The action principle in quantum theory

In summary, the conversation discusses the possibility of using the action principle to deduce the conserved current equation and generator of symmetry transformations from a quantum L. The concept of effective action in the path integral formalism is mentioned, as well as the use of Ward-identities to prove the existence of conserved quantities in quantum theory. It is noted that the construction of conserved charges is typically done at the classical level, and the path integral formalism remains close to the classical approach in this regard. The conversation ends with gratitude for guidance on learning more about effective action.
  • #1
Dyson
21
0
Hello!

I wonder is there exist a way to deduct the conserved current equation, generator of

the symmetry transformation and so on from a total quantum L with the help of action

principle?

Many books i have seen deduct the physical quantity from the classical L or construct

the quantum generator from the comparasion with classical one.


Thanks for reply!
 
Physics news on Phys.org
  • #2
What you call "quantum L" is called effective action in the path integral formalism. There are so-called Ward-identities corresponding to a "quantized charge conservation". But the construction of the conserved charge is always done before quantization = at the classical level.

Within quantum (field) theory one has to proof that the corresponding operator identities / Ward-identities continue to exist w/o anomaly.

The path integral formalism is rather close to the classical one when it comes to conserved quantities as it is based on an action integral, no operators.
 
  • #3
tom.stoer said:
What you call "quantum L" is called effective action in the path integral formalism. There are so-called Ward-identities corresponding to a "quantized charge conservation". But the construction of the conserved charge is always done before quantization = at the classical level.

Within quantum (field) theory one has to proof that the corresponding operator identities / Ward-identities continue to exist w/o anomaly.

The path integral formalism is rather close to the classical one when it comes to conserved quantities as it is based on an action integral, no operators.

Thanks! You give me a guide to learn more knowledge on effective action!
 

Related to The action principle in quantum theory

What is the action principle in quantum theory?

The action principle in quantum theory is a mathematical formulation that describes the behavior of particles at the microscopic level. It is based on the concept that all physical systems tend to follow the path that minimizes the action, which is a quantity that represents the difference between the total energy of a system and the external forces acting on it.

How does the action principle differ from classical mechanics?

The action principle differs from classical mechanics in that it incorporates the principles of quantum mechanics, which describe the behavior of particles at the subatomic level. In classical mechanics, the path of a particle is determined by its initial position and velocity, while in quantum mechanics, the path is described by a wave function that represents the probability of finding the particle at a particular location.

What is the significance of the action principle?

The action principle is significant because it provides a fundamental framework for understanding and predicting the behavior of particles at the quantum level. It allows scientists to make precise calculations and predictions about the properties of particles, such as their energy levels and interactions with other particles.

What are some applications of the action principle in quantum theory?

The action principle has numerous applications in various fields of physics, including quantum field theory, particle physics, and condensed matter physics. It is also used in the development of technologies such as quantum computing and quantum cryptography.

Are there any limitations to the action principle in quantum theory?

While the action principle has been successful in explaining many phenomena at the quantum level, it is not a complete theory of quantum mechanics. It does not fully account for certain phenomena, such as the measurement problem and the collapse of the wave function. Additionally, it is still an area of active research and there may be limitations that have not yet been discovered.

Similar threads

A Is the quantum mechanics explanation for the propagation of light adequate enough to be understood?
    • Quantum Physics
Replies
6
Views
661
I Uncertainty Principle in QFT & Early Universe Conditions
    • Quantum Physics
Replies
1
Views
855
A How useful are quantum-classical hybrid theories?
    • Quantum Physics
Replies
5
Views
1K
B Is gravitized quanta the solution rather than quantum gravity?
    • Quantum Physics
Replies
3
Views
886
I How does a nanogenerator work in quantum field theory?
    • Quantum Physics
Replies
22
Views
2K
I Quantum field theory: an informative approach
    • Quantum Physics
Replies
5
Views
1K
A Cause of spontaneous emission?
    • Quantum Physics
Replies
15
Views
2K
A X measurement modeled in non-separable Hilbert space
    • Quantum Physics
Replies
9
Views
340
I What is the failure of superposition in quantum mechanics?
    • Quantum Physics
Replies
8
Views
1K
I QED/Quantum Mechanics: Probability or Spatial Function?
    • Quantum Physics
Replies
8
Views
1K

Hot Threads

Recent Insights

Back
Top