Just Thought You Would Like to Know
Edward Schreiber
edwschreiber at icloud.com
Thu Nov 20 03:05:23 UTC 2014
One point of interest to me is "law of universal gravitation" and this calls to interest JLM's Law of Social Gravitation.
Bill do you see a relationship?
Ed
On Nov 19, 2014, at 5:04 PM, William H. Wysong wrote:
> Lagrangian formalismt
> Quantum field theory frequently makes use of the Lagrangian formalism from classical field theory. This formalism is analogous to the Lagrangian formalism used in classical mechanics to solve for the motion of a particle under the influence of a field. In classical field theory, one writes down a Lagrangian density, , involving a field, φ(x,t), and possibly its first derivatives (∂φ/∂t and ∇φ), and then applies a field-theoretic form of the Euler–Lagrange equation. Writing coordinates (t, x) = (x0, x1, x2, x3) = xμ, this form of the Euler–Lagrange equation is[3]
>
> where a sum over μ is performed according to the rules of Einstein notation.
> By solving this equation, one arrives at the "equations of motion" of the field.[3] For example, if one begins with the Lagrangian density
>
> and then applies the Euler–Lagrange equation, one obtains the equation of motion
>
> This equation is Newton's law of universal gravitation, expressed in differential form in terms of the gravitational potential φ(t, x) and the mass density ρ(t, x). Despite the nomenclature, the "field" under study is the gravitational potential, φ, rather than the gravitational field, g. Similarly, when classical field theory is used to study electromagnetism, the "field" of interest is the electromagnetic four-potential (V/c, A), rather than the electric and magnetic fields E and B.
> Quantum field theory uses this same Lagrangian procedure to determine the equations of motion for quantum fields. These equations of motion are then supplemented by commutation relations derived from the canonical quantization procedure described below, thereby incorporating quantum mechanical effects into the behavior of the field.
>
> Bill Wysong, MA, LPC, EMDR II, TEP
> Aspen Counseling Center
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>
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