Quantization of Relativistic action in multiples of Planck's (constant) Quantum of action
POSTER
Abstract
Quantization of Relativistic action in multiples of Planck's (constant) Quantum of action. a new Postulate for special relativity theory. The third Postulate of special relativity: Relativistic action is limited to Planck's Quantum of action. $\mathcal {S}=\int^{t_f}_{t_i}\mathcal {L}dt=n.h \quad n \in Z.$ where the $\mathcal {L}=-m_oc^2\gamma^{-1},$ is the Lagrangian. action for a point particle in a curved spacetime. $\mathcal S =-Mc \int ds = -Mc \int_{\xi_0}^{\xi_1}\sqrt{g_{\mu\nu}(x)\frac{dx^\mu(\xi)}{d\xi} \frac{dx^\nu(\xi)}{d\xi}} \ \ d\xi=nh$ Quantization of Nambu-Goto action: $\mathcal{S} ~=~ -\frac{1}{2\pi\alpha'} \int \mathrm{d}^2 \Sigma \sqrt{{\dot{X}} ^2 - {X'}^2}~=~nh \quad n \in Z.$ point: The action $S= - E_0 ~ \Delta \tau$ of a relativistic particle is minus the rest energy $E_0=m_0c^2$ times the change $\Delta \tau=\tau_f-\tau_i$ in proper time. Single relativistic particle When relativistic effects are significant, the action of a point particle of mass ``m'' travelling a world line ``C'' parametrized by the proper time $\tau$ is :$S = - m_o c^2 \int_{C} \, d \tau$. If instead, the particle is parametrized by the coordinate time ''t'' of the particle and the coordinate time ranges from $t_1$ to $t_2$, then the action becomes :$\int_{t1}^{t2}\mathcal {L} \, dt$ where the Lagrangian is :$\mathcal {L} = - m_o c^2 \sqrt {1 - \frac{v^2}{c^2}}$.
Authors
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Ahmad Reza Estakhr
Researcher