This study investigates the thermal and statistical properties of the Dirac oscillator within the framework of two prominent formulations of doubly special relativity(DSR):the Amelino-Camelia and Magueijo-Smolin model...This study investigates the thermal and statistical properties of the Dirac oscillator within the framework of two prominent formulations of doubly special relativity(DSR):the Amelino-Camelia and Magueijo-Smolin models.DSR extends Einstein's special relativity by introducing an additional invariant scale—the Planck energy—leading to modified energy-momentum relations that encode potential quantum-gravitational effects at ultra-high energies.In this context,we derive the modified Dirac equations for both DSR scenarios and analytically determine the corresponding energy spectra.These spectra are subsequently used to compute the partition function and key thermodynamic quantities,including specific heat,by employing the Euler-Maclaurin formula to facilitate an efficient approximation of the partition function.The analysis is restricted to the positive-energy sector,enabled by the exact Foldy-Wouthuysen transformation,which effectively decouples positive and negative energy states.The findings reveal that Planck-scale deformation parameters induce significant modifications in the energy spectrum and thermodynamic behavior of the Dirac oscillator in each DSR framework,thereby offering valuable insights into possible observable imprints of quantum gravitational phenomena in relativistic quantum systems.展开更多
We compute the dark energy and ordinary energy density of the cosmos as a double Eigenvalue problem. In addition, we validate the result using two different theories. The first theory is based on Witten’s 11 dimensio...We compute the dark energy and ordinary energy density of the cosmos as a double Eigenvalue problem. In addition, we validate the result using two different theories. The first theory is based on Witten’s 11 dimensional spacetime and the second is based on ‘tHooft’s fractal renormalization spacetime. In all cases, the robust result is E(O) = mc2/22 for ordinary energy and E(D) = mc2(21/22) for dark energy. Adding E(O) to E(D) we obtain Einstein’s famous equation which confirms special relativity, although it adds a quantum twist to its interpretation. This new interpretation is vital because it brings relativity theory in line with modern cosmological measurements and observations. In particular, we replace calculus by Weyl scaling in all computation which is essentially transfinite discrete.展开更多
基金funded by the Science Committee of the Ministry of Science and Higher Education of the Republic of Kazakhstan,Program No.BR24992759。
文摘This study investigates the thermal and statistical properties of the Dirac oscillator within the framework of two prominent formulations of doubly special relativity(DSR):the Amelino-Camelia and Magueijo-Smolin models.DSR extends Einstein's special relativity by introducing an additional invariant scale—the Planck energy—leading to modified energy-momentum relations that encode potential quantum-gravitational effects at ultra-high energies.In this context,we derive the modified Dirac equations for both DSR scenarios and analytically determine the corresponding energy spectra.These spectra are subsequently used to compute the partition function and key thermodynamic quantities,including specific heat,by employing the Euler-Maclaurin formula to facilitate an efficient approximation of the partition function.The analysis is restricted to the positive-energy sector,enabled by the exact Foldy-Wouthuysen transformation,which effectively decouples positive and negative energy states.The findings reveal that Planck-scale deformation parameters induce significant modifications in the energy spectrum and thermodynamic behavior of the Dirac oscillator in each DSR framework,thereby offering valuable insights into possible observable imprints of quantum gravitational phenomena in relativistic quantum systems.
文摘We compute the dark energy and ordinary energy density of the cosmos as a double Eigenvalue problem. In addition, we validate the result using two different theories. The first theory is based on Witten’s 11 dimensional spacetime and the second is based on ‘tHooft’s fractal renormalization spacetime. In all cases, the robust result is E(O) = mc2/22 for ordinary energy and E(D) = mc2(21/22) for dark energy. Adding E(O) to E(D) we obtain Einstein’s famous equation which confirms special relativity, although it adds a quantum twist to its interpretation. This new interpretation is vital because it brings relativity theory in line with modern cosmological measurements and observations. In particular, we replace calculus by Weyl scaling in all computation which is essentially transfinite discrete.
