Infinite sets of conserved charges and duality in quantum field theory
Infinite sets of conserved charges have been found in a number of 1 + 1 dimensional quantum field theories. Many of these theories have been found to be completely integrable. Polyakov and others have suggested that such charges may exist in the four-dimensional loop space Yang-Mills equations in analogy with the two-dimensional chiral models. A Kramers-Wannier dual transformation has also been sought for the Yang-Mills system. The purpose of this thesis is to attempt to relate these ideas - i.e. to find a relationship between Kramers-Wannier duality, or specifically self-duality, and infinite sets of conserved charges. The result found is that given any self-dual quantum Hamiltonian of the form H = KB + Gamma B, one can construct an infinite set of conserved commuting charges provided that one additional condition is met: (B,(B,(B,B))) = 16(B,B), or essentially that the first charge in the set is conserved. Thus for a class of theories, a connection between self-duality and infinite sets of conserved charges is established. Several simple models such as the XY spin chain and lsing model in a transverse magnetic field are found to meet this requirement and the resulting infinite set of charges appears to be the same as that previously known from the complete quantum integrability of these systems (i.e. the first few charges in the sets match). The procedure found has an advantage over previous methods for generating infinite sets of conserved charges in that much less effort is required to find the explicit form of the higher charges. Since the result is an operator statement it does not depend upon the number of space-time dimensions or the nature of the space-time continuum - i.e. lattice, continuum, or loop space.
- Research Organization:
- Rockefeller Univ., New York (USA)
- OSTI ID:
- 6209608
- Resource Relation:
- Other Information: Thesis (Ph. D.)
- Country of Publication:
- United States
- Language:
- English
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