed procedure, we need a parameter of the system that satisfies two conditions: (i) we can obtain explicit analytical expressions (as a function of our parameter) for coefficients for all divergent and unphysical terms in divergent sum for Casimir energy; (ii) infinite value of this parameter should be the “natural” renormalization point, i.e. Casimir energy must tend to zero when parameter tends to infinity.

We study the electromagnetic form factors of $\mathrm{\Lambda }$ hyperon in the time-like region using the experimental data in the exclusive production of $\bar{\mathrm{\Lambda }}\mathrm{\Lambda }$ pair in electron–positron annihilation. We present a pQCD inspired parametrization of $G_E(s)$ and $G_M(s)$ with only two parameters, and we consider a suppression mechanism of the electric form factor $G_E(s)$ compared to the magnetic form factor $G_M(s)$. The parameters are determined through fitting our parametrization to the data of the effective form factor $G_{\mathrm{\text{eff}}}$ from the DM2, BaBar and BESIII Collaborations in the reaction $e^{+}{e}^{-}\to \bar{\mathrm{\Lambda }}\mathrm{\Lambda }$. We use the parametrizations for $G_E(s)$ and $G_M(s)$ to calculate the Born cross-sections as well as the ratio $|G_E/G_M|$. Except the threshold region, our parametrization can describe the known behavior of the existing data of effective form factor, Born cross-section and the ratio $|G_E/G_M|$ from the BaBar, DM2 and BESIII Collaborations. We also predict the double spin polarization observables $A_{xx}$, $A_{yy}$ and $A_{zz}$ in $e^{+}{e}^{-}\to \bar{\mathrm{\Lambda }}\mathrm{\Lambda }$ which could provide more information on the size of the lambda EMFFs as well as their phase angles.