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cragar
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does the multi Path integral formulation violate special relativity ! do we get speeds faster than c.
cragar said:does the multi Path integral formulation violate special relativity ! do we get speeds faster than c.
Neither. He's talking about path integrals, which add up the probability amplitudes associated with each classical path, and some of those paths correspond to speeds >c.feynmann said:What speed are you talking about? Group speed or phase speed?
They are no less and no more real than the ones with speed less than c, and this doesn't have anything to do with convergence.zetafunction said:the particles with speed greater than 'c' are no physical particles they have no meaning at all, i think they are introduced just as a mathematical trick to make thing converge.
The path integral formulation is a mathematical framework used in quantum field theory to describe the evolution of a quantum system over time. It involves summing over all possible paths that a system can take between two points in space and time, with each path having a certain probability amplitude associated with it.
The path integral formulation differs from other quantum mechanical formulations, such as the Schrödinger equation or the Heisenberg picture, in that it does not rely on a fixed basis of states. Instead, it considers all possible paths that a system can take, including those that may not be captured by a traditional basis.
The path integral formulation is significant because it allows for a more intuitive and visual understanding of quantum mechanics. It also provides a framework for calculating physical quantities, such as transition probabilities, in a more efficient manner compared to other formulations.
The path integral formulation is used in various fields of physics, including quantum field theory, condensed matter physics, and statistical mechanics. It has also been applied in other areas, such as finance and biology, to model complex systems and phenomena.
While the path integral formulation is a powerful tool in quantum mechanics, it does have some limitations. For instance, it may not be applicable to systems with large numbers of particles or strong interactions. Additionally, numerical calculations using the path integral can become computationally intensive for complex systems.