Abstract
In this paper, we analyze the correction to the mean field theory potential for a system of nucleons. It will be argued that these corrections can be obtained by deforming the Schrödinger’s equation describing a system of nucleons by a minimal length in the background geometry of space-time. This is because such a minimal length occurs due to quantum gravitational effects, and modifies the low energy quantum mechanical systems. In fact, as the mean field potential for the nucleons is represented by the Woods–Saxon potential, we will explicitly analyze such corrections to this potential. We will obtain the corrections to the energy eigenvalues of the deformed Schrödinger’s equation for the Woods–Saxon potential. We will also construct the wave function for the deformed Schrödinger’s equation.
Highlights
It is not possible to probe space-time below Planck scale, and Planck length acts as an intrinsic minimal length in a e-mail: barun@utk.edu space-time. Such a minimal length exists even in asymptotically safe gravity [20] and conformally quantized quantum gravity [21]. Such a minimal length in the background geometry of space-time exists in loop quantum gravity [16,17,18,19] because of polymer quantization, as the polymer length acts as a minimal length in loop quantum gravity
It can be argued that there exists a minimal length of the order of Planck length in the background geometry of spacetime [7]
There is an intrinsic zero point length, associated with such propagators, even if the string oscillation modes are neglected. It may be noted as the double field theory is constructed using the T-duality [11,12], it is expected that a such zero point length can occur in the double field theory
Summary
It can be argued that there exists a minimal length of the order of Planck length in the background geometry of spacetime [7]. It is possible to construct an effective path integral for the center of mass of the strings compactified on a circle, by neglecting all the string oscillation modes This effective path integral can be used to obtain suitable propagators in such a theory, and it can be explicitly demonstrated that such propagators. There is an intrinsic zero point length, (larger than the Planck length) associated with such propagators, even if the string oscillation modes are neglected It may be noted as the double field theory is constructed using the T-duality [11,12], it is expected that a such zero point length can occur in the double field theory. The existence of such a minimal length, larger than the Planck length, can have interesting physical consequences It is possible for such a minimal length to deform the low energy quantum mechanical systems [22,23]. It may be noted that the deformation of the angular momentum algebra consistent with this algebra has been studied [73,74], and we will use this deformation of the angular momentum algebra to analyze the deformed Woods–Saxon potential
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