archipatelin said:Do know anybody explicit form of variation action quadratic in Riemann tensors (for general dimension)?
Link to internet sources?
Or computer program for symbolic and tensors algebra, which the variation tell me (preferably open-source)?
Thx
Variation of quadratic action refers to the process of finding the minimum or maximum value of a quadratic function by changing its variables and determining the resulting change in the function's value. This is commonly used in physics and mathematics to optimize systems and find solutions to problems.
The quadratic action principle is a fundamental concept in physics that states that the motion of a system can be described by minimizing the action, which is a measure of the energy of the system. This principle is based on the idea that nature tends towards the most efficient solution, and can be applied to various physical phenomena, such as the motion of particles and fields.
In optimization, variation of quadratic action is used to find the optimal values of variables in a system in order to minimize or maximize a certain quantity. This is done by setting the derivative of the action with respect to each variable to zero and solving the resulting equations. This method is particularly useful in problems with quadratic functions, as it allows for efficient and accurate solutions.
In classical mechanics, the motion of a system can be described by the principle of least action, which states that the motion of a system can be determined by minimizing the action. This principle is closely related to the variation of quadratic action, as both involve finding the optimal values of variables in order to minimize the action and describe the behavior of a system.
Variation of quadratic action has a wide range of applications in various fields, including physics, engineering, and economics. It is commonly used to optimize systems and find efficient solutions, such as in the design of structures and machines, prediction of financial trends, and development of mathematical models in physics and biology.