Feynman's Path integral formulation

In summary, Feynman's Path integral formulation is a mathematical framework developed by physicist Richard Feynman to describe the behavior of quantum systems. It differs from other formulations of quantum mechanics by not relying on the concept of wavefunctions or operators, instead using the concept of path integrals. This approach has been applied to a wide range of problems in quantum mechanics and quantum field theory, but it has limitations when dealing with infinite particle systems and at very small length scales. It is closely related to Feynman diagrams, which are used to calculate probability amplitudes for particle interactions in quantum field theory.
  • #1
cragar
2,552
3
Does Feynman's path integral formulation violate relativity ,
we get path's that are faster than c.
 
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  • #2
Feynman paths are just a mathematical tool, they are not a problem, they can do whatever they want. The problem would arise if the probability amplitude for a particle to travel faster than c would come non-zero... And this is not happening.

Why didn't you post it in Quantum Physics? Would have received more attention...
 
  • #3


Feynman's path integral formulation is a mathematical framework used in quantum mechanics to describe the behavior of particles. It involves summing over all possible paths that a particle can take between two points in space and time. This approach allows for a more complete understanding of quantum phenomena, including the behavior of particles at the subatomic level.

One possible concern with Feynman's path integral formulation is the idea that it may violate the principles of relativity, specifically the idea that nothing can travel faster than the speed of light (c). However, this is not the case. The paths that are considered in the path integral are not actual physical paths that particles take, but rather mathematical constructs. They do not represent the actual motion of particles in space and time, but rather a mathematical tool used to calculate the probability of a particle's behavior.

In addition, the results obtained from the path integral formulation do not necessarily correspond to the actual speed of a particle. The concept of speed itself is not well-defined at the quantum level, and therefore, it is not accurate to say that Feynman's path integral formulation produces paths that are faster than c. The theory of relativity is still fully respected within the framework of quantum mechanics.

In conclusion, Feynman's path integral formulation does not violate relativity. It is a powerful mathematical tool that allows for a deeper understanding of quantum phenomena, and its results do not contradict the principles of relativity.
 

What is Feynman's Path integral formulation?

Feynman's Path integral formulation, also known as the path integral approach, is a mathematical framework developed by physicist Richard Feynman to describe the behavior of quantum systems. It is based on the principle of considering all possible paths that a particle can take from one point to another, and then summing up the contributions of these paths to calculate the probability amplitude for the particle to move from one point to another.

How does Feynman's Path integral formulation differ from other formulations of quantum mechanics?

Feynman's Path integral formulation is different from other formulations of quantum mechanics, such as the Schrödinger equation or the Heisenberg picture, in that it does not rely on the concept of wavefunctions or operators. Instead, it is based on the concept of path integrals, which allows for a more intuitive and visual understanding of quantum phenomena.

What are the main applications of Feynman's Path integral formulation?

Feynman's Path integral formulation has been applied to a wide range of problems in both quantum mechanics and quantum field theory. It has been used to calculate the behavior of particles in various physical systems, such as the double-slit experiment, quantum tunnelling, and the behavior of subatomic particles. It has also been used in statistical mechanics, condensed matter physics, and cosmology.

What are the limitations of Feynman's Path integral formulation?

While Feynman's Path integral formulation is a powerful and versatile tool in quantum physics, it has some limitations. One of the main challenges is dealing with systems with an infinite number of particles, which requires more advanced mathematical techniques. Additionally, it is not suitable for describing the behavior of systems at very small length scales, where the effects of quantum gravity become significant.

How is Feynman's Path integral formulation related to Feynman diagrams?

Feynman's Path integral formulation is closely related to Feynman diagrams, which are graphical representations of the path integral. Each line in a Feynman diagram corresponds to a possible path that a particle can take, and the intersections of these lines represent the interactions between particles. These diagrams are used to calculate the probability amplitudes for particle interactions in quantum field theory.

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