From Classical Field Theory to Perturbative Quantum Field Theory: Progress in a Nutshell

From Classical Field Theory to Perturbative Quantum Field Theory (Progress in Mathematical Physics Book 74)

by Tracy Solheim

5 out of 5

Language	:	English
File size	:	16314 KB
Screen Reader	:	Supported
Print length	:	557 pages
Paperback	:	32 pages
Item Weight	:	2.72 ounces
Dimensions	:	6 x 0.08 x 9 inches

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Field theory is a fundamental branch of physics that deals with the behavior of fields, which are physical quantities that exist at every point in spacetime. Classical field theory, which emerged in the 18th and 19th centuries, provided a powerful framework for understanding phenomena such as electromagnetism and gravity. However, it was not until the development of quantum mechanics in the early 20th century that a truly quantum field theory could be formulated.

Perturbative quantum field theory (pQFT) is a powerful tool for understanding the behavior of particles and fields at the quantum level. It is based on the idea that interactions between particles can be treated as small perturbations to a free-field theory. This allows physicists to calculate the effects of these interactions using a series of approximations.

Key Concepts in pQFT

The following are some of the key concepts in pQFT:

• Lagrangian formulation: The Lagrangian is a function that describes the state of a field at every point in spacetime. The equations of motion for the field can be derived from the Lagrangian using the principle of least action.
• Feynman diagrams: Feynman diagrams are graphical representations of the interactions between particles and fields. They are used to calculate the probability of different processes occurring.
• Renormalization: Renormalization is a technique used to remove infinities from the calculations of pQFT. It is essential for making pQFT a practical tool for physicists.

Challenges in pQFT

Despite its successes, pQFT also faces a number of challenges. These include:

• Strong interactions: pQFT is not well-suited for describing strong interactions, such as those between quarks and gluons. This is because the strong interactions are not well-approximated by small perturbations.
• Non-renormalizable theories: Some theories in pQFT are not renormalizable. This means that the infinities that arise in the calculations cannot be removed using renormalization.
• The hierarchy problem: The hierarchy problem is the problem of explaining why the weak force is much weaker than the strong force. pQFT does not provide a satisfactory explanation for this.

Progress in pQFT

Despite these challenges, pQFT has made significant progress in recent decades. Some of the most important developments include:

• The development of new renormalization techniques: New renormalization techniques have been developed that make it possible to calculate the effects of strong interactions more accurately.
• The discovery of new particles: The discovery of new particles, such as the Higgs boson, has provided further confirmation of the Standard Model of particle physics, which is based on pQFT.
• The development of new theoretical ideas: New theoretical ideas, such as supersymmetry and string theory, have been proposed to address the challenges of pQFT.

Perturbative quantum field theory is a powerful tool for understanding the behavior of particles and fields at the quantum level. It has been used to make many important predictions that have been confirmed by experiment. However, pQFT also faces a number of challenges. These challenges are being actively addressed by physicists, and there is reason to believe that pQFT will continue to make progress in the years to come.

References

1. M. E. Peskin and D. V. Schroeder, An to Quantum Field Theory, Westview Press, 1995.
2. S. Weinberg, The Quantum Theory of Fields, Cambridge University Press, 1995.
3. C. Itzykson and J.-B. Zuber, Quantum Field Theory, Dover Publications, 2006.

From Classical Field Theory to Perturbative Quantum Field Theory (Progress in Mathematical Physics Book 74)

by Tracy Solheim

5 out of 5

Language	:	English
File size	:	16314 KB
Screen Reader	:	Supported
Print length	:	557 pages
Paperback	:	32 pages
Item Weight	:	2.72 ounces
Dimensions	:	6 x 0.08 x 9 inches

FREE