Phenomenologies in Hypersphere Soliton and Stringy Photon Models

We consider the Dirac quantization in the first-class formalism to investigate the hypersphere soliton model (HSM) defined on the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>S</mi><mn>3</mn></msup></semantics></math></inline-formula> hypersphere. To do this, we construct the first-class Hamiltonian possessing the Weyl ordering correction. In the HSM, we evaluate the baryon physical quantities such as the baryon masses, magnetic moments, axial coupling constant and charge radii, most predicted values of which are in good agreement with the corresponding experimental data. Moreover, shuffling the baryon and transition magnetic moments, we find the model independent sum rules. In the HSM we also evaluate the baryon intrinsic frequencies such as <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>ω</mi><mi>N</mi></msub><mo>=</mo><mn>0.87</mn><mo>×</mo><msup><mn>10</mn><mn>23</mn></msup><mspace width="3.33333pt"></mspace><msup><mrow><mi mathvariant="normal">s</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>ω</mi><mo>Δ</mo></msub><mo>=</mo><mn>1.74</mn><mo>×</mo><msup><mn>10</mn><mn>23</mn></msup><mspace width="3.33333pt"></mspace><msup><mrow><mi mathvariant="normal">s</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></semantics></math></inline-formula> of the nucleon and delta baryon, respectively, to yield the identity <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>ω</mi><mo>Δ</mo></msub><mo>=</mo><mn>2</mn><msub><mi>ω</mi><mi>N</mi></msub></mrow></semantics></math></inline-formula>. Next, making use of the Nambu-Goto string action and its extended rotating bosonic string theory, we formulate the stringy photon model to obtain the energy of the string configuration, which consists of the rotational and vibrational energies of the open string. Exploiting this total string energy, we evaluate the photon intrinsic frequency <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>ω</mi><mi>γ</mi></msub><mo>=</mo><mn>9.00</mn><mo>×</mo><msup><mn>10</mn><mn>23</mn></msup><mspace width="3.33333pt"></mspace><msup><mrow><mi mathvariant="normal">s</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></semantics></math></inline-formula>, which is comparable to the corresponding baryon intrinsic frequencies. We also predict the photon size <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mrow><mo>⟨</mo><msup><mi>r</mi><mn>2</mn></msup><mo>⟩</mo></mrow><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup><mrow><mo>(</mo><mi>photon</mi><mo>)</mo></mrow><mo>=</mo><mn>0.17</mn><mspace width="3.33333pt"></mspace><mi>fm</mi></mrow></semantics></math></inline-formula>, which is approximately 21% of the proton magnetic charge radius.