A Possible Role of Universal Length in the Theory of Weak Interactions

1973 ◽  
Vol 51 (14) ◽  
pp. 1577-1581 ◽  
Author(s):  
D. Y. Kim

The discovery and role of already existing universal constants h and c in modern physics have been reviewed from a particular point of view. This viewpoint is characterized by a pattern of logic in terms of which one may possibly find a new universal constant, i.e. the elementary length. One of the main objectives of this paper is to find out whether the elementary length introduced this way would resolve inherent difficulties in relativistic quantum field theory. This has been explicitly studied in terms of the nonlocal field theory in connection with the CP violating kaon decay. This produced a relation [Formula: see text] which leads, on the one hand, to a consistent explanation of the possible mechanism of CP violation and, on the other hand, gives a result which is most probably the first direct link between the elementary length (nonlocality) and an experiment without having the inherent disorder in the small distance behavior in quantum field theory.

Author(s):  
Jean Zinn-Justin

Chapter 3 illustrates by a number of examples the essential role of functional integrals in physics. For example, the path integral representation of quantum mechanics explains why many basic equations of classical physics satisfy a variational principle, the relation between quantum field theory and the theory of critical phenomena in macroscopic phase transitions. Field integrals are essential for gauge theory quantization, leading to the introduction of Faddeev–Popov ghost fields and BRST symmetry. Lattice gauge theory, the discretized form of field integrals, makes non–perturbative calculations possible. These are at the basis of the calculation of penetration effects in quantum field theory (instanton calculus).


Author(s):  
Michael Kachelriess

After a brief review of the operator approach to quantum mechanics, Feynmans path integral, which expresses a transition amplitude as a sum over all paths, is derived. Adding a linear coupling to an external source J and a damping term to the Lagrangian, the ground-state persistence amplitude is obtained. This quantity serves as the generating functional Z[J] for n-point Green functions which are the main target when studying quantum field theory. Then the harmonic oscillator as an example for a one-dimensional quantum field theory is discussed and the reason why a relativistic quantum theory should be based on quantum fields is explained.


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