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On field theory quantization around instantons

Damiano Anselmi

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Various aspects of the so-called topological embedding, a procedure recently proposed for quantizing a field theory around a non-discrete space of classical minima, are discussed and collected in a simple logical scheme. The possible physical implications are pointed out. The compatibility of the procedure with renormalization is illustrated in the case of the Yang - Mills theory expanded around instantons. The quantum topological properties of Yang - Mills instantons are re-derived in a simpler and illustrative way. Moreover, the general approach is applied to the free energy of the Ginzburg - Landau theory of superconductivity in the intermediate situation between type I and type II superconductors. The topological version of the theory is solved and the quantum topological sectors of the static vortices are classified.


PACS

11.15.-q Gauge field theories

74.20.De Phenomenological theories (two-fluid, Ginzburg-Landau, etc.)

11.10.Gh Renormalization

MSC

81T45 Topological field theories (See also 57R56, 58Dxx)

81T70 Quantization in field theory; cohomological methods (See also 58D29)

81T13 Yang-Mills and other gauge theories (See also 53C07, 58E15)

Subjects

Superconductivity

Particle physics and field theory

Dates

Issue 5 (May 1997)

Received 1 July 1996, in final form 13 February 1997



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