Quantization of Relativistic action in multiples of Planck’s (constant) Quantum of action

Quantization of Relativistic action in multiples of Planck’s (constant) Quantum of action.

a new axiom for special relativity theory.

The third axiom:
Relativistic action is limited to Planck’s Quantum of action.
\mathcal {S}=\int^{t_f}_{t_i}\mathcal {L}dt=n.h\qquad n \in\mathbb{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\qquad n \in\mathbb{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}}.

author: Mr. ESTAKHR, Ahmad reza

About these ads

About easteinstein

I am a physicist with experience of thousands physicists.
This entry was posted in Quantum General Relativity, Quantum Mechanics, special relativity and tagged , , , , , . Bookmark the permalink.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s