Instantons in Large Order of the Perturbative Series

Behavior of the Euclidean path integral at large orders of the perturbation series is studied. When the model allows tunneling, the path-integral functional in the zero instanton sector is known to be dominated by bounce-like configurations at large order of the perturbative series, which causes non-convergence of the series. We find that in addition to this bounce the perturbative functional has a subleading peak at the instanton and anti-instanton pair, and its sum reproduces the non-perturbative valley.Comment: 9 pages (without figures), KUCP-6

Classification of Type A N-fold supersymmetry

Type A N-fold supersymmetry of one-dimensional quantum mechanics can be constructed by using sl(2) generators represented on a finite dimensional functional space. Using this sl(2) formalism we show a general method of constructing Type A N-fold supersymmetric models. We also present systematic generation of known models and several new models using this method.Comment: 15 pages in LaTeX2e, some comments and a reference adde

Valley Instanton versus Constrained Instanton

Based on the new valley equation, we propose the most plausible method for constructing instanton-like configurations in the theory where the presence of a mass scale prevents the existence of the classical solution with a finite radius. We call the resulting instanton-like configuration as valley instanton. The detail comparison between the valley instanton and the constrained instanton in $\phi^4$ theory and the gauge-Higgs system are carried out. For instanton-like configurations with large radii, there appear remarkable differences between them. These differences are essential in calculating the baryon number violating processes with multi bosons.Comment: 37 pages, 8 eps figures, LaTeX, uses epsf.sty, citesort.sty and wrapfig2.sty. Minor modification

Path-Integral for Quantum Tunneling

Path-integral for theories with degenerate vacua is investigated. The origin of the non Borel-summability of the perturbation theory is studied. A new prescription to deal with small coupling is proposed. It leads to a series, which at low orders and small coupling differs from the ordinary perturbative series by nonperturbative amount, but is Borel-summable.Comment: 25 pages + 12 figures (not included, but available upon request) [No changed in content in this version. Problem with line length fixed.

Recent Developments in the Theory of Tunneling

Path-integral approach in imaginary and complex time has been proven successful in treating the tunneling phenomena in quantum mechanics and quantum field theories. Latest developments in this field, the proper valley method in imaginary time, its application to various quantum systems, complex time formalism, asympton theory for the large order analysis of the perturbation theory, are reviewed in a self-contained manner.Comment: 100 pages, LaTeX, PTPTeX.sty, 36 eps figures, To be published in Progress of Theoretical Physics Supplimen

N-fold Supersymmetry in Quantum Mechanics - General Formalism -

We report general properties of N-fold supersymmetry in one-dimensional quantum mechanics. N-fold supersymmetry is characterized by supercharges which are N-th polynomials of momentum. Relations between the anti-commutator of the supercharges and the Hamiltonian, the spectra, the Witten index, the non-renormalization theorems and the quasi-solvability are examined. We also present further investigation about a particular class of N-fold supersymmetric models which we dubbed type A. Algebraic equations which determine a part of spectra of type A models are presented, and the non-renormalization theorem are generalized. Finally, we present a possible generalization of N-fold supersymmetry in multi-dimensional quantum mechanics.Comment: 25 page

The Canonical Lattice Isomorphism between Topologies Compatible with a Linear Space

We consider all compatible topologies of an arbitrary finite-dimensional vector space over a non-trivial valuation field whose metric completion is a locally compact space. We construct the canonical lattice isomorphism between the lattice of all compatible topologies on the vector space and the lattice of all subspaces of the vector space whose coefficient field is extended to the complete valuation field. Moreover, in this situation, we use this isomorphism to characterize the continuity of linear maps between finite-dimensional vector spaces endowed with given compatible topologies, and also, we characterize all Hausdorff compatible topologies.Comment: 17 pages, no figures, references and a new proposition (Proposition 5.2) are adde

The Berkovits Method for Conformally Invariant Non-linear Sigma-models on G/H

We discuss 2-dimmensional non-linear sigma-models on the Kaehler manifold G/H in the first order formalisim. Using the Berkovits method we explicitly construct the G-symmetry currents and primaries, when G/H are irreducible. It is a variant of the Wakimoto realization of the affine Lie algebra using a particular reducible Kaehler manifold G/U(1)^r with r the rank of G.Comment: 13 page