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Conservation of the nonlinear curvature perturbation in generic
Conservation of the nonlinear curvature perturbation in generic

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... general form of a quadratic equation in the variable x called the standard form, is : ax2 + bx + c = 0, where a ≠ 0, a, b, c are real numbers.  Roots (or Solutions) of a Quadratic Equation : Those values of x, which satisfy a quadratic equation, are called roots (or solutions) of the equation. Thus ...
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Notes for Class Meeting 19: Uncertainty

... While I certainly agree with the above statement, I want to assert a more unconventional interpretation of !E !t " ! / 2 , since I believe that you are already too sophisticated to accept the standard interpretation as the full interpretation. We have learned through relativity that space and time a ...
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Noether's theorem



Noether's (first) theorem states that every differentiable symmetry of the action of a physical system has a corresponding conservation law. The theorem was proven by German mathematician Emmy Noether in 1915 and published in 1918. The action of a physical system is the integral over time of a Lagrangian function (which may or may not be an integral over space of a Lagrangian density function), from which the system's behavior can be determined by the principle of least action.Noether's theorem has become a fundamental tool of modern theoretical physics and the calculus of variations. A generalization of the seminal formulations on constants of motion in Lagrangian and Hamiltonian mechanics (developed in 1788 and 1833, respectively), it does not apply to systems that cannot be modeled with a Lagrangian alone (e.g. systems with a Rayleigh dissipation function). In particular, dissipative systems with continuous symmetries need not have a corresponding conservation law.
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